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ABSTRACT: We present a study of the existence, stability and bifurcation structure of
families of dark breathers in a one-dimensional uniform chain of spherical
beads under static load. A defocus- ing nonlinear Schrodinger equation (NLS) is
derived for frequencies that are close to the edge of the phonon band and is
used to construct targeted initial conditions for numerical computations.
Salient features of the system include the existence of large amplitude
solutions that bifurcate with the small amplitude solutions described by the
NLS equation, and the presence of a nonlinear instability that, to the best of
the authors knowledge, has not been observed in classical Fermi- Pasta-Ulam
lattices. Finally, it is also demonstrated that these dark breathers can be
detected in a physically realistic way by merely actuating the ends of an
initially at rest chain of beads and inducing destructive interference between
their signals.
10/2012;
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ABSTRACT: Osteoporosis is a well recognized problem affecting millions of individuals worldwide. The ability to diagnose problems in an effective, efficient, and affordable manner and identify individuals at risk is essential. Site-specific assessment of bone mechanical properties is necessary, not only in the process of fracture risk assessment, but may also be desirable for other applications, such as making intraoperative decisions during spine and joint replacement surgeries. The present study evaluates the use of a one-dimensional granular crystal sensor to measure the elastic properties of bone at selected locations via direct mechanical contact. The granular crystal is composed of a tightly packed chain of particles that interact according to the Hertzian contact law. Such chains represent one of the simplest systems to generate and propagate highly nonlinear acoustic signals in the form of compact solitary waves. First, we investigated the sensitivity of the sensor to known variations in bone density using a synthetic cancellous bone substitute, representing clinical bone quality ranging from healthy to osteoporotic. Once the relationship between the signal response and known bone properties was established, the sensor was used to assess the bone quality of ten human cadaveric specimens. The efficacy and accuracy of the sensor was then investigated by comparing the sensor measurements with the bone mineral density (BMD) obtained using dual-energy x-ray absorptiometry (DEXA). The results indicate that the proposed technique is capable of detecting differences in bone quality. The ability to measure site-specific properties without exposure to radiation has the potential to be further developed for clinical applications.
Journal of Biomechanical Engineering 10/2012; 134(10):101001. · 1.90 Impact Factor
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ABSTRACT: We present a mesoscopic approach to granular crystal dynamics, which comprises a three-dimensional finite-element model and a one-dimensional regularized contact model. The approach investigates the role of vibrational-energy trapping effects in the dynamic behavior of one-dimensional chains of particles in contact (i.e., granular crystals), under small to moderate impact velocities. The only inputs of the models are the geometry and the elastic material properties of the individual particles that form the system. We present detailed verification results and validate the model comparing its predictions with experimental data. This approach provides a physically sound, first-principles description of dissipative losses in granular systems.
Physical Review E 01/2012; 85(1 Pt 2):016604. · 2.26 Impact Factor
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ABSTRACT: The importance and benefits of nanotechnology in biology and medicine are now well-recognized by scientists, technologists,
as well as various governmental and private research funding agencies. The basis that enables the application of nanotechnology
is the availability of nanostructured materials. Therefore, it is essential to provide an insight on the state-of-the-art
methods to manufacture various nanostructures.
12/2011: pages 27-44;
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ABSTRACT: We propose a new biomedical sensing technique based on highly nonlinear solitary waves to assess orthopaedic implant stability in a nondestructive and efficient manner. We assemble a granular crystal actuator consisting of a one-dimensional tightly packed array of spherical particles, to generate acoustic solitary waves. Via direct contact with the specimen, we inject acoustic solitary waves into a biomedical prosthesis, and we nondestructively evaluate the mechanical integrity of the bone–prosthesis interface, studying the properties of the waves reflected from the contact zone between the granular crystal and the implant. The granular crystal contains a piezoelectric sensor to measure the travelling solitary waves, which allows it to function also as a sensor. We perform a feasibility study using total hip arthroplasty (THA) samples made of metallic stems implanted in artificial composite femurs using polymethylmethacrylate for fixation. We first evaluate the sensitivity of the proposed granular crystal sensor to various levels of prosthesis insertion into the composite femur. Then, we impose a sequence of harsh mechanical loading on the THA samples to degrade the mechanical integrity at the stem–cement interfaces, using a femoral load simulator that simulates aggressive, accelerated physiological loading. We investigate the implant stability via the granular crystal sensor–actuator during testing. Preliminary results suggest that the reflected waves respond sensitively to the degree of implant fixation. In particular, the granular crystal sensor–actuator successfully detects implant loosening at the stem–cement interface following violent cyclic loading. This study suggests that the granular crystal sensor and actuator has the potential to detect metal–cement defects in a nondestructive manner for orthopaedic applications.
