Conference PaperPDF Available

Additively manufactured lattice structures for precision engineering applications

Waiel A. Elmadih1, Wahyudin P. Syam1, Ian Maskery2 and Richard Leach1
1Manufacturing Metrology Team
2Centre for Additive Manufacturing
University of Nottingham
Nottingham, NG7 2RD, UK
Additive manufacturing (AM) is limited by fewer
design constraints than conventional
manufacturing [1]. Therefore, AM provides higher
design flexibility and allows fabrication of highly
complex geometries, for example, lattice
structures. Compared to solid structures, lattice
structures allow designs that incorporate highly-
tailored mechanical properties so that the
requirements of applications are met with efficient
use of resources [2].
Representative stress-strain curves for solid and
lattice structures are shown in FIGURE 1. In
FIGURE 1, the area under the curve up to the
densification strain is the energy absorbed per
unit volume of material. The energy absorption is
small for a solid, compared to lattice structures
that benefit from long plastic plateau regions in
their stress-strain curves.
FIGURE 1. Representative stress-strain curves
of a full density solid and lattice structures of
different density fraction, adapted from [1].
The length of this plateau region, and the stress
at which it occurs, depends on the lattice material,
volume fraction, unit cell configuration, and the
number of lattice cells in a structure [1]. As such,
with the same total volume, different lattice
configurations can have different mechanical
properties. There has been considerable
research focus on the manufacturability and
strength-to-weight ratio of some lattice structures
[3][5]. However, there is little published work
investigating lattice structures for vibration
isolation and thermal expansion control; both of
which are significant for precision engineering
applications. Many applications need structures
that can be isolated from external vibration, for
example, the tool in a CNC machine and the
probe of an optical metrology system. High
stiffness structures are often used, which
increase the natural frequency, achieving
vibration damping [6]. Taking an alternative and
complementary approach, this paper discusses
applications of lattice structures for vibration
FIGURE 2 shows the vibration response of a
structure, with natural frequency to an external
vibration source with frequency . When =,
a resonance occurs, leading to a large
displacement amplitude. [6]. To have higher
vibration isolation efficiency, a structure should
have a low , which can be achieved by lowering
the stiffness of the structure. But, there is a
practical limit: if the stiffness is too low, the
structure will be unable to sustain the mass load
of the body of interest (work tool/probe). Lattice
structures possess high strength-to-weight ratio
for their mass, providing low stiffness at relatively
high strength [1].
In this study, various configurations of strut-based
lattice structure are investigated with a
combination of finite element analysis (FEA) and
experimental assessment. Information gained in
this study shows that lattice structures can be
used to tune the design of a structure to have a
desired for a specific vibration isolation
application, effectively setting up a mechanical
band-gap. In practice, external vibration sources
commonly have multiple dominant frequencies,
so should be optimised for a specific range of
frequencies. A case study in which a metrology
frame for an optical system is to be designed, will
be used to demonstrate how for the lattice
structures can be optimised for a specific
frequency range.
FIGURE 2. Vibration damping and isolation.
Strut-based lattices are used in this study as they
are periodic open-cell cellular structures that
possess bending characteristics that give longer
plateau regions than closed cell cellular
structures, and thus can absorb more energy
than periodic closed-cell cellular structures
CAD design
The design of lattice structures for AM poses a
significant challenge. We have developed a
simple design tool, in the form of equation (1).
This allows us to construct a range of lattice unit
cells with predefined volume fraction, V. Lattice
strut diameters were calculated using equation
(1), thus
16 +
16 +2
16 +
16 +
16 +2
= 0
where the length of a unit cell is fixed at 30 mm;
is the strut diameter; is the cell length; is
the number of horizontal struts of length as
they appear in top and bottom views of a single
lattice cell; is the total number of vertical struts
of length as they appear in top and bottom
views of a single lattice cell; is the total number
of vertical struts of length as they appear in
front, back and side views; is the total number
of diagonal struts on all faces; is the number of
diagonal members across the centre of the lattice
cell; is the filled volume of the lattice cell; and
is the constant of intersection volume equal to 0
when = 0, 0.181021 when = 2, and 0.636638
when = 4 [8].
CAD was used for the design of single unit cells
which were then tessellated to create lattice
structures (as illustrated in FIGURE 3).
