arXiv subjects

Mahmoud I. Hussein

Publications and source records attributed to Mahmoud I. Hussein.

31 records · Page 2Linked to original sources

arXiv2019

Nonlinear dispersion relation predicts harmonic generation in wave motion

In recent work, we have proposed a theory for the derivation of an exact nonlinear dispersion relation for elastic wave propagation which here we consider for a thin rod (linearly nondispersive) and a thick rod (linearly dispersive). The derived relation has been validated by direct time-domain simulations examining instantaneous dispersion. In this Letter, we present a major extension of the theory revealing that our derived nonlinear dispersion relation provides direct and exact prediction of harmonic generation, thus merging two key tenets of wave propagation. This fundamental unification of nonlinear dispersion and harmonic generation is applicable to any arbitrary wave profile characterized initially by an amplitude and a wavenumber, irrespective of the type and strength of the nonlinearity, and regardless of whether the medium is dispersive or nondispersive in the linear limit. Another direct outcome of the theory is an analytical condition for soliton synthesis based on balance between hardening and softening dispersion.

nlin.PS↗

arXiv2018

Dissipation engineering in metamaterials by localized structural dynamics

In civil, mechanical, and aerospace engineering, structural dynamics is commonly understood to be a discipline concerned with the analysis and characterization of the vibratory response of structures. Key elements of the response are the amplitude, phase, and damping ratio, which are quantities that vary with the excitation frequency. In this paper, we extend the discipline of structural dynamics to the realm of materials engineering by intrinsically building localized substructures within, or attached to, the material domain itself$-$which is viewed as an extended medium without defined external boundaries. Our system is essentially a locally resonant elastic metamaterial, except here it is viewed from the perspective of unique dissipation characteristics rather than subwavelength effective properties or band gaps, as widely done in the literature. We provide a theory, validated by experiments, for substructurally synthesizing the dissipation under the conditions of free-wave motion, i.e., waves not constrained to a prescribed driving frequency. We use an extended elastic beam with attached pillars as an example of a metamaterial. When compared to an identical infinite beam with no attached substructures, we show that within certain frequency ranges the metamaterial exhibits either enhanced or reduced dissipation$-$which we refer to as positive and negative metadamping, respectively. These regimes are rigorously identified and characterized using the metamaterial's band structure and wavenumber-dependent dissipation diagram. This theory impacts applications that require a combination of high stiffness and high damping or, conversely, applications that benefit from a reduction in loss without the need to change the backbone constituent material.

physics.app-ph↗

arXiv2016

Two orders of magnitude reduction in silicon membrane thermal conductivity by resonance hybridizations

The thermal conductivity of a freestanding single-crystal silicon membrane may be reduced significantly by attaching nanoscale pillars on one or both surfaces. Atomic resonances of the nanopillars locally and intrinsically couple with the base membrane phonon modes causing these modes to hybridize and flatten at each coupling location in the phonon band structure. The ensuing group velocity reductions, which in principle may be tuned to take place across silicon's full spectrum, lead to a lowering of the in-plane thermal conductivity in the base membrane. Using equilibrium molecular dynamics simulations, we report a staggering two orders of magnitude reduction in the thermal conductivity at room temperature by this mechanism.

cond-mat.mes-hall↗

arXiv2016

Thermal transport size effects in silicon membranes featuring nanopillars as local resonators

Silicon membranes patterned by nanometer-scale pillars standing on the surface provide a practical platform for thermal conductivity reduction by resonance hybridization. Using molecular simulations, we investigate the effect of nanopillar size, unit-cell size, and finite-structure size on the net capacity of the local resonators in reducing the thermal conductivity of the base membrane. The results indicate that the thermal conductivity reduction increases as the ratio of the volumetric size of a unit nanopillar to that of the base membrane is increased, and the intensity of this reduction varies with unit-cell size at a rate dependent on the volumetric ratio. Considering sample size, the resonance-induced thermal conductivity drop is shown to increase slightly with the number of unit cells until it would eventually level off.

cond-mat.mes-hall↗

arXiv2016

Generalized Bloch's theorem for viscous metamaterials: Dispersion and effective properties based on frequencies and wavenumbers that are simultaneously complex