Smart Materials and Structures 12/2011; 21(1):012002. · 2.09 Impact Factor
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ABSTRACT: We develop lightweight, multilayer materials composed of alternating layers of poly dimethyl siloxane (PDMS) polymer and vertically aligned carbon nanotube (CNT) arrays, and characterize their mechanical response in compression. The CNT arrays used in the assembly are synthesized with graded mechanical properties along their thickness, and their use enables the creation of multilayer structures with low density (0.12-0.28 g/cm(3)). We test the mechanical response of structures composed of different numbers of CNT layers partially embedded in PDMS polymer, under quasi-static and dynamic loading. The resulting materials exhibit a hierarchical, fibrous structure with unique mechanical properties: They can sustain large compressive deformations (up to ∼0.8 strain) with a nearly complete recovery and present strain localization in selected sections of the materials. Energy absorption, as determined by the hysteresis observed in stress-strain curves, is found to be at least 3 orders of magnitude larger than that of natural and synthetic cellular materials of comparable density. Conductive bucky paper is included within the polymer interlayers. This allows the measurement of resistance variation as a function of applied stress, showing strong correlation with the observed strain localization in compression.
ACS Nano 09/2011; 5(10):7713-21. · 10.77 Impact Factor
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ABSTRACT: We study the dynamic response of a one-dimensional chain of ellipsoidal particles excited by a single compressive impulse. We detail the Hertzian contact theory describing the interaction between two ellipsoidal particles under compression, and use it to model the dynamic response of the system. We observe the formation of highly nonlinear solitary waves in the chain, and we also study their propagation properties. We measure experimentally the traveling pulse amplitude (force), the solitary wave speed, and the solitary wave width. We compare these results with theoretical predictions in the long wavelength approximation, and with numerical results obtained with a discrete particle model and with finite element simulations. We also study the propagation of highly nonlinear solitary waves in the chain with particles arranged in different configurations to show the effects of the particle's geometry on the wave propagation characteristics and dissipation. We find very good agreement between experiment, theory, and simulations for all the ranges of impact velocity and particle arrangements investigated.
Physical Review E 08/2011; 84(2 Pt 2):026610. · 2.26 Impact Factor
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ABSTRACT: Highly nonlinear solitary waves (HNSWs) are stress waves that can form and travel in highly nonlinear systems. They are characterized by a constant spatial wavelength and by a tunable propagation speed, dependent on the wave amplitude. Conventionally, HNSW's are generated in one-dimensional chains of spherical particles by means of a mechanical impact. In this paper, we demonstrate that short-duration laser pulses can be used to generate HNSW's, and we characterize their propagating properties in terms of shape, speed, and duration. We compare the waves' characteristics with theoretical predictions, finding excellent agreement. In addition a simplified formulation is given to estimate the dynamic contact force generated by laser pulses onto the chain.
Physical Review E 08/2011; 84(2 Pt 2):026601. · 2.26 Impact Factor
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ABSTRACT: We study the interaction of highly nonlinear solitary waves propagating in granular crystals with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary and secondary reflected waves. Experimental tests are performed to correlate the linear medium geometry, materials, and mass with the formation and propagation of reflected waves. We compare the experimental results with theoretical analysis based on the long-wavelength approximation and with numerical predictions obtained from discrete particle models. Experimental results are found to be in agreement with theoretical analysis and numerical simulations. This preliminary study establishes the foundation for utilizing reflected solitary waves as novel information carriers in nondestructive evaluation of elastic material systems.
Physical Review E 04/2011; 83(4 Pt 2):046606. · 2.26 Impact Factor
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ABSTRACT: We design and test nonlinear acoustic materials for amplitude dependent filtering of audible signals. We study the dynamic response of one-dimensional arrays of elastic particles in contact with each other, supported by deformable elastic rods, using experiments and numerical simulations. We study the effects of different curvatures of the support rods on the transmission of impacts and structural vibrations. We find that the combination of a nonlinear granular medium with linear support rods allows obtaining tunable filtering of the incoming signal, and selecting desired ranges of the transmitted frequency and amplitude. We conclude our study building a 3D prototype of the new filtering material using a 3D printer.