FIGURE 3. (a) Example of single lattice cell as
designed with Creo Parametric CAD software,
and (b) example of 2×2×2 periodic lattice cells as
tessellated with Autodesk Inventor CAD software.
Samples with lattice behaviour
There is a minimum required number of lattice
unit cells that a structure should have in order for
it to exhibit lattice behaviour, hence, the designed
lattices should be tested to determine whether
they exhibit lattice behaviour [9]. Experimental
compression tests were carried out on samples of
similar overall size, volume fraction and, cell
configuration, but of variable number of
tessellations: 2×2×2, 3x3×3 and 4×4×4. The
samples are shown in FIGURE 4. The purpose of
these experimental compression tests is to
determine the minimum number of cells that
represent a lattice structure, which will later be
used in the study.
Three replicas of each sample were compressed
at a constant compression speed of 1 mmmin-1.
The results of the compression tests with the
three samples are shown in the form of
load-displacement curves in FIGURE 5. All
samples took the curves up to the
densification area, which essentially means all
tested samples exhibited lattice behaviour. This
means that 2×2×2 lattices represent the minimum
number of lattices that can be used in this study.
FIGURE 4. (a) Design of compression test
samples, and (b) compression test samples as
manufactured from Nylon 12 powder on an EOS
P100 selective laser sintering machine with a
building powder layer height of 100 µm.
FIGURE 5. Compression test curves of lattice
samples of different unit cells.
Lattice structure identification
The lattice structures used in this study are of
different volume fraction, different number of
nodes and different cell configurations. For the
purpose of individual characterisation, every
lattice cell was assigned a unique code in the
form of (-), where is the number of
nodes in a 2D view of the single cell,
denotes the volume fraction taking, for example,
a value of010for a 10 % lattice cell, and is
an identification number of the struts
configuration. A total of twenty-three lattice cell
configurations were developed based on a fixed
number of nodes. Each configuration formed the
basis for three different volume fraction cells:
10 %, 20 % and 30 %. FIGURE 6 shows the
lattice cells of 10 % volume fraction in a 2×2×2
FIGURE 6. CAD models of the lattices used in
this study, all in 2×2×2 tessellation and of 10 %
volume fraction.
The CAD models shown in FIGURE 6, along with
their corresponding versions of 20 % and 30 %
volume fraction, were analysed using ANSYS
Workbench FEA. To ensure the calculations had
converged with respect to the element size, we
determined the first of the structures using a
range of element sizes from 25 mm to 0.25 mm.
At an element size of 1 mm, the difference
between subsequent results had fallen below 1 %
for Nylon-12 samples of (60×60×60) mm size.
Therefore, we used elements of 1 mm for all
subsequent calculations. The base surfaces of
the models were constrained in all degrees of
freedom. The harmonic response to a vertical
load of 0.1 N, vibrating at a frequency in the range
0.1 Hz to 1000 Hz (with 10 Hz frequency
intervals) acting on the upper surface was
simulated. The displacements due to the
generated harmonic vibration in the vertical
direction were calculated. The simulated spectra
of the 4010-x and 5010-x lattice models are
shown in FIGURE 7, where the peaks represent
of each model. The 5010-x lattice types have
peaks at higher frequencies than the
corresponding 4010-x lattices with the same
number of unit cells, except for the 5010-3 lattice,
which has the lowest natural frequencies among
all the tested samples. This makes the 5010-3
cell a good candidate for vibration isolation.
However, the 5010-3 cell has more resonance
frequencies within the testing range than the
4010-8 cell. Consequently, the 5010-3 cell can
complicate the control of vibration isolation
0 5 10 15 20
Compressive force/N
2×2×2 Sample 3×3×3 sample
4×4×4 sample
because the 5010-3 cell has high number of
resonance peaks that need to be controlled for
providing vibration isolation, and thus, the 4010-8
cell is more appropriate for vibration isolation
FIGURE 7. Results from harmonic response
simulations of the 4010-x and 5010-x lattice types
in 2×2×2 tessellations.
The models with lower volume fraction showed
lower natural frequencies than models of higher
volume fraction. This is most likely due to the
lower stiffness of the lower volume fraction
For experimental verification of these results,
three samples each of the 4010-8 and 4030-1
lattices were manufactured and the harmonic
responses in the vertical direction were tested.
