Dispersion Of Elastic Waves Research Articles

Low-frequency propagating and evanescent waves in strongly inhomogeneous sandwich plates

The paper aims at studying dispersion of elastic waves in a sandwich plate with the parameters, characteristic of aerogel core and hard skin layers, typical for aerospace applications including optimal design of fuselage structural components. The proposed approach relies on multiparametric analysis, taking into account the effect of strong transverse inhomogeneity. It is demonstrated that both an additional low-frequency propagating wave and a slowly decaying evanescent one appear due to a high contrast in geometric and mechanical parameters of the layers. The key findings include the derivation of two-mode asymptotic expansions of the full dispersion relation at the low-frequency limit, as well as elucidation of the non-trivial link between long-wave evanescent and propagating modes. A sophisticated composite nature of the obtained expansions involving various shortened forms is investigated. The range of validity for each of these forms over frequency and wave-number domains is evaluated. Comparison of asymptotic results with the numerical solution of the full dispersion relation is presented.

The acoustic Galton board

Phononic crystals are a class of materials with periodic structures that influence the propagation characteristics of acoustic waves through periodically arranged structural units. Here, we have developed the acoustic Galton board (AGB), a groundbreaking apparatus that serves as a cost-effective and user-friendly tool for demonstrating phononic crystal properties such as band gaps, Bragg scattering, and local resonance. The device comprises an elastic wave signal generator, an enhanced Galton board featuring a sophisticated pillar-nail array, and a signal receiver. The experimental results we have obtained demonstrate the significant impact of the AGB on elastic wave dispersion, effectively creating bandgaps that impede wave transmission within specific frequency ranges while allowing unhindered propagation in others. Furthermore, the AGB can simulate phononic crystals using both the Bragg scattering mechanism, achieved through the design of periodic rigid pillar-nail arrays, and the locally resonant mechanism, facilitated by the design of pillar-nail arrays with composite material structures. Additionally, the AGB can extend its applications to serve as a simulation tool for elastic metamaterials.

Modeling the Dispersion of Waves in a Multilayered Inhomogeneous Membrane with Fractional-Order Infusion

The dispersion of elastic shear waves in multilayered bodies is a topic of extensive research due to its significance in contemporary science and engineering. Anti-plane shear motion, a two-dimensional mathematical model in solid mechanics, effectively captures shear wave propagation in elastic bodies with relative mathematical simplicity. This study models the vibration of elastic waves in a multilayered inhomogeneous circular membrane using the Helmholtz equation with fractional-order infusion, effectively leveraging the anti-plane shear motion equation to avoid the computational complexity of universal plane motion equations. The method of the separation of variables and the conformable Bessel equation are utilized for the analytical examination of the model’s resulting vibrational displacements, as well as the dispersion relation. Additionally, the influence of various wave phenomena, including the dependencies of the wavenumber on the frequency and the phase speed on the wavenumber, respectively, with the variational effect of the fractional order on wave dispersion is considered. Numerical simulations of prototypical cases validate the formulated model, illustrating its applicability and effectiveness. The study reveals that fractional-order infusion significantly impacts the dispersion of elastic waves in both single- and multilayer membranes. The effects vary depending on the membrane’s structure and the wave propagation regime (long-wave vs. short-wave). These findings underscore the potential of fractional-order parameters in tailoring wave behavior for diverse scientific and engineering applications.

Rainbow trapping of out-of-plane mechanical waves in spatially variant beam lattices

We numerically and experimentally investigate the propagation of mechanical waves in two-dimensional periodic and spatially graded elastic beam lattices. Experiments on metallic lattices admit the characterization of the linear elastic wave dispersion over a wide range of frequencies, resulting in complete, experimentally-constructed dispersion surfaces in excellent agreement with predictions obtained from finite element-based Bloch wave analysis. While Timoshenko beam theory is shown to be sufficiently accurate for predicting the lowest modes, experiments prove that solid finite elements are required to capture the dispersion relations at higher frequencies as well as when mode coupling occurs. Based on an improved numerical procedure, group velocity maps further highlight the directionality of wave dispersion and allow for the simple identification of bandgaps. In addition to classically studied periodic trusses, we extend the framework to spatially graded structures and demonstrate acoustic rainbow trapping in beam lattices undergoing out-of-plane vibrations. Our experiments confirm broadband vibration attenuation of the typical meta-wedge type previously observed only in optics and few mechanical studies. Results further show convincing agreement between Bloch theory-based predictions, finite element simulations, and experimental measurements. Such spatially-variant architected lattices show great promise for steering the motion of elastic waves in applications from wave guiding and wave shielding to energy harvesting.

