Passive Vibration Damping Using Polymer Pads With Microchannel Arrays

Abstract

Passive vibration control using blocks of viscoelastic materials with macro- and microscopic inclusions has been widely investigated. Significant changes in the vibration response have been observed with such inclusions. We have found that their response changes much more significantly if thin microstructures and channels are carved within these materials and are filled with a high-viscosity fluid. In this paper, we report the passive response of a replicated array of oil-filled microchannels, structured within a block made up of polydimethylsiloxane. Constrained and unconstrained vibration-damping experiments are performed on this block, wherein its vibration suppression ability is detected by applying an excitation signal transversely at the geometric center of the lower face of the block. We observe an increase in the fundamental frequency due to change in stiffness of the block and an increase in damping ratio and loss factor owing to the development of a slip boundary condition between the oil and the microchannel walls causing frictional dissipation of the coupled energy. All vibration experiments have been performed using a single-point laser to ascertain the experimental behavior of the system. We have also modeled the vibration suppression characteristics of such systems both analytically and by using simulation tools $hfill$[2011-0273]

Full text

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL.22, NO. 3, JUNE 2013 695
Passive Vibration Damping Using Polymer Pads
With Microchannel Arrays
Rajeev Kumar Singh, Rishi Kant, Shashank Shekhar Pandey, Mohammed Asfer,
Bishakh Bhattacharya, Pradipta K. Panigrahi, and Shantanu Bhattacharya
Abstract—Passive vibration control using blocks of viscoelastic
materials with macro- and microscopic inclusions has been widely
investigated. Significant changes in the vibration response have
been observed with such inclusions. We have found that their
response changes much more significantly if thin microstructures
and channels are carved within these materials and are filled with
a high-viscosity fluid. In this paper, we report the passive re-
sponse of a replicated array of oil-filled microchannels, structured
within a block made up of polydimethylsiloxane. Constrained and
unconstrained vibration-damping experiments are performed on
this block, wherein its vibration suppression ability is detected
by applying an excitation signal transversely at the geometric
center of the lower face of the block. We observe an increase
in the fundamental frequency due to change in stiffness of the
block and an increase in damping ratio and loss factor owing
to the development of a slip boundary condition between the oil
and the microchannel walls causing frictional dissipation of the
coupled energy. All vibration experiments have been performed
using a single-point laser to ascertain the experimental behavior
of the system. We have also modeled the vibration suppression
characteristics of such systems both analytically and by using
simulation tools [2011-0273]
Index Terms—Aluminium plate, damper, damping ratio, funda-
mental frequency, loss factor, microchannel, polydimethylsiloxane
(PDMS), vibration.
I. INTRODUCTION
VIBRATION damping is essential in prolonging the lifecy-
cle of machinery and structures, in reducing human dis-
comfort, and in high-precision machining and can be performed
by vibration reduction at the source, vibration isolation, system
modification, active vibration control, energy harvesting, etc.
Manuscript received September 13, 2011; revised November 18, 2012;
accepted January 1, 2013. Date of publication February 22, 2013; date of
current version May 29, 2013. This work was supported in part by the Dean of
Research and Development, Indian Institute of Technology, Kanpur, India, and
in part by the Department of Biotechnology and National Program on Materials
and Smart Structures, Government of India. Subject Editor C. Mastrangelo.
R. K. Singh, R. Kant, M. Asfer, P. K. Panigrahi, and S. Bhattacharya are
with the Microsystems Fabrication Laboratory, Department of Mechanical
Engineering, Indian Institute of Technology, Kanpur 208016, India (e-mail:
rajeevme@iitk.ac.in; rishikt@iitk.ac.in; mdasfer@iitk.ac.in; panig@iitk.ac.in;
bhattacs@iitk.ac.in).
S. S. Pandey is with the University of Utah, Salt Lake City, UT 84112 USA.
B. Bhattacharya is with the SMSS Laboratory, Department of Mechanical
Engineering, Indian Institute of Technology, Kanpur 208016, India (e-mail:
bishakh@iitk.ac.in).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JMEMS.2013.2241392
[1]. Also, high-precision machines require very low vibration
ambience to work properly. Vibrations may be linear or non-
linear. If all of the basic components of vibrating systems, like
mass, damper, and spring, are working linearly, the resulting
vibrations are known as linear, while if one or more of the
vibrating systems work nonlinearly, then vibrations are said
to be nonlinear. The choice of suitable material plays an im-
portant role in vibration isolation and system modification. For
example, polymers are good candidates for vibration damping,
and they work very efficiently near the glass transition tem-
perature [2]. In viscoelastic polymers, the energy dissipation
takes place as a result of friction between different chains of
oligomers during their cyclic deformation. There are many vis-
coelastic polymers, such as polyurethanes, poly(vinyl acetate),
acrylics, natural rubber, styrene-butadiene rubber, and poly-
dimethylsiloxane (PDMS), used commonly for vibration sup-
pression, depending on the temperature and frequency range of
operation.
The distinguishing features of these polymers are their enor-
mous resilience and high energy dissipation capacity, although
their elastic modulus and damping capacity are highly sensitive
to change in vibration frequency (i.e., the loading rate) and tem-
perature [3]. A vibration isolator made up of such viscoelastic
solids can be shaped either as an insert, which can be placed in
a cavity anywhere within the structure or a laminate which is
placed between external surfaces of the structure [4].
In the laminate configuration, vibration isolation can be
achieved in a constrained mode in which the damping layer
(PDMS in our case) is sandwiched between two metallic plates
of equal thickness, with one acting as a supporting plate (host)
and the other acting as a stiff constraining layer, resulting in
shear deformation of the damping layer. In the other configura-
tion, the laminate can be used in unconstrained mode, wherein
the damping layer does not have the constraining aluminum
layer and the vibration damping is primarily due to the exten-
sional deformation of the damping layer [3]. The objective of an
effective damping treatment is to add the viscoelastic material
in a manner so that it can withstand the heaviest amount of
cyclic deformation. The main reason of investigating the damp-
ing behavior as constrained and unconstrained cases is that,
in the former, the dominant mechanism of vibration isolation
is shear deformation and, in the later, it is through flexural
bending. The theory of damped structures has been thoroughly
investigated in recent years. Teng et al. [5] have performed de-
tailed studies of the damping characteristics of viscoelastic lam-
inates in both the constrained and unconstrained cases and have
studied the effects of temperature, frequency, and dimensions
1057-7157/$31.00 © 2013 IEEE