Each sample was fixed to a shaker (shown in
FIGURE 8) which vibrated in the range of 0.1 Hz
to 1000 Hz for the 4010-8 samples, and a range
of 0.1 Hz to 3000 Hz for the 4030-1 samples (all
with < 1 Hz frequency intervals) and the reaction
of the bottom surface of the sample was
measured using a force sensor attached to the
shaker. The frequency range for the experimental
testing of each sample was chosen based on the
range at which was obtained using FEA for
each sample. The positions of the natural
frequency peaks are in 90.6 % average
agreement with the frequencies at which they
appeared in the simulation results. Comparison
between average experimental results and
simulation results are shown in FIGURE 9.
FIGURE 8. (a) Selective laser sintering
manufactured samples for experimental
verification, (b) vibration experiment setup.
FIGURE 9. Experimental verification of the
natural frequencies for vertical excitation of the
4030-1 (top) and 4010-8 (bottom) lattice
The effect of the size of the lattice cells on the
natural frequencies was simulated. The following
sizes were chosen: 30 mm, 22.5 mm and
16.875 mm, while keeping the number of
tessellations constant at 2×2×2. From the FEA
results, it can be concluded that decreasing the
cell size results in higher natural frequencies.
This is likely due to the excitation of shorter
wavelength vibration modes than are permitted in
larger structures of the same volume fraction, as
shown in FIGURE 10.
FIGURE 10. The effect of lattice cell size on .
FIGURE 11. The effect of the number of
tessellations of lattice cells on .
In addition, increasing the number of
tessellations, for a constant cell size and volume
fraction, reduces of the structure, which is
thought to be related to increased strut bending
in structures with a higher number of
tessellations. This was confirmed by testing
samples of tessellations of 2, 4, 5 and 10, in
three-dimensions, as shown in FIGURE 11.
The structural frame of a new all-optical
coordinate measuring system was manufactured
with selective laser sintering from Nylon-12 using
lattice structures to hold the mass of a 1 kg probe
and isolate mechanical vibrations in the -
direction arising from the movement of the stage
which drives the probe, which vibrates in the
range from 40 Hz to 80 Hz.
Determining the lattice cell size
There are two options for the selection of the cell
size and number of cell tessellations that can fill
a volume in space with low : (a) large size cells
with low number of tessellations, or (b) smaller
cells with a higher number of tessellations. The
results, so far, do not suggest which route is more
appropriate. As a result, a study was conducted
with the aim of suggesting the most appropriate
route to obtain lower . The study comprised the
design of (30×30×30) mm lattice structure
samples using 4010-8 cells of different sizes:
15 mm, 7.5 mm, and 3.75 mm. By default, cells of
less size need a higher number of tessellations to
fill the (30×30×30) mm space. FEA (results are
summarised in TABLE 1) showed that larger size
cells had lower first mode than smaller ones
with a higher number of tessellations.
TABLE 1.The coupled effect of cell size and
number of tessellations at constant volume
fraction on the first of the lattice structures.
Cell size/
mm Sample
size/mm Number
of cells 1st mode
/ Hz
As a result, the most suitable cell size for the
structural frame must have two tessellations in
the direction of the shortest dimension (two is the
lowest number of tessellations that can represent
a lattice as discussed previously). Subsequently,
30 mm cells were used to construct the body of
the structural frame because the shortest
dimension was the thickness of the structural
frame (60 mm). The structure used the 4010-8
cell, for the reasons discussed above, and then
varied the volume fraction, and the number of
tessellations to get the isolation to the desired
Verification with in-situ harmonic test
The design of the structural frame comprises
three identical sub-frames each kinematically
coupled to the stage of the optics through balls in
v-grooves located on top of each sub-frame. The
sub-frame, shown in FIGURE 12, is stiffened at
the back through the use of a solid swept
stiffener, and in both sides through the use of
perforated swept surfaces to further damp the
vibration in - and - directions. The harmonic
response to the compressive working load of
10 N, with excitations ranging from
0.1 Hz to 1500 Hz, was modelled with frequency
intervals of 1 Hz. A safety factor of two was used
for the maximum working load which was applied
to the top of the frame.