Twist-Induced Hyperbolic Shear Metasurfaces

Following the discovery of moiré-driven superconductivity and density waves in twisted-graphene multilayers, twistronics has spurred a surge of interest in tailored broken symmetries through angular rotations enabling new properties, from electronics to photonics and phononics. Analogously, in monoclinic polar crystals a nontrivial angle between nondegenerate dipolar phonon resonances can naturally emerge due to asymmetries in their crystal lattice, and its variations are associated with intriguing polaritonic phenomena, including axial dispersion, i.e., the rotation of the optical axis with frequency, and microscopic shear effects that result in an asymmetric distribution of material loss. So far, these phenomena have been restricted to specific midinfrared frequencies difficult to access with conventional laser sources and fundamentally limited by the degree of asymmetry and by the strength of light-matter interactions available in natural crystals. Here, we leverage the twistronics concept to demonstrate maximal axial dispersion and loss redistribution of hyperbolic waves in elastic metasurfaces, achieved by tailoring the angle between coupled metasurface pairs featuring tailored anisotropy. We show extreme control over elastic wave dispersion and absorption via the twist angle and leverage the resulting phenomena to demonstrate enhanced propagation distance, in-plane reflection-free negative refraction and diffraction-free defect detection. Our work welds the concepts of twistronics, non-Hermiticity, and extreme anisotropy, demonstrating the powerful opportunities enabled by metasurfaces for tunable, highly directional surface-acoustic-wave propagation of great interest for a wide range of applications spanning from seismic mitigation to on-chip phononics and wireless communication systems, hence paving the way toward their translation into emerging photonic and polaritonic metasurface technologies. Published by the American Physical Society 2024

An inerter-based concept of locally resonant fluid-conveying pipe

Preventing damage or failure caused by vibrations in periodic fluid-conveying pipes needs appropriate mitigation strategies. This paper proposes a novel concept of locally resonant fluid-conveying pipe resting on periodically spaced inerter-based resonant supports, each including an inerter and linear springs. On adopting a Timoshenko beam model for the pipe, two types of inerter-based resonant supports are investigated, differing by the arrangement of the internal components, i.e., inerter and springs. For both types, elastic wave dispersion analyses of the infinite pipe demonstrate the existence of two low-frequency band gaps in the frequency response. The second band gap, caused by local resonance, exhibits better attenuation over a relevant part of its frequency range; its lower/upper edge frequencies and amplitude may be suitably changed depending on the parameters of the inerter-based resonant supports, and very considerable amplitudes can be obtained thanks to the large inertia effects warranted by the grounded inerter. The influence on the band gaps of key parameters such as fluid velocity and ratio of fluid mass to total pipe mass is assessed. Moreover, the effect of damping is considered, assuming a Kelvin–Voigt viscoelastic behavior for the pipe material and including viscous dashpots in parallel with the springs within the inerter-based resonant supports. An original exact dynamic-stiffness method is formulated for computational purposes, targeting wave dispersion analysis of the infinite pipe as well as frequency-domain analysis of the finite pipe. In particular, the main novelty is the derivation of the exact dynamic-stiffness matrix and exact load vector of the unit cell of the Timoshenko pipe with Kelvin–Voigt viscoelastic behavior. Remarkably, the transmittance of the finite pipe confirms the predictions from wave dispersion analysis of the infinite pipe and substantiates the effectiveness of the proposed concept of locally resonant fluid-conveying pipe.

Elastic wave dispersion and polarization in a chiral elastic metamaterial

Elastic wave dispersion and polarization in a chiral elastic metamaterial

Simulation and analysis of elastic waves in partially saturated double-porosity media based on finite difference method

Double-porosity poroelastic model takes into account the effect of mesoscopic flow induced by rock heterogeneity on dispersion and attenuation of elastic waves, and has obtained good application results in the quantitative explanation of seismic data in heterogeneous reservoirs. Wavefield simulation based on double-porosity model not only helps visualize the propagation characteristics of the elastic waves but also lays the foundation for seismic imaging. In this work, we perform wavefield simulation and analysis based on the Santos-Rayleigh model which incorporates mesoscopic and global flow in a partially-saturated double-porosity medium. Specifically, the mesoscopic flow mechanism is represented with a Zener viscoelastic model. The comparison shows that the Zener model can accurately capture the propagation characteristics of fast P-wave, but fails to describe the attenuation characteristics of slow P3 wave in the low-frequency band. It implies that Zener viscoelastic model and slow wave modes follow different mechanisms. Then the staggered grid finite-difference method is used to simulate wave propagation in a double-porosity medium, and the stiff problem is solved with a time-splitting algorithm, which can significantly improve computational efficiency. Based on the above methods, the correctness of our algorithm is verified with derived analytical solution for a P-wave source in a uniform partially saturated poroelastic medium. Analytical and numerical solutions are in good agreement and mean error is 0.33%. We provide some examples of wavefield snapshots and seismograms in homogeneous and layered heterogeneous media at seismic and ultrasonic frequencies. The simulation results demonstrate the strong attenuation of fast P-wave and no change of S-wave in the seismic band due to mesoscopic flow mechanism, which is consistent with the theoretical prediction of double-porosity model. Moreover, the energy of fast P-wave is concentrated in solid phase while slow waves are stronger in fluid phase. This work contributes to the understanding of broadband elastic wave propagation in a heterogeneous partially saturated porous medium and can be applied to the reservoir imaging with broadband geophysical data.