696 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL.22, NO. 3,JUNE 2013
of damped structures on vibration-damping characteristics.
Kerwin et al. [6] developed a theory for flexural beams to study
damping effects of viscoelastic material for constrained layer
damping (CLD). Ross et al. [7] derived the loss factor in terms
of energy dissipation for such viscoelastic materials. Rao et al.
[8] examined unsymmetric sandwich beams and plates with
cores made up of viscoelastic materials. Johnson et al. [9]
briefly reviewed the techniques employed for design in passive
damping for vibration control. The investigation also catego-
rized viscoelastic materials as one of the most commonly used
material for damping and discussed some of the design meth-
ods and testing/characterization of these materials for passive
damping. Marcelin et al. [10] analyzed a beam constrained by
a viscoelastic layer for optimal damping by covering several
portions of the beam. Thus, one can tune the viscoelastic
damper, making it efficient in a specified frequency range.
However, such tuning is limited to a prespecified frequency
band. Bhattacharya et al. [1] have worked on different active
CLD strategies where an active layer placed on top of the
constraining layer has been used to maximize shear deforma-
tion in the viscoelastic layer. This has shown a larger band-
width and better tenability. Researchers have also investigated
the influence of passive micro- and macroscale inclusions in
viscoelastic composites on their vibration-damping properties.
Patel et al. [11] have modeled the effect of microscale in-
clusions in polymers and have predicted that nanostructured
viscoelastic inclusion can change significantly the loss factor
of a matrix over a wide frequency band. Goel et al. [12] studied
the effects of gold, silver, and platinum nanoparticles embedded
in PDMS on vibration-damping properties and found out a
change in the damping factor from 0.09 to 0.13 (1.4 times) in a
frequency range of 1–9 Hz. They further observed a fall in the
damping factor beyond this range of frequency. Kaully et al.
[13] studied the microscale damping behavior of PDMS with
calcium carbonate inclusions by varying the volume fraction of
calcium carbonate and operational temperature. The optimum
range of operational temperature was found as −120−−35 ◦C,
and a loss factor variation of 0.01–0.19 (19 times) was observed
for various volume fractions of the inclusion within this tem-
perature range. Wang et al. [14] studied the damping behavior
of shape memory alloys with graphite particulate inclusions
present in macroscopic sizes and observed an increase in the
internal friction (representing the loss factor) from 0.02 to 0.18
at an optimum operational temperature of 323 ◦C.
Although a lot of work has been done on viscoelastic lami-
nates using them as damping layers (in both constrained and un-
constrained modes) either directly or with various additives and
inclusions, the impact of microstructuring of these laminates to
vibration suppression remains by and large unexplored. In this
paper, we have developed a novel viscoelastic laminate (made
up of PDMS) slab by replicating microchannel arrays within
the slab and then by filling them with viscous oil, followed
by sealing the ends of this microchannel with PDMS. We have
further found out the impact of this replication and filling on vi-
bration damping. We have observed that both damping ratio and
fundamental frequencies can be customized by appropriately
microstructuring the viscoelastic layer. Unlike the methods
cited earlier, the significance of this method lies in its ability to
incorporate vibration suppression at room temperature and high
frequency bandwidth. Also, this methodology is independent
of any other constraint imposed by dispersion of phases, like
clustering or change in size, which has been always prominent
in the inclusion methods as illustrated earlier.
Fundamental mode frequency and damping ratio are ob-
tained experimentally for the constrained and unconstrained
configurations, and a mathematical model is developed for the
unconstrained treatment case. This observation is of funda-
mental importance as this would open a new dimension of
structuring of damping layers to achieve a desirable level of
passive vibration control. We have also evaluated the behavior
of the oil contained within these microchannel arrays and have
found that a slip boundary condition gets created, owing to
which there is a substantial frictional energy dissipation at the
fluid structure interface. This explains the increase in damping
ratio for the microstructured laminates.
A. Theory
A mathematical model is proposed to analyze the uncon-
strained configuration of the microstructured laminate. The
PDMS slab is fixed on the aluminum base plate (damper assem-
bly) to avoid any relative motion between the two, particularly,
while applying the excitation signal or impact. In the damper
assembly, as the PDMS slab is pasted by a thin layer of liquid
PDMS material, there is some shrinkage of the adhesive layer
(1%–3% for the PDMS layer) [15] on heat curing, which causes
the PDMS slab to have a residual compressive load. In the
unconstrained case, this load emanates from the bottom face,
thus emerging a trapezoidal structure, and in the constrained
case, it emanates from both faces [bitrapezoidal structure;
Fig. 1(a) and (b)].
Our analysis consists of laminates from one to four layers
of microchannel arrays (rowwise) with 20 microchannels in
each row. We have tried to find out the analytical solution of
the fundamental frequency using the indicated geometries, with
negligible adhesive layer thickness between the laminate and
the aluminum base plate. The analytical model constructed here
is that of a composite damper, with one phase as the PDMS
matrix and the other phase as the silicone-oil-filled microchan-
nels. Since microchannels have a large surface-area-to-volume
ratio, their mechanical properties can be well estimated using
the whole surface area of the channel instead of the cross-
sectional area. The total surface area “Am” occupied by these
microchannels is
Am=n×2πr(r+l)(1)
where nis the total number of microchannels, ris the channel
radius, and lis the length of the channels. Let us assume the
transverse cross-sectional area of the whole PDMS slab and
aluminum plate to be “As” and “Al,” respectively. In case of the
microchannels filled with silicone oil, the entire surface of the
channels is the source of dissipating vibrational energy because
of the shear between the oil and the channel surface, and thus,
the total surface available is very critical to vibration damping
or frequency change. Therefore, total area of the composite

SINGH et al.: PASSIVE VIBRATION DAMPING USING POLYMER PADS WITH MICROCHANNEL ARRAYS 697
Fig. 1. (a) Trapezoidal shape of microvibration damper in unconstrained
treatment. (b) Bitrapezoidal shape of microvibration damper in constrained
treatment.
damper (Atotal)is calculated by considering a contribution of
the whole surface of an array of microchannels instead of the
cross-sectional area. Thus,
Atotal =Am+As+Al.(2)
The area fraction occupied by the microchannel array is
Afmc =Am
Atotal
.(3)
The area fraction of the PDMS layer is
AfPDMS =As
Atotal
.(4)
The area fraction of the aluminum plate is
Afal =Al
Atotal
.(5)
The density of the composite damper is calculated by using the
rule of mixture as [16]
ρ=ρmAfmc +ρPDMSAfPDMS +ρal Afal (6)
where ρal,ρPDMS , and ρmare the densities of aluminum,
PDMS, and the material within the microchannels, which, in
our case, is silicone oil.
According to classical theory for the free vibrations of rect-
angular thin plates, the governing equation for free vibration
may be expressed as
D∇4w+ρ∂2w
∂t2=0 (7)
where wis the transverse deflection of the plate, ∇2is the bihar-
monic differential operator (i.e., ∇4=∇2∇2,∇2=∂2/∂x2+
∂2/∂y2in rectangular coordinates), D=Eh3/12(1 −v2)is
the flexural rigidity, Eis the Young’s modulus, his plate
thickness, vis the Poisson’s ratio, ρis mass density per unit
area of plate surface, and tis time.
The boundary conditions for an edge parallel to the y-axis of
the aforementioned equation for a clamped edge are
w=∂w
∂x =0 (8)
and for a free edge are
∂2w
∂x2+v∂2w
∂y2=∂3w
∂x3+(2−v)∂3w
∂x∂y2=0.(9)
In order to solve (7), the Rayleigh–Ritz method can be used,
wherein a function W(x, y)is defined as
W(x, y)=
p,q
ApqXp(x)Yq(y)(10)
where Xpand Yqare normalized eigenfunctions exactly sat-
isfying the equation of motion of a freely vibrating uniform
beam, and also, these satisfy the clamped, simply supported,
or free-edge conditions at the ends of the beam. Apq is the
amplitude of W(x, y)which can be used as a trial function for
the solution of (7). The coefficients are determined by the Ritz
method, with a view of minimizing an energy function to get
the best approximation of the equation of motion (7). Clamped
boundary conditions are exactly satisfied by the use of the beam
functions, making the solution of (7) accurate, whereas for the
clamped–free–clamped–free (C-F-C-F) case, four symmetry
classes of modes exist, making the solution approximate. The
procedure then reduces to yielding four ninth-order eigenvalue
determinants on the right side of (10). Expanding the deter-
minant and collecting terms yields a characteristic equation.
We obtain a nondimensional frequency parameter λfrom this
characteristic equation, which is defined in the following:
λ=ωa2ρ/D (11)
where ω,a,D, and ρare the angular frequency of vibration of
the plate, length, flexural rigidity, and density of the damper
which possesses free vibrations analogous to the rectangular
plate. The length-to-width ratio of the microvibration dampers
is a/b =1.22 ≈1.5.
The calculated nondimensional frequency parameter λfor
a C-F-C-F case for a length-to-width ratio of 1.5 is given
as 22.272 [17]. The density of the microvibration damper in
kilograms per square meter is defined as ρ=ρ·a, where ais
length of the damper between fixed ends.
The λparameter in (11) corresponds to a thin plate of a single
material. In order to calculate the fundamental mode frequency
of the microvibration damper laminates using (11), the twin
laminate structure of the PDMS slab and aluminum plate needs
to be reduced to an equivalent structure made up of aluminum
using [18]
t=E
Et(12)