Natural frequency/Hz
Vibration mode
4010-8 2x2x2 30 mm
4010-8 2x2x2 22.5 mm
4010-8 2x2x2 16.875 mm
Natural frequency/Hz
Vibration mode
4010-8 2x2x2 4010-8 3x3x3
4010-8 4x4x4 4010-8 10x10x10
FIGURE 12: Design of the structural sub-frame
for isolating vertical excitations arising from the
movement of the stage of the optics using lattice
structure, dimensions in millimetres.
FIGURE 13: Harmonic response of one
The structure succeeds in isolating excitations in
the range of 38 Hz and 83 Hz, with maximum
displacement of 2 % of the length of the frame,
see FIGURE 13. Additional metal support was
used to mount the sub-frame on the shaker which
affected the harmonic results obtained from
experiment. The positions of peaks from FEA
of similar conditions to the conditions of the
experiment are in 89.8 % average agreement
with the frequencies at which they appeared in
the experiment results.
Before lattice structures can be used for vibration
isolation of a system, the dynamic behaviour of
the system has to be understood. Then, the
lattice characteristics can be tailored to isolate the
resonance peaks of the system. The control of
the natural frequency is the major step towards
tailoring the lattice structure. The study reveals
that the natural frequency of a lattice structure
can be reduced by increasing cell size, reducing
volume fraction, and/or increasing the number of
tessellations of a singular lattice cell, and vise
versa. The work was funded by the EPRSC
project EP/M008983/1.
[1] L. J. Gibson and M. F. Ashby. Cellular
Solids: Structure and Properties.
Cambridge University Press, Cambridge:
[2] O. Rehme and C. Emmelmann. Rapid
Manufacturing of Lattice Structures with
Selective Laser Melting, Proc. SPIE 2006;
[3] C. Yan, L. Hao, A. Hussein, P. Young, and
D. Raymont. Advanced Lightweight 316L
Stainless Steel Cellular Lattice Structures
Fabricated via Selective Laser Melting,
Mater. Des. 2014; 55: 533-541.
[4] C. Yan, L. Hao, A. Hussein, and D.
Raymont. Evaluations of Cellular Lattice
Structures Manufactured Using Selective
Laser Melting, Int. J. Mach. Tools Manuf.
2012; 62: 32-38.
[5] M. Santorinaios, W. Brooks, C. J.
Sutcliffe, and R. A. W. Mines. Crush
Behaviour of Open Cellular Lattice
Structures Manufactured Using Selective
Laser Melting, WIT Trans. Built Environ.
2006; 85: 481-490.
[6] T. L. Schmitz and K. S. Smith. Mechanical
Vibrations: Modeling and Measurement.
Springer, New York: 2011.
[7] O. Rehme. Cellular Design for Laser
Freeform Fabrication. Gottingen: 2010.
[8] M. Moore. Symmetrical Intersections of
Right Circular Cylinders, Math. Gaz. 1974;
58: 181-185.
[9] W. P. Syam, J. Wu, B. Zhao, I. Maskery,
W. Elmadih, and R. K. Leach. Design and
Analysis of Strut-based Lattice Structures
for Vibration Isolation. Precision
Engineering. 2017; In press.
... Tuning of natural frequency for vibration isolation with lattice structures Part of the results in this chapter are published in these journal and conference papers [54,163]. Lattice structures have high strength to weight ratio and good energy absorption properties. ...
... The BCCxyz unit cell, shown in Figure 7.1, was designed using the strut-based lattice design equations presented in our previous work [163]. In designing BCCxyz lattice structures for this study, a range of volume fractions was considered from 5 % to 30 %. ...
... The results for WP1 can be seen in Chapter 5, results for WP2 are presented in Chapter 6, and the results of WP3 are available in Chapter 7 and Chapter 8. The methodology presented in this chapter formed part of these publications[54,56,[159][160][161][162][163]. ...