Mechanical vibration absorber for flexural wave attenuation in multi-materials metastructure

Vibration isolation is a promise to suppress mechanical vibration from a host structure, similarly, a mechanical vibration absorber, a simple but effective device to attenuate flexural wave propagation, which has been implemented in civil and mechanical engineering. This paper presents a type of composite sandwich phononic crystal to attenuate the flexural wave propagation in a beam structure, which can effectively suppress mechanical vibration in a broad band gap by repetitively arranging phononic crystal. First, the elastic wave dispersion characteristic in a composite sandwich beam structure is derived, and a triangular shape phononic crystal for flexural wave attenuation by taking advantage of destructive interference is presented. Then two dimensional phononic crystals are designed by assembling four different unit-cells of metabeam. Finally, numerical experiments are conducted to verify the effectiveness of the proposed mechanical metamaterial absorbers to attenuate flexural wave propagation, the numerical results indicate that the proposed metamaterial is of good performance in mechanical vibration suppression, which can effectively mitigate structure vibration in low-frequency domain than the structure without phononic crystal and single layer metamaterial beam structure. It is the first attempt to design a mechanical metamaterial absorber with the mechanism of destructive interference with composite sandwich phononic crystal.

Impedance characterization of substrate leakage in wafer bonded CMUTs

This work investigates substrate leakage in Capacitive Micromachined Ultrasonic Transducers, (CMUTs) having thin backings. CMUTs produced with solid or rigid substrates have a high Q resonance with flat baseline. However, if the operating wavelength of CMUT becomes larger than the thickness of substrate the real part of cell impedance shows elevated baselines with more leakage at DC than at higher frequencies. When a clamped CMUT membrane is excited harmonically the vibrations produced are counterbalanced by the backing medium. Hence some of the energy is coupled to substrate as loss resulting in a lower mechanical Q of resonance. We first derive this energy coupled to the backing medium using FEA analysis considering the velocity field and associated tensile stresses in a thin backing. Substrate impedance is found numerically from isotropic damping of dispersive elastic waves in the backing. This backing impedance is introduced as a shunt mechanical loss across the transduction force in equivalent circuit model. We characterize the measured impedance of CMUT cells with both FEMs and linear circuit models. Simulations results closely agree with the measured impedance levels, frequency and bandwidth of resonance.

Prediction of frequency band gaps in one-dimensional endohedral fullerene and carbon nano-onion chains.

Acoustics have always played a central role in contemporary engineering, especially in the fields of communication, sensing, and even in more extraordinary applications such as non-invasive high-intensity focused ultrasound surgery. The rapid development of nano-scale-based technologies makes imperative the need for novel acoustic devices that take advantage of nanomaterials as well as their extraordinary physical properties. The successful design of such acoustic components requires the implementation of efficient nanostructures accompanied by fast and accurate modeling. Here, endohedral fullerene and carbon nano-onion one-dimensional nano-chains are explored as possible candidate nanodevices that generate unique frequency band gaps. The wave propagation in chains of fullerene-based molecules is predicted by representing them as infinite one-dimensional mass-in-mass chains properly assembled by the use of springs whose coefficients are expressed according to the van der Walls (vdW) atomistic interactions. Based on Bloch's theorem, interesting elastic wave dispersion curves are obtained and illustrated, characterized by distinctive frequency ranges that waves cannot propagate, revealing the unique vibroacoustic behavior of the proposed nano-systems.