698 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL.22, NO. 3,JUNE 2013
where tand tare the thicknesses of the equivalent aluminum
layer and PDMS layer and Eand Eare the Young’s modulus
of aluminum and PDMS, respectively. It is clear that the equiv-
alent aluminum thickness of the PDMS slab should come much
lesser, thus approximating the thin rectangular plate model
described previously. A reverse conversion into an all PDMS
equivalent would have a very high thickness which may not be
solved using the thin-plate free-vibration equation.
The overall thickness of the microdamper assembly is given
by h=t+t, where t and hare the thickness of the aluminum
plate and the equivalent thickness of the damper assembly,
henceforth referred to as “laminate equivalent.” The flexural
rigidity of the laminate equivalent is D=Eh3/12(1−v2)[15],
where Eand vare the Young’s modulus and Poisson’s ratio
of aluminum, respectively. Furthermore, the fundamental mode
frequency fof the microvibration damper is given by ω=2πf.
The measurement of damping characteristics is carried out
using two general methods as described in the following
discussion.
1) Logarithmic Decrement Method: When a single degree
of freedom oscillatory system with viscous damping is excited
by an impulse input, its response takes the form of a time decay.
The logarithmic decay δ[2]isgivenby
δ=1
rln Ai
Ai+r(13)
where Aiand Ai+rdenote first peak point and peak point r
cycles later in the time decay, respectively. This method then
yields the damping ratio, which is a dimensionless quantity
that is used to measure the decay of vibration in a system. The
damping ratio ζis expressed as
ζ=1
1+2π
δ2.(14)
2) Half-Power Bandwidth Method: It is a frequency re-
sponse method. Bandwidth is defined as the width of the fre-
quency response magnitude curve (Δω.)when the magnitude
is 1/√2times the peak value of the displacement amplitude.
This also corresponds to the half-power point. The damping
characteristic can then be estimated by calculating the loss
factor η(indicative of dissipated energy)
η=CΔω
ωr
(15)
where C=1/√n2−1and ωris the resonant frequency. For
our case (half-power point), n=√2, and
η=Δω
ωr
.(16)
The mathematical model described previously estimates the
unconstrained behavior very well, and we have calculated the
fundamental frequency based on this model to be having
the same order of magnitude. For the constrained treatment
case, it is difficult to obtain the system parameters in closed
form due to the presence of shear deformation, and hence, we
have tried to model such cases using COMSOL MultiPhysics
(version 4.1) and compared with the experimental data.
II. EXPERIMENTAL
A. Fabrication of the Microstructured Vibration Damper Slabs
In order to make a microstructured viscoelastic (PDMS) lam-
inate, we use a process of replication through desirably sized
copper wires duly knit in a plastic box in an array format. The
array is created in a plastic box (breadth =51mm, thickness =
17 mm, and length =80 mm) by drilling 200-μm diameter
holes in a rowwise and columnar fashion with a center-to-
center distance of 2 mm rowwise and 2 mm columnwise, using
Integrated Multi-process Machine Tool DT 110 (Mikro-tools,
Singapore) using CNC programming. The holes drilled are laid
out face to face on opposite walls of the box. Furthermore,
copper wires with a diameter of 80 μm are inserted using
special tweezers, bridging the gap between these holes on
opposite faces, and the assembly is tightened on an in-house
designed and developed fixture, as shown in Fig. 2(b). Here,
we have used an 80-μm wire because of the following two
reasons. First, its strength is high so that the replication of the
microchannel can be complete and the wiremold can be taken
out without breakage. Second, the diameter is large enough for
a complete filling of the microchannel with silicone oil. If we
use a lesser diameter of the wire, then due to wire breakage
during the replication process, we are unable to formulate
100% through channels, and some of them get blocked. Thus,
the complete array of microchannels seems to be utilized for
vibration damping when the diameter is 80 μm. The wires
are tightened longitudinally on the fixture using tightener pins.
Replication of the slab is then performed using this architecture.
PDMS prepolymer and its curing agent premixed in a ratio of
10 : 1 are poured in this mold and degassed in a desiccator,
following which a curing step is proceeded in an oven main-
tained at 85 ◦C for 45 min. The fixture stands over a tripod
arrangement, and leveling is performed prior to pouring the liq-
uid PDMS. The polymer mix solidifies and entraps the copper
wires, and this assembly is released carefully from the fixture
and also the plastic housing. The hole diameter is slightly
bigger than 80 μm, and this ensures that the wire is loosely
inserted in the plastic box and thus easy to get removed with
the embedding PDMS slab from the plastic box. This results in
a slab with dangling copper wires across both ends, which is
further swelled by immersing in toluene for 24 h. The toluene
swells the PDMS matrix and loses the grip on the copper wires,
which can then be taken out with the help of tweezers. The
polymer is then subsequently deswelled by keeping it at room
temperature for two days or in an oven maintained at 85 ◦C
for 3 h. The hole center of the top row array is around 3 mm
from the top surface of the final PDMS slab. Each row has 20
microchannels. Once the structured slab is ready, silicone oil is
filled partially in the microchannels in a controlled manner with
the help of a 1-ml syringe while the meniscus is observed with
a magnifying glass. The injection of oil is made up to the point
when the oil bead starts to formulate on the other end of the
channel, indicating complete filling. We use silicone oil as it can
be filled easily without substantial modification of the overall
mass of the damper. The characteristic properties of silicone oil
are density = 960−1050 kg/m3and viscosity of 950–1050 cSt.
Vibrational energy is dissipated because of the shear between