Advancements in additive manufacturing technology have allowed the realisation of geometrically complex structures with enhanced capabilities in comparison to solid structures. One of these capabilities is vibration attenuation which is of paramount importance for the precision and accuracy of metrology and machining instruments. In this project, new additively manufactured lattice structures are proposed for achieving vibration attenuation. The ability of these lattices to provide vibration attenuation at frequencies greater than their natural frequency was studied first. This is referred to as vibration isolation. For the vibration isolation study, a combination of finite element modelling and an experimental setup comprising a dynamic shaker and laser vibrometer was used. The natural frequencies obtained from the experimental results were 93 % in agreement with the simulated results. However, vibration attenuation was demonstrated only along one dimension and vibration waves were allowed to propagate, meaning the transmissibility was allowed to be greater than 0 dB. To achieve lower transmissibility, the project demonstrated that lattice structures can develop Bragg-scattering and internal resonance bandgaps. The bandgaps were identified from the lattices' dispersion curves calculated using a finite element based wave propagation modelling technique. Triply periodic minimal surface lattices and strut-based lattices developed Bragg-scattering bandgaps with a normalised bandgap frequency (wavelength divided by cell size) of ~ 0.2. The bandgap of the tested lattices was demonstrated to be tunable with the volume fraction of the lattice unit cell, thus, providing a tool to design lattice structures with bandgaps at required frequencies. An internal resonance mechanism in the form of a solid cube or sphere with struts was designed into the inner core of the unit cell of strut-based lattices. These new internal resonance lattices can provide (a) lower frequency bandgaps than Bragg-scattering lattices within the same design volume, and/or (b) comparable bandgaps frequencies with reduced unit cell dimensions. In comparison to lattices of higher normalised bandgap frequencies, lattices with lower normalised bandgap frequencies have cell sizes that are more suitable for manufacturing with the current additive manufacturing technologies and have higher periodicity within a constrained design volume, resulting in higher attenuation within the bandgaps and more homogenous structures. Similar to the Bragg-scattering lattices, the bandgaps of the internal resonance lattices were demonstrated to be tunable through modification of the geometry of the lattice unit cell. The internal resonance lattice experimentally demonstrated a bandgap of normalised frequency between 0.039 to 0.067 and an attenuation of up to -77 dB. These results are essential for engineering vibration attenuation capabilities within the macro-scale of materials for complete elimination of all mechanical vibration waves at tailorable frequencies. Future work will include further reduction of the bandgap frequencies and increasing the bandgap width by exploring new unit cell designs and new materials for additive manufacturing.
... For this reason, Lou et al., (2014) and Li et al., (2015) explored the dynamic performance of lattice structures made from a hot-pressing process and studied the effects of damage on their dynamic behavior [15][16]. Another more recent study by Syam et al., (2018) and Elmadih et al., (2017) investigated the dynamic performance of strut-based lattice structures made by utilizing different manufacturing techniques within the additive manufacturing process (AM) [17][18]. Using AM to fabricate lattice structures allows a higher degree of complexity to be incorporated within lattice designs and therefore possibly to reduce their size. ...
... For this reason, Lou et al., (2014) and Li et al., (2015) explored the dynamic performance of lattice structures made from a hot-pressing process and studied the effects of damage on their dynamic behavior [15][16]. Another more recent study by Syam et al., (2018) and Elmadih et al., (2017) investigated the dynamic performance of strut-based lattice structures made by utilizing different manufacturing techniques within the additive manufacturing process (AM) [17][18]. Using AM to fabricate lattice structures allows a higher degree of complexity to be incorporated within lattice designs and therefore possibly to reduce their size. ...
... In the example of Syam et al., (2018) there is a design of a lattice unit cell which is obtained by fixing the number of nodes and varying the strut configuration while maintaining the symmetry, and from these six models are proposed [17]. On the other hand, Elmadih et al., (2017) designed a lattice structure based on a developed equation design tool which allowed the construction of a range of lattice unit cells with predefined volume fractions [18]. Therefore, lattice structures in this study were constrained using other design parameters, the strut diameter size on the octahedral cell. ...
Full-text available
This paper presents a vibration characteristics of BCC lattice structure with quatrefoil node which has been made using the fused deposition modelling (FDM) additive manufacturing (AM) technique. By conducting vibration testing, the effect of strut diameter design parameter on the natural frequency values of the BCC lattice structure with quatrefoil node is investigated. The results showed that the natural frequency values of the lattice structure material can be greatly affected by the strut diameter sizes due to increase in stiffness as the strut diameter increases. The mathematical equation is also derived to calculate the total area moments of inertia of the lattice structure model and the validity of this developed model is shown through comparison of the results with experimental work of the three-point bending test which shown similar increase trend. Thus, this study provides information on the influence of strut diameter design parameter on its vibration characteristic.