03/2011;
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ABSTRACT: In this paper we present the design of two actuators for the generation of highly nonlinear solitary waves (HNSWs), which are mechanical waves that can form and travel in highly nonlinear systems. These waves are characterized by a constant spatial wavelength and by a tunable propagation speed, dependent on the wave amplitude. To date, the simplest and widely adopted method to generate HNSWs is by impacting a striker onto a chain of beads of equal size and mass. This operation is conducted manually and it might be impracticable if repetition rates higher than 0.1 Hz are necessary. It is known that the HNSWs' properties, such as amplitude, duration, and speed can be modified by changing the size or the material of the particles, the velocity of the striker, and/or the precompression on the chain. To address the limitations associated with the manual generation of HNSWs we designed, built, and tested two actuators. The first actuator consists of a chain of particles wrapped by an electromagnet that induces static precompression on the chain. This design allows for the generation of solitary waves with controlled properties. The second actuator consists of a chain surmounted by an electromagnet that lifts and releases a striker. This actuator permits the remote and noncontact generation of solitary waves. The performance of both actuators is evaluated by comparing the experimental HNSWs to theoretical predictions, based on the long wavelength approximation.
The Review of scientific instruments 03/2011; 82(3):034902. · 1.52 Impact Factor
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ABSTRACT: Osteoporosis is a well recognized problem affecting millions of individuals
worldwide. Consequently, the need to effectively, efficiently, and affordably
diagnose and identify those at risk is essential; moreover, site-specific
assessment of bone quality is necessary, not only in the process of risk
assessment, but may also be desirable for other applications. The present study
evaluated a new one-dimensional granular crystal sensor, composed of a tightly
packed chain of beads under Hertzian contact interaction, representing the most
suitable fundamental component for solitary wave generation and propagation.
First, the sensitivity of the novel sensor was tested using densities of rigid
polyurethane foam, representing clinical bone quality ranging from healthy, to
severely osteoporotic. Once the relationship between the signal response and
known densities was established, the sensor was used to measure several sites
located in the proximal femur of ten human cadaveric specimens. The accuracy of
the model was then further investigated, using measurements of bone quality
from the same cadaveric specimens, independently, using DEXA. The results
indicate not only that the novel technique is capable of detecting differences
in bone quality, but that the ability to measure site-specific properties
without exposure to radiation, has the potential to be further developed for
clinical applications.
12/2010;
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ABSTRACT: We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin," so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: in low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatiotemporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for a transition between the two regimes. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.
Physical Review E 08/2010; 82(2 Pt 1):021301. · 2.26 Impact Factor
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ABSTRACT: Acoustic lenses are employed in a variety of applications, from biomedical imaging and surgery to defense systems and damage detection in materials. Focused acoustic signals, for example, enable ultrasonic transducers to image the interior of the human body. Currently however the performance of acoustic devices is limited by their linear operational envelope, which implies relatively inaccurate focusing and low focal power. Here we show a dramatic focusing effect and the generation of compact acoustic pulses (sound bullets) in solid and fluid media, with energies orders of magnitude greater than previously achievable. This focusing is made possible by a tunable, nonlinear acoustic lens, which consists of ordered arrays of granular chains. The amplitude, size, and location of the sound bullets can be controlled by varying the static precompression of the chains. Theory and numerical simulations demonstrate the focusing effect, and photoelasticity experiments corroborate it. Our nonlinear lens permits a qualitatively new way of generating high-energy acoustic pulses, which may improve imaging capabilities through increased accuracy and signal-to-noise ratios and may lead to more effective nonintrusive scalpels, for example, for cancer treatment.