SINGH et al.: PASSIVE VIBRATION DAMPING USING POLYMER PADS WITH MICROCHANNEL ARRAYS 699
Fig. 2. (a) Different steps of fabrication of the damper assembly. (I) Drilling holes in the plastic mold. (II) Inserting the wire array and using the fixture to
provide longitudinal tension for consistency of the microchannels and replication with PDMS. (III) Removal of the molding wires to obtain a straight array of
microchannels. (IV) Pasting the aluminum plates at the bottom for unconstrained damping and at both top and bottom for constrained damping. (b) Tensioner
fixture for tightening the replicating wires to ensure straightness of the features.
TAB L E I
GEOMETRIC DETAILS OF THE MICRODAMP ER ASSEMBLY (SIX ROWS OF MICROCHANNELS—CONSTRAINED TREATMENT)
the layers of the confined oil volume within the microchannels
and also because of the frictional dissipation due to the relative
movement of the confined oil within the PDMS. The lengths
of the slab and the embedded microchannels are both 81 mm.
In order to plug the injected oil filled in the microchannels,
both ends (along the channel length) of the slab are cut using
a sharp cutter, this slab (shorter length) is placed upside down
and centered in another new box (without any drilled holes),
and liquid PDMS mix is filled on both cut ends and then heat
cured. PDMS on curing gets cross-bonded and becomes an
integral part of the slab, thus plugging and enclosing the filled
up oil. In this way, the microchannels are plugged so that oil

700 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL.22, NO. 3,JUNE 2013
does not come out. The oil moves within the channel as the
PDMS flexes, and the channels deform, causing movement of
oil within their various sections so that the continuity can be
maintained. Also, in this way, there is control on the positioning
of the microchannel array from the top of the slab as there
is no level difference on the lower side of the slab. The level
difference on the opposite side of the slab (facing up in the
box) is controlled by metering the liquid PDMS in a manner
so that it just rides over the top surface of the slab. On curing,
the whole liquid becomes an integral part of the slab. The slab
is further pasted to a well-milled aluminum base plate of the
size of the slab and with a thickness of 1.46 mm by using the
PDMS mix (PDMS prepolymer and its curing agent) and then
again curing the assembly for the unconstrained treatment. In
the constrained treatment, the only difference is that a similar
aluminum plate is pasted on the top side of the assembly,
sandwiching the microstructured slab between this and the
base plate. Fig. 2(a) shows the fabrication flowchart with some
photographs of the various steps. Fig. 2(b) shows a photograph
of the wire tensioner used to replicate the microchannels. Mi-
crochannel rows 1–6 were fabricated in different PDMS blocks
by the aforementioned method for the dampers. In one case,
the equivalent volume of the microchannels corresponding to
the maximum row case (six rows) was carved in PDMS as
two large channels at the geometrically centered plane of the
block with equal internal spacing. This was performed to gauge
the efficacy of microstructuring over macroscopic features and
structures. This is referred to as macroscale equivalent of six
rows (MESR).
B. Simulation Details
The eigenfrequencies for all samples of unconstrained and
constrained treatment cases have been solved using COMSOL
MultiPhysics (version 4.1; simulation tool). All simulations
have been performed using a business PC with 16-GB RAM
and Intel (R) Core (TM) i7 CPU @ 3.07 GHz running on 64-b
Windows 7 Professional operating system.
The microdamper geometries have been created according
to Table I and have been meshed with normal mesh type. The
mesh size and density get self-regulated upon approaching a
channel cavity or a corner. Mesh optimization was done by
running the simulation on different mesh densities. The param-
eters evaluated were z-displacement of the geometric center of
the top surface of the damper assembly. The simulation was
performed with “both ends fixed configuration.” While doing
simulations, the aluminum plate, PDMS layer, and silicone-oil-
filled microchannels have been assigned linear elastic material
model, viscoelastic material model, and hyperelastic material
model as required by the material properties. The silicone-
oil-filled microchannels were modeled as hyperelastic mate-
rial to accommodate high strain values. Young’s modulus of
aluminum as confirmed by tensile tests run on UTM comes
out as 53.51 GPa, and this value has been used for all of the
calculations as well as simulations. The degradation of the
tensile strength of the metal plate from around 70 GPa as in
the case of pure aluminum is probably because of alloying and
impurities. We assume zero displacement and velocity at time
TAB L E I I
INPUT MATERIAL PROPERTIES FOR THE COMSOL
MULTIPHYSICS SIMULATION
Fig. S1. Mesh optimization plot with the target parameter of amplitude
displacement for the four-channel case. The plot shows consistency in reported
displacement amplitudes for normal, finer, and extrafine meshes.
t=0. The microdamper was modeled using solid mechanics
module, and the eigenfrequencies were determined.
The following are the governing equations executed by the
solver:
−ρω2−∇.σ =Fv
−iω =λ
where ρ,ω,σ,λ, and Fvare density, angular frequency, stress,
eigenvalue variable, and excitation force, respectively. We have
presented the simulations of microdamper for constrained and
unconstrained treatment cases from one row of microchannel
up to six rows of microchannels by calculating the fundamental
frequency. Simulations are also done on the MESR case. The
simulation software also computes the vertical displacement
of the surface of microdamper and shows along with the
fundamental mode frequency. The input parameters that were
used in generating the simulation are illustrated in Table II.
The simulation also computes the strain energy at every point
of the microdamper. The mesh optimization was also done,
and the same is shown in supplementary Fig. S1. The number
of elements for various mesh types is given in supplementary
Table S1.