It is common for dispersion curves of damped periodic materials to be based on real frequencies versus complex wavenumbers or, conversely, real wavenumbers versus complex frequencies. The former condition corresponds to harmonic wave motion where a driving frequency is prescribed and where attenuation due to dissipation takes place only in space alongside spatial attenuation due to Bragg scattering. The latter condition, on the other hand, relates to free wave motion admitting attenuation due to energy loss only in time while spatial attenuation due to Bragg scattering also takes place. Here, we develop an algorithm for 1D systems that provides dispersion curves for damped free wave motion based on frequencies and wavenumbers that are permitted to be simultaneously complex. This represents a generalized application of Bloch's theorem and produces a dispersion band structure that fully describes all attenuation mechanisms, in space and in time. The algorithm is applied to a viscously damped mass-in-mass metamaterial exhibiting local resonance. A frequency-dependent effective mass for this damped infinite chain is also obtained.

cond-mat.mtrl-sci↗

arXiv2015

Inertial amplification of continuous structures: Large band gaps from small masses

Wave motion in a continuous elastic rod with a periodically attached inertial-amplification mechanism is investigated. The mechanism has properties similar to an "inerter" typically used in vehicle suspensions, however here it is constructed and utilized in a manner that alters the intrinsic properties of a continuous structure. The elastodynamic band structure of the hybrid rod-mechanism structure yields band gaps that are exceedingly wide and deep when compared to what can be obtained using standard local resonators, while still being low in frequency. With this concept, a large band gap may be realized with as much as twenty times less added mass compared to what is needed in a standard local resonator configuration. The emerging inertially enhanced continuous structure also exhibits unique qualitative features in its dispersion curves. These include the existence of a characteristic double-peak in the attenuation constant profile within gaps and the possibility of coalescence of two neighbouring gaps creating a large contiguous gap.

cond-mat.other↗

arXiv2015

Spectral energy analysis of locally resonant nanophononic metamaterials by molecular simulations

A nanophononic metamaterial is a new type of nanostructured material that features an array, or a forest, of intrinsically distributed resonating substructures. Each substructure exhibits numerous local resonances, each of which may hybridize with the phonon dispersion of the underlying host material causing significant reductions in the group velocities and consequently a reduction in the lattice thermal conductivity. In this paper, molecular dynamics simulations are utilized to investigate both the dynamics and the thermal transport properties of a nanophononic metamaterial configuration consisting of a freely suspended silicon membrane with an array of silicon nanopillars standing on the surface. The simulations yield results consistent with earlier lattice-dynamics based predictions which showed a reduction in the thermal conductivity due to the presence of the local resonators. Using a spectral energy density approach, in which only simulation data is utilized and no a priori information on the nanostructure resonant phonon modes is provided, we show direct evidence of the existence of resonance hybridizations as an inherent mechanism contributing to the slowing down of thermal transport in this system.

cond-mat.mes-hall↗

arXiv2013

Nanophononic metamaterial: Thermal conductivity reduction by local resonance

We present the concept of a locally resonant nanophononic metamaterial for thermoelectric energy conversion. Our configuration, which is based on a silicon thin-film with a periodic array of pillars erected on one or two of the free surfaces, qualitatively alters the base thin-film phonon spectrum due to a hybridization mechanism between the pillar local resonances and the underlying atomic lattice dispersion. Using an experimentally-fitted lattice-dynamics-based model, we conservatively predict a drop in the metamaterial thermal conductivity to as low as 50% of the corresponding uniform thin-film value despite the fact that the pillars add more phonon modes to the spectrum.

cond-mat.mtrl-sci↗

arXiv2013

Trampoline metamaterial: Local resonance enhancement by springboards

We investigate the dispersion characteristics of locally resonant elastic metamaterials formed by the erection of pillars on the solid regions in a plate patterned by a periodic array of holes. We show that these solid regions effectively act as springboards leading to an enhanced resonance behavior by the pillars when compared to the nominal case of pillars with no holes. This local resonance amplification phenomenon, which we define as the "trampoline effect", is shown to cause subwavelength band gaps to increase in size by up to a factor of 4. This outcome facilitates the utilization of subwavelength metamaterial properties over exceedingly broad frequency ranges.