... Conventional practice is to design the mechanical system to have a natural frequency much greater than or lower than the frequencies of the input waves [1][2][3]. Using the conventional practice, our previous work has shown that additively manufactured (AM) lattice structures can be used for vibration isolation in one degree of freedom (DOF) by designing the lattice to have a resonant frequency lower than a particular frequency of interest [4]. Further to this, Wang et al. showed how topology optimisation and density grading could be implemented with AM lattice structures to provide isolation in a selected frequency region [5]. ...
... The volume fraction and size of the cells shown in Fig. 1 is 20% and 15 mm (initial settings), respectively. These values are based on the properties of unit cells that have provided vibration isolation in previous work [1,4]. ...
... The finite length of the structure can be the cause of resonances in the frequency regions of some bandgaps. From our previous work [1,4], we assert that 40 mm cells are less stiff than 15 mm cells of similar configurations due to higher dominance of bending behaviour in larger cells. This lower stiffness, of the 40 mm gyroid cell compared to the 15 mm cell, is translated into lower bandgap frequency. ...
In this paper, the phonon dispersion curves of several surface-based lattices are examined, and their energy transmission spectra, along with the corresponding bandgaps are identified. We demonstrate that these bandgaps may be controlled, or tuned, through the choice of cell type, cell size and volume fraction. Our results include two findings of high relevance to the designers of lattice structures: (i) network and matrix phase gyroid lattice structures develop bandgaps below 15 kHz while network diamond and matrix diamond lattices do not, and (ii) the bandwidth of a bandgap in the network phase gyroid lattice can be tuned by adjusting its volume fraction and cell size.
... Within these properties lies vibration isolation, which depends mainly on the mass and stiffness of the structure. Traditional techniques for providing vibration isolation promote shifting the resonant frequency above or below the frequency of interest [1][2][3]. There has been little focus on methods to completely eliminate vibration waves from a precision engineering component. ...
... where is the cell size, ' is the length of an internal strut, is the length of the resonator and is the diameter of the struts making up the supporting scaffold. The reader is referred to the design tool in reference [2] for information on designing strut-based lattices of different volume fractions and sizes. ...
... C / takes values in the range of 0 to 1− / . The parameter / takes a value of 0.13 for a 30% volume fraction cell [2]. Thus, the identified parameter C / takes values between 0 and 0.87. ...
... On the other hand, AM can be used to fabricate complex structures in shorter time with saving more bulk material. Different AM technologies used to fabricate complex structures are extrusion based fused deposition method (FDM), selective laser melting (SLM), selective laser sintering (SLS), stereolithography (SLA), etc. 20,22,[28][29][30][31][32] The current study aims to cover modeling, mechanical properties, and vibration methods of PCS and metamaterials along with theoretical works. Emphasis is given on metamaterials through explaining the damping enhancement by such materials in details. ...
... Each sample was loaded by different amount of mass to study the response by calculating resonant frequency and isolation frequency. Furthermore, Elmadih et al. 28 explored several types of lattice structures under vibration excitation using shaker with signal producer. They have explored vibration modes, natural frequency, and isolation frequency of each specimen. ...
Full-text available
The adverse effect of mechanical vibration is inevitable and can be observed in machine components either on the long- or short-term of machine life-span based on the severity of oscillation. This in turn motivates researchers to find solutions to the vibration and its harmful influences through developing and creating isolation structures. The isolation is of high importance in reducing and controlling the high-amplitude vibration. Over the years, porous materials have been explored for vibration damping and isolation. Due to the closed feature and the non-uniformity in the structure, the porous materials fail to predict the vibration energy absorption and the associated oscillation behavior, as well as other the mechanical properties. However, the advent of additive manufacturing technology opens more avenues for developing structures with a unique combination of open, uniform, and periodically distributed unit cells. These structures are called metamaterials, which are very useful in the real-life applications since they exhibit good competence for attenuating the oscillation waves and controlling the vibration behavior, along with offering good mechanical properties. This study provides a review of the fundamentals of vibration with an emphasis on the isolation structures, like the porous materials (PM) and mechanical metamaterials, specifically periodic cellular structures (PCS) or lattice cellular structure (LCS). An overview, modeling, mechanical properties, and vibration methods of each material are discussed. In this regard, thorough explanation for damping enhancement using metamaterials is provided. Besides, the paper presents separate sections to shed the light on single and 3D bandgap structures. This study also highlights the advantage of metamaterials over the porous ones, thereby showing the future of using the metamaterials as isolators. In addition, theoretical works and other aspects of metamaterials are illustrated. To this end, remarks are explained and farther studies are proposed for researchers as future investigations in the vibration field to cover the weaknesses and gaps left in the literature.