SINGH et al.: PASSIVE VIBRATION DAMPING USING POLYMER PADS WITH MICROCHANNEL ARRAYS 701
TAB L E S 1
NUMBER OF ELEMENTS FOR VARIOUS MESH TYPES
C. Experimental Setup for Vibration Measurements
The experimental setup for investigating the vibration sup-
pression qualities of the microstructured damper (realized ear-
lier) is based on the study of the transmissibility of an excitation
signal by scanning the damper surface with a single-point laser
detector. The damper is mounted with both ends fixed in a
simply supported beam configuration. The ends are clamped
using a knife edge support on both ends which overlaps about
10 mm on both sides of the damper to provide a firm grip.
The excitation signal is applied from the geometric center
on the bottom surface of the aluminum base plate on the
damper assembly by means of a shaker (model V201, LDS,
Germany). The direction of the excitation signal used was
vertical. Longitudinal damping is mostly investigated in high-
frequency vibrations. The transverse or vertical damping is in-
vestigated for low-frequency vibrations. Longitudinal damping
is a phenomenon of mass-dominated damping. It means that,
if fluid heavier than silicone oil or PDMS is used, then an
analysis of longitudinal damping would be necessary. As we
are using silicone oil (the density is the same as PDMS) in the
channels, the overall change of mass is insignificant; although
there is an overall stiffness change, the oil confined within the
microchannels increases the stiffness of the structure. Thus, it
is appropriate to investigate the transverse damping behavior
of our system, which is performed by coupling the shaker to
the damper assembly as illustrated previously. The shaker is
connected to an amplifier (model PA 25E, LDS, Germany)
and a function generator (model ST 4060, ScienTECH, India)
which applied a sinusoidal signal (1.5 V peak to peak) and an
amplifier gain of 2. The excitation is provided over a range of
frequency values by manually varying the output of the signal
generator from 0 to 1000 Hz in steps of 1 Hz, which can be
read on the screen of the generator. We scan the top surface
of the damper by recording the displacement of its geometric
center by a single-point laser sensor (model OptoNCDT 1700,
MICRO-EPSILON, Germany). The recorded data are acquired
by a software ILD 1700 Tool V2.31.
When the external signal matches with the natural frequency
of vibration of the damper slab, there are large amplitudes of
motion due to resonance, and this point is identified by means
of an increased humming sound (the vibrating beam produces
a series of compression and rarefaction in air). The frequency
corresponding to this point is recorded from the signal genera-
tor’s screen and is the fundamental mode frequency. This is also
shown by surface displacement (top) of microdamper by single-
point laser, as shown by supplementary Fig. S2. Fig. 3 shows a
schematic of the setup. We also record the vibration suppression
Fig. S2. Snapshot of the computer screen connected to a single-point laser
sensor.
Fig. 3. Schematic of the test setup for measurement of the fundamental
mode frequency with a shaker table connected to a feeding function generator
(range 0–1070 Hz), an amplifier (model PA 25E, LDS), and a power supply,
and a single-point laser sensor (model OptoNCDT 1700, MICRO-EPSILON)
connected to a computer interface for real-time data acquisition.
of the damper slab by providing it an impact through a hard
hammer on the aluminum base plate of the assembly and record
the amplitude of displacement of the top surface temporally
using the single-point laser scanner described earlier and subse-
quently plotted using Origin 8. We have observed a difference
in the time taken by the damper for suppressing this impact as
we modify the damper structurally. We further analyze the data
and find out the logarithmic decrement of amplitude from this
plot from which we get the damping ratio (the details are in the
theoretical section).

702 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL.22, NO. 3,JUNE 2013
TABLE III
FUNDAMENTAL MODE FREQUENCY VALUES FOR UNCONSTRAINED AND CONSTRAINED CASES
OBTAINED THROUGH SIMULATION AND EXPERIMENTAL METHOD
D. Particle Image Velocimetry
In order to see the flow behavior of the enclosed fluid
within the microchannel (coupled with the external vibrational
energy), a platform is realized in PDMS containing a mi-
crochannel with a width of 200 μm and a depth of 40 μm.
This microchannel is plasma bonded to a hard glass substrate
which is imaged from the top side by the 10×objective of a
fluorescence microscope (NIKON Eclipse 80i). The microchan-
nel structure is made hydrophilic by treating with polyethy-
lene glycol [19] and is then filled with a water solution of
fluorescently labeled polymer microbeads with a size of 1 μm
(concentration of 0.05% by volume). After filling this solution,
the inlet and outlet ports of this microchannel are closed by
silicone sealant (Silastic 732 RTV, Dow Corning India Pvt. Ltd.,
Pune, India). The microchannel is coupled with the mechanical
vibrations coming out of a shaker connected to an amplifier
and a function generator supplying a sinusoidal input. The
excitation frequency and amplifier gain used were 7 Hz and
1.2, respectively. The CCD camera mounted on the microscope
recorded snapshots at an interval of 0.100 s using the Image Pro
Express 6.0 software. These snapshots were further analyzed
using Dynamic Studio version 1.45 (Dantec Dynamics Inc.)
software to find out the velocity vector plots.
III. RESULT AND DISCUSSION
A. COMSOL MultiPhysics (Version 4.1) Simulations
The fundamental mode frequency as obtained from simu-
lation is shown in Table III and also Fig. 4 (by the hatched
bars) for both constrained and unconstrained treatments. The
mesh optimization has been done on maximum mesh sizes
varying between 0.0305 m (for the extremely coarse mesh)
and 0.00213 m (for the extrafine mesh). It may be noted
that, for a certain mesh density, the meshing is self-regulated
upon approaching a crevice, corner, or cavity (microchannels).
Thus, as normal mesh is used, the mesh sizes may vary from
a maximum of 0.00213 m to 12 μm throughout the block
volume. The parameter for optimization was taken as the z-
displacement of the geometric center of the damper assembly’s
top surface, and the optimized mesh size obtained corresponds
to 0.0061 m (see supplementary Table S1). We assume that the
z-displacement is the most critical parameter in our experiments
for the calculation of the damping ratio and the fundamental
frequency should be the target parameter for optimization.
All simulations therefore are performed using normal mesh
size. We observe an increase in fundamental mode frequency
with increasing number of microchannel rows from 304.7 Hz
(corresponding to one row) to 526.7 Hz (corresponding to
six rows) for the unconstrained damping and an identical be-
havior in case of constrained damping. The frequency in the
constrained case varies from 388.3 to 632.9 Hz. The overall
increase in the fundamental mode frequency from the uncon-
strained to constrained case can be attributed to an increase in
the flexural rigidity of the constrained configuration because of
an additional aluminum plate sandwiching the damper assem-
bly (refer to (11), assuming a constant frequency parameter for
all of our experiments [17]).
The increase of the fundamental mode frequency in the
unconstrained case is 72.9% as the number of microchannel
rows is varied from one to six. This increase for the constrained
case is similar (around 62.9%). Therefore, the variation in the
frequency by adding more number of rows of microchannels
can be attributed to the fact that the stiffness of the viscoelastic
slab increases as more rows of oil-filled and plugged mi-
crochannels are added. Stiffness is proportional to the square
of the fundamental mode frequency [f=(1/2π)k/m].As
the volume density of the silicone oil (980 Kg/m3)usedtoplug
the microchannels is slightly above that of the PDMS material
(970 Kg/m3), the increase in overall mass of the damper due
to the addition of rows is quite compensated by the increase in
rigidity due to the addition of the first set of rows. However, as
additional rows are added, the stiffness increases significantly
in comparison to the increase of mass. Thus, the frequency
suddenly increases from 304.7 to 490.9 Hz in the unconstrained
case and from 388.3 to 580.1 Hz in the constrained case as
the number of rows is increased from one to two. After this,
any additional increase in the number of rows results in an
increase in fundamental mode frequency primarily attributing
to the enhancement of volume stiffness. We found out from
our simulation results that there are hardly any deflections in
both rigid aluminum plates, and the slice plot shows a huge
nonuniform deformation of the viscoelastic damping layer,
which is quite in line with any sandwich layer of a damping