Proceedings of the National Academy of Sciences 04/2010; 107(16):7230-4. · 9.68 Impact Factor
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ABSTRACT: Wave propagation characteristics of nonlinear one-dimensional periodic structures are investigated analytically, numerically
and experimentally. A novel perturbation analysis is first applied to predict the band gap location and extent in terms of
linear and nonlinear system parameters. Approximate closed-form expressions capture the effect of nonlinearities on dispersion
and depict amplitude dependent cut-off frequencies. The predictions from the perturbation analysis are verified through numerical
simulations of harmonic wave motion. Results indicate the possibility of input amplitude as a tuning parameter through which
cut-off frequencies can be adjusted to achieve filtering properties over selected frequency ranges. A periodic diatomic chain
of stainless steel spheres alternating with aluminium spheres is experimentally investigated. The dynamic behavior of the
chain is governed by Hertzian interaction of spheres and by a compressive pre-load which can be adjusted to obtain linear,
weakly nonlinear and highly nonlinear behavior. For a weakly nonlinear case, preliminary results in experiments show the tendency
for a shift in the band gap edges by varying input amplitude. The paper is a work in progress, for which the experimental
results for a weakly nonlinear system are interpreted by the perturbation analysis developed for a specific case of linear
and nonlinear power law interaction of exponent 3/2
12/2009: pages 209-219;
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ABSTRACT: We study localized modes in uniform one-dimensional chains of tightly packed and uniaxially compressed elastic beads in the presence of one or two light-mass impurities. For chains composed of beads of the same type, the intrinsic nonlinearity, which is caused by the Hertzian interaction of the beads, appears not to support localized, breathing modes. Consequently, the inclusion of light-mass impurities is crucial for their appearance. By analyzing the problem's linear limit, we identify the system's eigenfrequencies and the linear defect modes. Using continuation techniques, we find the solutions that bifurcate from their linear counterparts and study their linear stability in detail. We observe that the nonlinearity leads to a frequency dependence in the amplitude of the oscillations, a static mutual displacement of the parts of the chain separated by a defect, and for chains with two defects that are not in contact, it induces symmetry-breaking bifurcations.
Physical Review E 12/2009; 80(6 Pt 2):066601. · 2.26 Impact Factor
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ABSTRACT: We investigate for the first time hydrophobic carbon nanotube-based electrochemical cells as an alternative solution to hydrogen sorting. We show that the electrically conducting surface of the nanotube arrays can be used as a cathode for hydrogen generation and absorption by electrolyzing water. We support our findings with Raman and gas chromatography measurements. These results suggest that carbon nanotube forests, presenting a unique combination of hydrophobicity and conductivity, are suitable for application in fuel cells and microelectromechanical devices.
ACS Nano 11/2009; 3(12):3903-8. · 10.77 Impact Factor
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ABSTRACT: We study the existence of stationary shock waves in uniform and periodic heterogeneous highly nonlinear granular chains governed by a power-law contact interaction, comparing discrete and continuum approaches, as well as experiments. We report the presence of quasisteady shock fronts without the need for dissipative effects. When viscous effects are neglected, the structure of the leading front appears to be solely the result of dispersive effects related to the lattice wave dispersion and, for heterogeneous bead chains, to the impedance mismatch between material domains. We report analytically and numerically the shock-width scaling with the variation in the particles periodicity (cell size) and compare the obtained results with experiments. We check the state (-) behind the shock front via quasistatic compression analysis and report a very good agreement between theory and numerical data.
Physical Review E 11/2009; 80(5 Pt 2):056602. · 2.26 Impact Factor
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ABSTRACT: Acoustic lenses are employed in a variety of applications, from biomedical imaging and surgery, to defense systems, but their performance is limited by their linear operational envelope and complexity. Here we show a dramatic focusing effect and the generation of large amplitude, compact acoustic pulses (sound bullets) in solid and fluid media, enabled by a tunable, highly nonlinear acoustic lens. The lens consists of ordered arrays of granular chains. The amplitude, size and location of the sound bullets can be controlled by varying static pre-compression on the chains. We support our findings with theory, numerical simulations, and corroborate the results experimentally with photoelasticity measurements. Our nonlinear lens makes possible a qualitatively new way of generating high-energy acoustic pulses, enabling, for example, surgical control of acoustic energy. Comment: 19 pages, 7 figures, includes supplementary information
08/2009;
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ABSTRACT: We investigate nonlinear localized modes at light-mass impurities in a
one-dimensional, strongly-compressed chain of beads under Hertzian contacts.
Focusing on the case of one or two such "defects", we analyze the problem's
linear limit to identify the system eigenfrequencies and the linear defect
modes. We then examine the bifurcation of nonlinear defect modes from their
linear counterparts and study their linear stability in detail. We identify
intriguing differences between the case of impurities in contact and ones that
are not in contact. We find that the former bears similarities to the single
defect case, whereas the latter features symmetry-breaking bifurcations with
interesting static and dynamic implications.
06/2009;