... Hence, these features can be combined to produce lightweight structural parts with vibration isolation performance (Lee, 2016). Macro size lattice structure made of Nylon-12 polymer fabricated using selective laser sintering (SLS) additive manufacturing (AM) was reported as one possible alternative to the vibration isolators by constructing the lattice to have a resonant frequency lower than that of a given operating frequency (Elmadih et al., 2016;Syam et al., 2018). Another study by Soe et al. (2021) also designed a closed-cell fluid-filled lattice structure that attenuates acceleration upon impact. ...
The purpose of this study is to correlate the influence of multiple size-based design parameters of lattice structure, namely, the unit cell (UC) and strut diameter (SD) through the static and dynamics analyses for passive vibration isolation application. The lattice structures were prepared by utilizing the fused deposition modeling (FDM) additive manufacturing (AM). The samples were designed to retain lattice structure’s unique advantages while also conserving material consumption to fulfill the energy and cost demand. Through the static test, the crush behavior, failure mechanism, and mechanical properties were determined. The stiffness of lattice structure exhibited an increasing relationship with the unit cell and strut diameter where smaller unit cell and bigger strut diameter produced higher strength, and with that, higher load can be sustained. Through the dynamic vibration transmissibility test, it was found that the dynamic vibration results follow closely the trend in the static analysis. Lattice structure with larger unit cell and smaller strut diameter showed larger effective isolation region due to lower natural frequency value. The trade-off limit between stiffness for a lower natural frequency of the proposed design parameters was determined from the two parts analyses. The results suggest that most lattice isolators from the pool of design parameter combinations in this study have sufficient strength to withstand the predefined mass load and provide the most region for vibration isolation. The two proposed design parameters can later be used for a major or minor tuning of lattice isolators for other specific applications.
... Similar to Iyibilgin et al., (2013) and Maskery et al., (2017), their results revealed that models with vertical struts produced significantly higher stiffness. Meanwhile, Elmadih et al., (2017) explored the effect of unit cell size with different pre-defined volume fractions and number of layers. Changes in these design parameters can significantly affect the results of natural frequency in dynamic analysis. ...
... The BCCxyz unit cell, shown in Figure 2, was designed using the strut-based lattice design equations presented in our previous work [47]. In designing BCCxyz lattice structures for this study, we considered a range of volume fractions from 5% to 30%. ...
Full-text available
We report on numerical modelling of three-dimensional lattice structures designed to provide phononic bandgaps. The examined lattice structures rely on two distinct mechanisms for bandgap formation: the destructive interference of elastic waves and internal resonance. Further to the effect of lattice type on the development of phononic bandgaps, we also present the effect of volume fraction, which enables the designer to control the frequency range over which the bandgaps exist. The bandgaps were identified from dispersion curves obtained using a finite element wave propagation modelling technique that provides high computational efficiency and high wave modelling accuracy. We show that lattice structures employing internal resonance can provide transmissibility reduction of longitudinal waves of up to −103 dB. Paired with the manufacturing freedom and material choice of additive manufacturing, the examined lattice structures can be tailored for use in wide-ranging applications including machine design, isolation and support platforms, metrology frames, aerospace and automobile applications, and biomedical devices.
... Lattice structures show potential as vibration isolating support frames for metrology instruments [1][2]. There is limited understanding regarding how lattice defects impact their performance in terms of natural frequency and compressive strength. ...
Full-text available
The intersection of two circular cylinders of equal radius is not only of mathematical interest but also has application in both engineering and architecture. The joining of pipes of circular cross-section at a variety of given angles is an obvious example. The Romans and Normans, in using the barrel vault to span their buildings, were familiar with the geometry of intersecting cylinders where two such vaults crossed one another to form a cross vault. Larger numbers of equal intersecting cylinders arise in the following way.