SINGH et al.: PASSIVE VIBRATION DAMPING USING POLYMER PADS WITH MICROCHANNEL ARRAYS 703
Fig. 4. Fundamental mode frequency versus the number of rows of microchannels, indicating the frequency bars for cases with no channel (with the numberof
channel rows as one to six and the MESR case). (a) For unconstrained treatment. (b) For constrained treatment.
arrangement. Maximum deformation is observed in this layer
and accounts for the dissipation of vibrational energy by friction
heating. In the MESR case, the simulated frequency comes
out as 290.5 Hz in the unconstrained case and 350.9 Hz in
the constrained treatment. Thus, the MESR block frequency is
higher than the “no channel” case but lower than the “single
row” case. This indicates that the stiffness-to-mass ratio of the
blocks increases as microchannels are distributed throughout
the bulk. If an equivalent volume is carved out in a manner
concentrated at a few regions, the stiffness-to-mass ratio does
not show much increase.
The experimental analysis shows a similar trend in the funda-
mental mode frequency as detailed later. We have also observed
experimentally that the damping ratio of these microvibration
dampers increases with an increase in the number of rows of
channel layers. In order to explain this behavior, we performed
TAB L E I V
COMSOL MULTIPHYSICS SIMULATION—STRAIN ENERGY PER UNIT
VOLUME (IN JOULES PER CUBIC METER)AT 20 mm OF MIDDLE
CHANNEL IN FIRST ROWS OF FOUR ROWS O F MICROCHANNELS
OF THE CONSTRAINED TREATMENT CASE
simulations for predicting the strain energy per unit volume.
The strain energy per unit volume data were extracted from
the oil filled in the microchannel region (along the axis of the

704 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL.22, NO. 3,JUNE 2013
Fig. 5. (a) Microchannel image using an optical magnification of 10×with microbeads (fluorescently labeled) in motion that are inserted inside the damper block
with a single representative channel filled up. (b) Contour plot of velocity vectors, using Dynamic Studio analysis software, possessed by the moving microbeads
on coupling of vibrational energy to the damper block (the velocities are time averaged on the basis of 10 frames/s speed of acquisition. (c) Comparison of velocity
profile in the radial direction between pressure driven flow and vibration coupled flow, indicating a slip boundary condition with a negligible velocity reduction in
case of the solid lines for vibration coupled flow.
microchannel), the polymer layer close to the microchannel sur-
face (at a depth of 40 μm), and the channel wall. All data were
extracted at a length of 20 mm from the end of the microchannel
(Table IV). The energy dissipation is represented by negative
strain energy, with the highest dissipation at the interface of
the oil and the PDMS channels (−7.29 ×104J/m3).Wehave
separately studied the fluid structure interaction model to find
out a suitable reason for this extremely high energy dissipation
at the interface. As the microdamper is subjected to mechanical
vibrations, the oil inside the microchannels creates a slip condi-
tion with the channel walls, and due to the friction generated
at the oil–PDMS interface owing to the relative motion, the
energy is dissipated. In other words, we could observe finite
velocities of the fluid very near to the channel wall, and this
shows a slip boundary at the channel walls. We hypothesize
that this slip boundary comes from the bending and deforming
of the channel, thus squeezing out the fluid containment of the
silicone oil. Fig. 5(a) and (b) shows the microchannel image
with microbeads in motion and the contour plot of the average
bead velocity of a completely filled microchannel coupled with
vibration energy. In this plot, region “A,” which is very near
the excitation source, has a negligible average velocity due to
very less available relaxation time for the microbeads between
their bidirectional motions (which is caused by the squeezing
and expansion of the microchannel as the excitation source is
coupled to the structure). The particles which are far away from
the source get more relaxation time and thus possess a higher
average velocity (region “B”). Also, the average velocity is
higher in the direction of suction created because of the post-
squeezing expansion of the microchannel. We are able to see
very clearly velocity vectors near the channel walls, suggesting
a slip boundary condition. Fig. 5(c) shows a comparison of
the average velocity profiles in the same microchannel in two
different experiments, where, in one, a pressure driven flow
is analyzed and, in the other experiment, a vibration coupled
flow is analyzed by the use of Dynamic Studio. As can be
clearly seen in the parabolic case represented by the dotted
curve, the average velocity near the walls has almost an order
of magnitude change, and in the vibration coupled case, the
magnitude of the velocity remains almost the same at the center
of the channel as well as the walls (as represented by the
continuous curve). If the number of microchannels is increased,
the energy dissipated on the channel surfaces is more, and thus,
with the increase in the number of microchannels, the damping
ratio increases. The same result is reflected with experimental
studies.