Stress dependence of elastic wave dispersion and attenuation in fluid-saturated porous layered media

Stress dependence of elastic wave dispersion and attenuation in fluid-saturated porous layered media

Beyond-nearest-neighbour metamaterials

Engineering the dispersion of acoustic or elastic waves using coupling terms that spatially reach beyond the immediate local environment, or unit cell, is an “emerging topic” in Metamaterial design. In this talk, we present experimental studies in acoustic and elastic systems that realize beyond-nearest-neighbour coupling to introduce dispersion relations with extrema within the first Brilloun Zone. In acoustics, we use mixed waveguide-surfacewave coupling, while in elasticity we develop an elastic scaffold (made from meccano) with reconfigurable coupling elements and demonstrate the effects of structural symmetries on these exotic dispersion relations. Applications to enhanced energy harvesting structures are presented by leveraging zero-group-velocity modes.

Anisotropy and dispersion of elastic waves in periodically multilayered anisotropic media

The propagation characteristics of elastic waves in general periodically multilayered media formed by alternate arrangement of two or more arbitrarily-anisotropic materials are comprehensively studied. Combining with the state-space formalism for obtaining the wave solutions to the constituent layers, the Floquet-Bloch theorem for providing the periodic relations between neighboring unit cells, the method of reverberation-ray matrix (MRRM) is employed to derive the general dispersion equations of the periodically multilayered anisotropic media. By solving the dispersion equations in cases of all possible sorts of wavenumber components, the complete anisotropic and dispersion characteristics of elastic waves can be provided. By numerical examples, the slowness and the phase velocity curves are provided to summarize the innovative anisotropic characteristics of elastic waves in three coordinate planes. The effects of the anisotropic parameters on the slowness/phase velocity curves have also been discussed. Moreover, all kinds of dispersion curves including the frequency-related and phase velocity-related curves along the directions perpendicular, parallel, and oblique to the layering are provided to reflect the general dispersion characteristics of elastic waves from various viewpoints. It is found that the innovative anisotropy characteristics of elastic waves in the periodically multilayered anisotropic media include that the slowness curves have periodicity in the thickness direction and the least positive period decreases with the increasing of frequency. As the frequency becomes big enough, the slowness/phase velocity curves show interactions between the modes within the overlapping neighboring periods. The common dispersion characteristics of elastic waves along various directions include the symmetry of wavenumber, the asymptotic of the wavelength and the phase velocity curves to the frequency lines corresponding to zero wavenumber, as well as the cutoff property of the phase velocities of the lowest three basis modes. The waves in oblique directions are special in that the mode transition and repulsion due to the zone folding effect of periodicity along thickness as well as the cutoff property of higher-than-third-order overtones along layering are simultaneously in effective.

Local gradient theory of dielectrics incorporating polarization inertia and flexodynamic effect

A higher-grade theory of non-ferromagnetic thermo-elastic dielectrics which incorporates the local mass displacement, the heat flux gradient, polarization inertia, and flexodynamic effects is developed. The process of local mass displacement is associated with changes in material microstructure. Using the fundamental principles of continuum mechanics, electrodynamics, and non-equilibrium thermodynamics, the gradient-type constitutive equations are derived. Due to accounting for the polarization inertia, the rheological constitutive equation for the polarization vector is obtained. In the balance equation of linear momentum, an additional term with the second time derivative of the polarization vector appears in comparison with the classical theory. This term controls the influence of the dynamic flexoelectric effect on the mechanical motion of dielectric solids. The propagation of a plane harmonic wave is analyzed within the context of the developed theory. It is shown that the theory allows for capturing the experimentally observed phenomenon of high-frequency dispersion of a longitudinal elastic wave. The theory may be useful for modeling coupled processes in nanodielectrics and heterogeneous polarized systems.

Elastic wave dispersion in layered media with suture joints: influence of structural hierarchy and viscoelasticity

Suture joints contribute to the exceptional combination of stiffness, strength, toughness and efficient load bearing and transmission of many biological structures like the cranium or ammonite fossil shells. However, their role in the attenuation of vibrations and effect on dynamic loads is less clear. Moreover, the self-similar hierarchical geometry often associated with suture joints renders its treatment with standard numerical approaches computationally prohibitive. To address this problem, this paper investigates the dynamic response of periodic layered media with suture joints using an analytical approach based on material homogenization. A general trapezoidal suture geometry is considered together with the fundamental ingredients of hierarchy and viscoelasticity. The Spectral Element Method and Bloch theorem are used to derive the dispersion relation and band diagram of the system, including propagating and evanescent dispersion modes. A strong influence of the suture morphology and material properties emerges, and the analysis reveals an important advantage of adding hierarchy, i.e. the possibility of simultaneously obtaining wider bandgaps and their shift to higher frequencies. A synergy between hierarchy and structure is also observed, providing superior levels of wave attenuation. These findings suggest a possible design concept for bioinspired devices with efficient and tailorable wave attenuation properties.