cond-mat.mtrl-sci↗

arXiv2012

Wave dispersion under finite deformation

We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the Euler-Bernoulli kinematic hypothesis and consider both a conventional transverse motion model and an inextensional planar motion model. The underlying formulation uses the Cauchy stress and the Green-Lagrange strain. For all models, we consider linear constitutive relations in order to isolate the effect of finite motion. The proposed methodology, however, is applicable to problems that also exhibit material nonlinearity. For the rod model, we obtain the exact analytical explicit solution of the derived finite-deformation dispersion relation, and compare it with data obtained via numerical simulation of nonlinear wave motion in a finite rod. For the beam model, we obtain a solution by numerical root finding. The results allow us to quantify the deviation in the dispersion curves when exact large deformation is considered compared to following the assumption of infinitesimal deformation. We show that incorporation of finite deformation following the chosen definitions of stress and strain raises the frequency branches for both axial and flexural waves above the nominal values associated with linear motion. For the beam problem, only the inextensional planar motion model provides an accurate description of the finite-deformation response for both static deflection and wave dispersion. Our findings, which represent the first derivation of finite-strain, amplitude-dependent dispersion relations for any type of elastic media, draw attention to 1) the tangible effect of finite deformation on wave dispersion and consequently on the speed of sound in an elastic medium and 2) the importance of incorporating longitudinal-transverse motion coupling in nonlinear analysis of thin structures.

math-ph↗

arXiv2012

Metadamping: An emergent phenomenon in dissipative metamaterials

We theoretically demonstrate the concept of metadamping in dissipative metamaterials. We consider an infinite mass-spring chain with repeated local resonators and a statically equivalent periodic chain whose wave propagation characteristics are based on Bragg scattering. For each system we introduce identical viscous damping (dashpot) elements and compare the damping ratio associated with all Bloch modes. We find that the locally resonant metamaterial exhibits higher dissipation overall which indicates a damping emergence phenomena due to the presence of local resonance. We conclude our investigation by quantifying the degree of emergent damping as a function of the long-wave speed of sound in the medium or the static stiffness.

cond-mat.mtrl-sci↗

arXiv2011

Ultrawide phononic band gap for combined in-plane and out-of-plane waves

We consider two-dimensional phononic crystals formed from silicon and voids, and present optimized unit cell designs for (1) out-of-plane, (2) in-plane and (3) combined out-of-plane and in-plane elastic wave propagation. To feasibly search through an excessively large design space (10e40 possible realizations) we develop a specialized genetic algorithm and utilize it in conjunction with the reduced Bloch mode expansion method for fast band structure calculations. Focusing on high symmetry plain-strain square lattices, we report unit cell designs exhibiting record values of normalized band-gap size for all three categories. For the combined polarizations case, we reveal a design with a normalized band-gap size exceeding 60%.

physics.comp-ph↗

arXiv2008

Reduced Bloch mode expansion for periodic media band structure calculations

Reduced Bloch mode expansion is presented for fast periodic media band structure calculations. The expansion employs a natural basis composed of a selected reduced set of Bloch eigenfunctions. The reduced basis is selected within the irreducible Brillouin zone at high symmetry points determined by the medium's crystal structure and group theory (and possibly at additional related points). At each of the reciprocal lattice selection points, a number of Bloch eigenfunctions are selected up to the frequency range of interest for the band structure calculations. Since it is common to initially discretize the periodic unit cell and solution field using some choice of basis, reduced Bloch mode expansion is practically a secondary expansion that uses a selected set of Bloch eigenvectors. Such expansion therefore keeps, and builds on, any favorable attributes a primary expansion approach might exhibit. Being in line with the well known concept of modal analysis, the proposed approach maintains accuracy while reducing the computation time by up to two orders of magnitudes or more depending on the size and extent of the calculations. Results are presented for phononic, photonic and electronic band structures.

physics.comp-ph↗