SINGH et al.: PASSIVE VIBRATION DAMPING USING POLYMER PADS WITH MICROCHANNEL ARRAYS 705
B. Fundamental Mode Frequency: A Comparison Between
Simulations and Experimentally Obtained Values
The experimental values for fundamental frequency as ob-
tained at the point of resonance show a similar behavior with
the theoretical values and simulation in the unconstrained case.
These values are represented by open bars in Fig. 4(a) and
(b). The fundamental mode frequency for the unconstrained
case [Fig. 4(a)] as obtained experimentally varies from 290
to 529 Hz for cases 1–6 rows, respectively. The theoretical
model estimates these values as 475.7–483.67 Hz, but the
simulations estimate these values from 304.7 to 526.7 Hz. The
theoretically obtained values do not show much variation with
varying number of microchannels but do report the fundamental
frequency within the same order of magnitude. The theoretical
model in our opinion would need further fine tuning, which will
be included in a future endeavor. The numerical calculations,
experimental analysis, and simulations are repeated for the no
channel case and the MESR for a comparison. Simultaneously
through simulations and experiments, this value is reported as
288.1 Hz (lower than the one-row case) and 272 Hz, respec-
tively. For the MESR, these values (i.e., through simulations
and experiments) come out as 290.5 and 275.0 Hz. Therefore,
in this case as well, the MESR value comes in between the no
channel and one-row cases for reasons indicated earlier. The
experimental values are in close proximity to the simulation
results, which is not true for the analytically predicted values. A
similar behavior is observed in the constrained case [Fig. 4(b)],
where the fundamental mode frequencies are estimated with
simulations and compared with experiments. For the no channel
case, the fundamental mode frequency is observed experimen-
tally as 348.0 Hz and through simulations as 337.9 Hz. The fre-
quency for the MESR is experimentally determined as 391 Hz
and through simulation as 350.9 Hz. For the remaining case
1–6 rows, the values obtained through experimentation are
351–617 Hz, and through simulations, this is observed as
388.3–632.9 Hz. This demonstrates that the microstructured
dampers exhibit a higher frequency bandwidth with microstruc-
turing, which has never been reported earlier by some of the
other researchers who studied the effects of damping and nat-
ural frequency by incorporating micro-/macroscale inclusions
in viscoelastic materials. Therefore, most certainly for high-
frequency damping applications, the use of such a technique
is quite beneficial.
C. Damping Ratio and Loss Factor: COMSOL MultiPhysics
Simulations and Experimental Findings
The damping ratio for the unconstrained and constrained
treatment cases is calculated by the logarithmic decrement
method as detailed earlier, wherein x0and xnare from the
time-displacement plot of the vibrating damper assembly. The
damping ratio is seen to be increasing with more number of
microchannel rows (Fig. 6). The reason for this is as follows.
When a microdamper is subjected to vibration, the oil inside
the microchannels moves in it. We have already shown through
fluid structure interactions that the fluid movement along the
channel walls results in a substantial amount of dissipation
of vibration energy. As the number of channels is increased,
Fig. 6. Damping ratio in the unconstrained and constrained treatment cases
for the block with no microchannels and with microchannel rows varying from
one to six and the MESR case.
this interfacial area with the silicone oil also increases, re-
sulting in more frictional dissipation. For the unconstrained
case, the damping ratio varies from 0.055 to 0.14 (2.7 times
increase), whereas for the constrained case, this is recorded
to vary between 0.056 and 0.16 (2.8 times increase) as the
rows vary from one to six. These values are almost double
that of earlier reported literature [12] on room temperature
damping using microscale inclusions in viscoelastic materials.
The damping ratio for the constrained treatment cases is more
than the unconstrained treatment case for all corresponding
samples. This can be attributed to the contribution coming from
the shear deformation initiated by the top plate. As per (11),
the fundamental mode frequency is proportional to the square
root of rigidity if the other parameter remains constant. The
equivalent thickness is dependent on the thickness of the layers
used. The rigidity is proportional to the equivalent thickness
of the layers used. For the same configuration, the equivalent
thickness of the constrained treatment mode is more than that
for the unconstrained treatment mode. In this way, we can
say that, due to more rigidity, the damping capacity of the
microdamper is more in case of constrained treatment.
The loss factors of the constrained and unconstrained cases
are calculated by using the half-power bandwidth method.
Fig. 7(a) shows the amplitude versus normalized frequency
(Ω=ω−ωr, where ωris the fundamental mode frequency)
representative plots for one (solid line), three (dashes), and
five (dotted line) channel cases on experimentally acquired
amplitude–frequency data. The plot clearly illustrates a de-
creasing sharpness corresponding to increasing bandwidth and
a reduction in the overall displacement amplitude for all of
these cases as the number of rows is increased. The reduction in
displacement amplitude further indicates the energy dissipative
behavior of the system. Fig. 7(b) shows the calculated loss
factor from this half-power bandwidth curve for both uncon-
strained and constrained cases, respectively. The loss factor of
the unconstrained case varies from 0.02 to 0.11 (about 5.5 times
increase), and in the constrained case, it varies from 0.019 to

706 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL.22, NO. 3,JUNE 2013
Fig. 7. (a) Plot of displacement amplitude versus half-power bandwidth in
case of a representative sample of one, three, and five rows for the unconstrained
treatment case. (b) Plot of calculated loss factor for the number of channel rows
of one to six and MESR cases.
0.28 (about 14.7 times increase) for the one- to six-row cases,
respectively. This increase in loss factor is indicative of a higher
energy dissipation in the constrained case for similar reasons
as in the case of the damping ratio. Also, worth noting is the
fact that the loss factor for the constrained case has an order
of magnitude increase with the increase in number of channel
rows and compares reasonably with earlier reported work of
Kaully et al. [13], although in our case, the operating tempera-
ture is room temperature throughout the experiments.
This energy dissipative behavior explored in the aforemen-
tioned experiments shows a good promise because of high
damping ratio and loss factor which is observed mostly at
room temperature. In the process of energy dissipation, there
is an overall increase in the temperature of the damper, but
the properties of the material remain unchanged due to this
temperature rise as the damper shows identical behavior in
successive runs.
IV. CONCLUSION
We have developed a novel custom-made damping pad with
different damping ratios and fundamental frequencies using a
microstructuring technique. As we have discussed, by virtue of
adding more number of rows of microchannels in the PDMS
damping slab, we can suitably vary its damping properties. We
have further found out a relationship between the fundamental
frequency for two different test cases of constrained and uncon-
strained treatment and number of microchannel layers or rows.
Damping ratios can be changed from 0.056 to 0.16 (around
3 times), and fundamental mode frequency can be increased
from 288 to 617 Hz by virtue of this microstructuring. We have
also observed a high energy dissipation at the interface of the
microchannels and the oil containment within them, and this
results from the creation of a slip zone causing frictional dissi-
pation of energy. While the current study has shown that high
damping is achievable using microscale channels, the nature
of damping with respect to the change in vibration amplitude
per cycle will be studied in the future to find the linearity
of the damping phenomena. The approach demonstrated in
this paper will open a future domain for customized damping
arrangements and would find a lot of applications in electronic
devices and systems, automobile seating system, etc., which
may need custom-made vibration suppression mechanisms at
a variety of operational frequencies.
ACKNOWLEDGMENT
The authors would like to thank the Center for Nanosciences,
Indian Institute of Technology, Kanpur, India, and Prof. S.
Gangopadhyay, Prof. K. Gangopadhyay, and A. Ghosh of the
University of Missouri, Columbia, MO, USA, for their help,
advice, and valuable suggestions. The authors would also like
to gratefully acknowledge the help rendered by S. Varanasi
in the experimental work.
REFERENCES
[1] B. Bhattacharya, J. A. Rongong, and G. R. Tomlinson, “Vibration sup-
pression performance of piezoceramic and magnetostrictive materials
in hybrid constrained layer damping,” in Proc. SPIE, 1999, vol. 3672,
pp. 242–250.
[2] C.W.D.Silva,Vibration Fundamentals and Practice. Boca Raton, FL,
USA: Taylor & Francis, 2007.
[3] A. K. Mallik, Principles of Vibration Control. New Delhi, India: Affili-
ated East West Press Pvt. Ltd., 2010.
[4] B. Bhattacharya, G. R. Tomlinson, and J. R. House, “Vibration sup-
pression of structures with viscoelastic inserts,” Proc. Inst. Mech. Eng.,
J. Mech. Eng. Sci., vol. 216, pt. 10, pp. 983–995, Oct. 2002.
[5] T.-L. Teng and N.-K. Hu, “Analysis of damping characteristics for vis-
coelastic laminated beams,” Comput. Methods Appl. Mech. Eng., vol. 190,
no. 29, pp. 3881–3892, Apr. 2001.
[6] E. M. Kervin, “Damping of flexural waves by a constrained viscoelastic
layer,” J. Acoust. Soc. Amer., vol. 31, no. 7, pp. 952–962, 1959.
[7] D. Ross, E. E. Unger, and E. M. Kervin, Jr., “Damping of plate flexural
vibrations by means of viscoelastic laminates,” in Proc. ASME Struct.
Damping ASME, New York, NY, USA, 1959, pp. 49–88.
[8] Y. V. K. S. Rao and B. C. Nakra, “Vibrations of unsymmetrical sandwich
beam and plates with viscoelastic cores,” J. Sound Vibrat., vol. 34, no. 3,
pp. 309–326, 1974.
[9] C. D. Johnson, “Design of passive damping systems,” J. Mech . Des. ,
vol. 117, no. B, pp. 171–176, Jun. 1995.
[10] J. L. Marcelin, S. Shakhesi, and F. Pourroy, “Optimal constrained layer
damping of beams: Experimental and numerical studies,” Shock Vibrat.,
vol. 2, no. 6, pp. 445–450, 1995.
[11] R. K. Patel, B. Bhattacharya, and S. Basu, “A finite element based investi-
gation of obtaining high material damping over a large frequency range in
viscoelastic composite,” J. Sound Vibrat., vol. 303, no. 3–5, pp. 753–766,
2007.