This paper presents the design, analysis and experimental verification of strut-based lattice structures to enhance the mechanical vibration isolation properties of a machine frame, whilst also conserving its structural integrity. In addition, design parameters that correlate lattices, with fixed volume and similar material, to natural frequency and structural integrity are also presented. To achieve high efficiency of vibration isolation and to conserve the structural integrity, a trade-off needs to be made between the frame’s natural frequency and its compressive strength. The total area moment of inertia and the mass (at fixed volume and with similar material) are proposed design parameters to compare and select the lattice structures; these parameters are computationally efficient and straight-forward to compute, as opposed to the use of finite element modelling to estimate both natural frequency and compressive strength. However, to validate the design parameters, finite element modelling has been used to determine the theoretical static and dynamic mechanical properties of the lattice structures. The lattices have been fabricated by laser powder bed fusion and experimentally tested to compare their static and dynamic properties to the theoretical model. Correlations between the proposed design parameters, and the natural frequency and strength of the lattices are presented.
This paper investigates the manufacturability and performance of advanced and lightweight stainless steel cellular lattice structures fabricated via selective laser melting (SLM). A unique cell type called gyroid is designed to construct periodic lattice structures and utilise its curved cell surface as a self-supported feature which avoids the building of support structures and reduces material waste and production time. The gyroid cellular lattice structures with a wide range of volume fraction were made at different orientations, showing it can reduce the constraints in design for the SLM and provide flexibility in selecting optimal manufacturing parameters. The lattice structures with different volume fraction were well manufactured by the SLM process to exhibit a good geometric agreement with the original CAD models. The strut of the SLM-manufactured lattice structures represents a rough surface and its size is slightly higher than the designed value. When the lattice structure was positioned with half of its struts at an angle of 0 degrees with respect to the building plane, which is considered as the worst building orientation for SLM, it was manufactured with well-defined struts and no defects or broken cells. The compression strength and modulus of the lattice structures increase with the increase in the volume fraction, and two equations based on Gibson-Ashby model have been established to predict their compression properties.
Mechanical Vibrations: Modeling and Measurement describes essential concepts in vibration analysis of mechanical systems. It incorporates the required mathematics, experimental techniques, fundamentals of model analysis, and beam theory into a unified framework that is written to be accessible to undergraduate students, researchers, and practicing engineers. To unify the various concepts, a single experimental platform is used throughout the text. Engineering drawings for the platform are included in an appendix. Additionally, MATLAB programming solutions are integrated into the content throughout the text. © 2012 Springer Science+Business Media, LLC. All rights reserved.
Since the development of layered freeform manufacturing processes some technologies have emerged such as the Selective Laser Melting process (SLM) which uses layers of metal powder to manufacture 3D-objects from CAD-data by melting targeted geometries. The main goal using this process is to obtain functional products from engineering materials that feature desired properties such as given strength, hardness, surface roughness and residual stress behaviour. Rapid production with short throughput times due to only few process steps, a high individuality and a high degree of geometric freedom are considered to be its major advantages. However one disadvantage to all laser-based freeform manufacturing is the immense consumption of time since only considerably small quantities of material can be processed per time unit. Therefore it is desirable to review oldfashioned engineering design rules and develop part geometries that allow for hollow shaped parts with interior lattice structures providing the part with virtually the same stiffness and strength. Thus the process cost could be massively cut down due to reduced production time and less need for costly powder material. The SLM-process is meeting the requirements to fulfil this intention. Based on using fiber laser technology that delivers high beam quality the process is capable of producing thin walled structures of high tensile strength. Here development, production and testing of such lightweight yet sustainable SLM-parts will be presented along with their possible applications.
Crush Behaviour of Open Cellular Lattice Structures Manufactured Using Selective Laser Melting
  • M Santorinaios
  • W Brooks
  • C J Sutcliffe
  • R A W Mines
M. Santorinaios, W. Brooks, C. J. Sutcliffe, and R. A. W. Mines. Crush Behaviour of Open Cellular Lattice Structures Manufactured Using Selective Laser Melting, WIT Trans. Built Environ. 2006; 85: 481-490.
Cellular Design for Laser Freeform Fabrication
  • O Rehme
O. Rehme. Cellular Design for Laser Freeform Fabrication. Gottingen: 2010.