Dispersion of surface elastic waves on Z-LiNbO3 films on Z-sapphire

Epitaxial thin films of lithium niobate with a thickness of 160 nm, oriented along the crystallographic c axis, were grown by direct liquid injection chemical vapor deposition on c-sapphire substrates. Different families of very high-frequency surface acoustic waves with general polarization exist in such piezoelectric films on high-velocity substrates. Surface Brillouin light scattering measurements, complemented with fast finite element analysis of wave dispersion, demonstrate Rayleigh, leaky shear, and leaky longitudinal surface waves, excited at frequencies between 10 and 30 GHz. The Brillouin technique reveals dispersion and anisotropy of propagation without the implementation of high-frequency surface acoustic wave transducers.

Dispersion of elastic waves in the three-layered inhomogeneous sandwich plate embedded in the Winkler foundations.

This research article investigates the behavior of elastic waves in an inhomogeneous isotropic three-layered sandwich plate with soft-core and stiff-skin layers embedded in Winkler foundations, using anti-plane shear motion. The study establishes the exact antisymmetric dispersion relation, low-frequency spectrum, and overall cut-off frequency of the wave propagation. A shortened polynomial dispersion relation is developed for the long-wave low-frequency regime by considering the contrasting material setup and compared with the exact dispersion relation. This article also provides exact and asymptotic formulas for stresses and displacements in each layer of the plate, as well as approximate one-dimensional equations of motion. The results suggest that the approximate equations of motion for the three-layered sandwich plate are valid throughout the entire low-frequency range, despite the presence of Winkler foundations on both sides of the plate. This research is significant as it provides insights into the behavior of waves in composite materials and can be used to improve the design of sandwich structures used in various engineering applications. Additionally, the findings that the approximate equations of motion for the three-layered sandwich plate are valid throughout the low-frequency range, despite the presence of Winkler foundations, can help simplify calculations and make the design process more efficient.

Computation of high-frequency magnetoelastic waves in layered materials

The direct calculation of magnetoelastic wave dispersion in layered media is presented using an efficient, accurate computational technique. The governing, coupled equations for elasticity and magnetism, the Navier and Landau-Lifshitz equations, respectively, are linearized to form a quadratic eigenvalue problem that determines a complex web of wavenumber-frequency dispersion branches and their corresponding mode profiles. Numerical discretization of the eigenvalue problem via a spectral collocation method (SCM) is employed to determine the complete dispersion maps for both a single, finite-thickness magnetic layer and a finite magnetic-nonmagnetic double-layer. The SCM, previously used to study elastic waves in non-magnetic media, is fast, accurate, and adaptable to a variety of sample configurations and geometries. Emphasis is placed on the extremely high frequency regimes being accessed in ultrafast magnetism experiments. The dispersion maps and modes provide insight into how energy propagates through the coupled system, including how energy can be transferred between elastic- and magnetic-dominated waves as well as between different layers. The numerical computations for a single layer are further understood by a simplified analytical calculation in the high-frequency, exchange-dominated regime where the resonance condition required for energy exchange (an anticrossing) between quasi-elastic and quasi-magnetic dispersion branches is determined. Nonresonant interactions are shown to be well approximated by the dispersion of uncoupled elastic and magnetic waves. The methods and results provide fundamental theoretical tools to model and understand current and future magnetic devices powering spintronic innovation.

Wave dispersion analysis of natural fiber-strengthened composite beam lying on variable elastic foundation

For the first time, the dispersion of elastic waves in natural fiber-strengthened composite high-order beam rested on an elastic substrate is probed in the current article. Furthermore, a theoretical damage model is used to describe the mechanical degradation of natural fiber-strengthened composite beam during hygrothermal aging. Different three types of Winkler foundations are considered as a linear layer of the elastic foundation. To derive the equations of motion of natural fiber-strengthened composite beam, principle of Hamilton is implemented. In addition, the analytical solution is utilized to solve the derived governing equation of natural fiber-strengthened composite beam rested on Winkler–Pasternak substrate. The accuracy of using methodology is verified by those reported in the literature. The impacts of various parameters, i.e., wave number, aging time, fiber content, different types of Winkler foundation, Winkler and Pasternak parameters, α parameter and slenderness ratio on the variation of wave propagation of natural fiber strengthened composite beam are explored. Some tables and figures are provided to illustrate the obtained outcomes. The obtained results indicate that elastic foundation coefficient and wave number have an increasing effect and slenderness ratio and α parameter have decreasing effect. Furthermore, the effect of fiber content on change in wave propagation behavior depends on aging time.