SINGH et al.: PASSIVE VIBRATION DAMPING USING POLYMER PADS WITH MICROCHANNEL ARRAYS 707
[12] A. Goel, A. Kumar, P. K. Patra, S. Mahendra, S. Tabatabaei, P. J. J.
Alvarez, G. John, and P. M. Ajayan, “In situ synthesis of metal nanopar-
ticle embedded free standing multifunctional PDMS films,” J. Macro-
molecular Rapid Commun., vol. 30, no. 13, pp. 1116–1122, 2009.
[13] T. Kaully, A. Siegmann, and D. Shacham, “Mechanical behavior of highly
filled natural CaCO3composites: Effect of particle size distribution and
interface reactions,” J. Polymer Composites, vol. 29, no. 4, pp. 396–408,
Apr. 2008.
[14] Q. Wang, F. Han, and C. Cui, “Effects of macroscopic graphite par-
ticulates on the damping behaviour of CuAlMn shape memory alloy,”
J. Mater. Sci., vol. 42, no. 13, pp. 5029–5035, Jul. 2007.
[15] A. Kocabas and A. Atilla, “Polymeric waveguide Bragg grating filter
using soft lithography,” Opt. Exp., vol. 14, no. 22, pp. 10228–10 232,
Oct. 2006.
[16] M. Meyers and K. Chawla, Mechanical Behaviour of Materials, 2nd ed.
Cambridge, U.K.: Cambridge Univ. Press, 2009.
[17] A. W. Leissa, “The free vibration of rectangular plates,” J. Sound Vibrat.,
vol. 31, no. 3, pp. 257–293, 1973.
[18] E. J. Hearn, Mechanics of Materials, vol. 1. Oxford, U.K.: Butterworth,
1997.
[19] P. B. Lillehoj and C.-M. Ho, “A long-term, stable hydrophilic
poly(dimethylsiloxane) coating for capillary-based pump,” in Proc. IEEE
23rd Int. Conf. MEMS, Sep. 4, 2011, pp. 1063–1066.
Rajeev Kumar Singh received the B.E. degree
in mechanical engineering from Nagpur University,
Nagpur, India, in 1992 and the M.Tech. degree in
industrial systems engineering from Kamla Nehru
Institute of Technology, Sultanpur, India, in 2007.
He is currently working toward the Ph.D. degree in
the Department of Mechanical Engineering, Indian
Institute of Technology, Kanpur, India.
His research interests include MEMS, microflu-
idics, and microfabrication.
Rishi Kant received the B.Tech. degree in mechan-
ical engineering from the University Institute of
Engineering and Technology, Chhatrapati Shahu Ji
Maharaj University, Kanpur, India, in 2004 and the
M.E. degree in mechanical engineering from Delhi
College of Engineering, University of Delhi, New
Delhi, India, in 2007. He is currently working toward
the Ph.D. degree in mechanical engineering at the
Indian Institute of Technology, Kanpur.
He was a Research Assistant with the Design
Manufacturing Integration (DFM) Laboratory, In-
dian Institute of Technology, New Delhi, from 2007 to 2008. His research
interests include bio-MEMS and micro-/nanofabrication for fluidic and other
applications.
Shashank Shekhar Pandey received the B.Tech.
and M.Tech. degrees in mechanical engineering from
the Indian Institute of Technology (IIT), Kanpur,
India, in 2010. He is currently working toward the
Ph.D. degree in bioengineering at the University of
Utah, Salt Lake City, UT, USA.
He was with Daimler India Commercial Vehicles
Pvt. Ltd. from 2010 to 2011. Thereafter, he was
a Research Associate with the BioMEMS and Mi-
crofluidics Laboratory, IIT, from 2011 to 2012. His
research interests include micro-/nanofabrication,
biosensors, bioinstrumentation, bio-MEMS, microfluidics, and their applica-
tions in various engineering and medical problems.
Mohammed Asfer received the B.E. degree in
mechanical engineering from Utkal University,
Bhubaneswar, India, in 2003 and the M.Tech. degree
from the Indian Institute of Technology, Kanpur,
India, in 2007, where he is currently working toward
the Ph.D. degree in mechanical engineering.
His research interests include development of mi-
crofluidic components (e.g., mixers, sensors, etc.)
and simulation of microscale flows.
Bishakh Bhattacharya received the B.E. degree in
civil engineering and the M.E. degree in applied
mechanics from Jadavpur University, Kolkata, India,
in 1988 and 1991, respectively, and the Ph.D. degree
in aerospace engineering from the Indian Institute of
Science, Bangalore, India, in 1997.
He subsequently carried out postdoctoral stud-
ies at the Department of Mechanical Engineering,
Sheffield University, Sheffield, U.K., for more than
two years. He joined the Department of Mechanical
Engineering, Indian Institute of Technology, Kanpur,
India, in 2000, where he is currently a Professor and the Head the Interdisci-
plinary School of Design. His research interests include smart materials and
intelligent system design for varied engineering applications.
Pradipta K. Panigrahi received the B.Tech.
(Honors) degree in mechanical engineering from
UCE Burla, India, in 1987. He received the M.S. de-
gree in mechanical engineering in 1993, the M.S. de-
gree in system science in 1997, and the Ph.D. degree
in mechanical engineering in 1997 from Louisiana
State University, Baton Rouge, LA, USA.
He is a Professor with the Department of Me-
chanical Engineering, Indian Institute of Technology,
Kanpur, India. His research focuses on development
and implementation of various experimental tech-
niques (primarily optical) for both macroscale and microscale applications to
study both fundamental and practical aspects of a wide range of engineering
systems.
Shantanu Bhattacharya received the B.S. degree
in industrial and production engineering from the
University of Delhi, New Delhi, India, in 1996, the
M.S. degree in mechanical engineering from Texas
Tech University, Lubbock, TX, USA, in 2003, and
the Ph.D. degree in biological engineering from
the University of Missouri, Columbia, MO, USA,
in 2006.
He was a Senior Engineer with Suzuki Motors
Corporation from 1996 to 2002. He also completed
postdoctoral training at the Birck Nanotechnology
Center, Purdue University, West Lafayette, IN, USA, for one year. He was an
Assistant Professor with the Department of Mechanical Engineering, Indian
Institute of Technology, Kanpur, India, from 2007 to 2012, where he is currently
an Associate Professor. His research interests include design and development
of microfluidics and MEMS platforms for varied engineering applications.