Low-Regularity Local Well-Posedness for the Elastic Wave System

The parametric coupling between traveling electromagnetic and elastic waves in a ferrimagnet supplied by magnetic pumping is theoretically investigated. The pumping threshold is calculated for steady-state wave propagation in the presence of loss for plane electromagnetic and longitudinal elastic waves in an infinite ferrite medium. This threshold is compared to the threshold for second-order spin-wave instabilities and it is found that these spin wave processes should not prevent the magnetoelastic process from occurring. It is shown that this traveling wave system may be useful for amplifying electromagnetic or elastic waves.

Bound states in the continuum (BICs) are perfectly confined resonances within the radiation continuum. The novel characteristics of single BICs have been studied in great detail in various wave systems, including electromagnetic waves, acoustic waves, water waves, and elastic waves in solids. In practice, the performance of BICs is limited by the finite size of the structure, while the combination of multiple BICs can further improve the localization of resonances. In this study, we experimentally demonstrate the combination of Fabry-Perot and symmetry-protected BICs at near infrared wavelengths by employing a compound photonic crystal system composed of a photonic crystal slab and a distributed Bragg reflector, resulting in an enhanced high quality factor.

In recent works1, 2 the possible propagation of envelope solitons having the nature of shear-horizontal (SH) elastic surface waves was unequivocally proved mathematically for an elastic structure likely to be experimentally tested. This phenomenon may occur along a composite structure made of a nonlinear elastic isotropic substrate coated with a thin “slow”linear elastic film. Couples of materials for which this is indeed realizable were also determined. However, a strong decoupling hypothesis layed dormant in that approach. Namely, it was assumed that the SH wave in question remains decoupled from the so-called Rayleigh component, i. e., that vectorial elastic component that is polarized parallel to the sagittal plane (plane spanned by the direction of propagation X1 and the normal to the limiting surface N). This was considered in order to simplify the analysis, but it does not hold true in all rigor. A simple way to realize this fact is to recall what happens for bulk waves in nonlinear isotropic (a fortiori anisotropic) elasticity (See Ref. 3, pp. 36–37). In that theory a longitudinal motion necessarilly accompanies a transverse motion; e. g., one can write $$ \left. {\begin{array}{*{20}{c}} {{\square _T}\;v = 0,} {{\square _L}\;u = \gamma {v_x}{v_{xx}},} \end{array}} \right\} $$ (1.1)

In a lossless system, the causal and acausal Green's function for elastic waves can be retrieved by cross-correlating the elastic field at two positions. This field, composed of converging and diverging waves, is interpreted in the frame of a time-reversal process. In this work, the near-field effects on the spatio-temporal focusing of elastic waves are analyzed through the elastodynamic Green's function. Contrary to the scalar field case, the spatial focusing is not symmetric preserving the directivity pattern of a simple source. One important feature of the spatial asymmetry is its dependency on the Poisson ratio of the solid. Additionally, it is shown that the retrieval of the bulk wave speed values is affected by diffraction. The correction factor depends on the relative direction between the source and the observed field. Experimental verification of the analysis is carried out on the volume of a soft-solid. A low-frequency diffuse-like field is generated by random impacts at the sample's free surface. The displacement field is imaged using ultrasound by a standard speckle tracking technique. One important application of this work is in the estimation of the shear elastic modulus in soft biological tissues, whose quantification can be useful in non-invasive diagnosis of various diseases.

In this paper, we consider an inverse problem for the simultaneous diffusion process of elastic and electromagnetic waves in an isotropic heterogeneous elastic body which is identified with an open bounded domain. From the mathematical point of view, the system under consideration can be viewed as the coupling between the hyperbolic system of elastic waves and a parabolic system for the magnetic field. We study an inverse problem of determining the external source terms by observations data in a neighborhood of the boundary and we prove the Hölder stability. For the proof, we show a Carleman estimate for the displacement and the magnetic field of the magnetoelastic system.

The temperature dependences of the sound velocity v and attenuation α of high-frequency (50–160 MHz) sound in the bulk amorphous alloy Zr41.2Ti13.8Cu12.5Ni10Be22.5 are studied at helium temperatures in the normal and superconducting states. The alloy is characterized by a relatively small constant C determining the intensity of interaction between an elastic wave and two-level systems. The density of states of the latter systems is estimated. The peculiarities in the variation of v during the superconducting transition point to the possibility of a gapless superconductivity in a narrow temperature interval near Tc.

The valley degree of freedom has attracted increasing attention in elastic wave systems owing to its energy extrema at valleys and great potential in energy transportation. This study investigated the transport of valley edge states by angularly selective excitation in elastic wave metamaterials plate and designed a bifunctional elastic wave device in the bent waveguide containing two different interfaces. The supercell analysis revealed that the valley edge states exhibit symmetrical and anti-symmetrical distributions at two different interfaces. The straight and bent waveguides containing a single interface are designed, and the selective transport of valley edge states is observed due to the symmetrical or anti-symmetrical distributions at the interfaces. The angularly selective excitation of valley edge states by external excitation is demonstrated at the straight and bent interfaces. Based on these transport characteristics of valley edge states and the valley conservation mechanism, a bifunctional elastic wave device composed of a bent waveguide containing both two interfaces is designed. It can realize both the functions of the diode and the backward diode. The designed elastic wave device has the advantages of being a single structure with bifunctions. This study of topological valley transport with angularly selective characteristic may also have practical applications such as energy harvesting and sensing.

Weyl phononic crystals (PCs), as a key platform for topological states, feature doubly degenerate Weyl points of band structures in three-dimensional (3D) space. Their investigation has expanded from electronic systems to classical waves, including electromagnetic, acoustic, and elastic waves, and has drawn extensive attention. However, elastic wave systems are limited by fixed structures, making the active modulation of topological surface states challenging. To overcome these limitations, we design a tunable 3D Weyl magnetoelastic PC composed of magnetostrictive materials integrated with an elastic substrate. Based on the magneto-mechanical–thermal coupled constitutive relation of magnetostrictive materials, we have achieved the spatial inversion symmetry breaking under the collaborative regulation of magnetic and thermal fields, and observed the elastic wave Weyl points and their frequency-tunable characteristics. We further examine the robust transport of Weyl surface states under waveguide and defect conditions, as well as layer-selective transmission achieved through boundary condition design. This work provides a new route for dynamic regulation of elastic wave topological transport and offers significant potential for the development of customizable topological devices.

Energy decay rates of elastic waves in unbounded domain with potential type of damping

The propagation of transient elastic waves in a three-dimensional multilayered medium subjected to general dynamic loadings is analyzed in this study. One of the objectives of this study is to develop an effective analytical method for determining transient full-field solutions in the multilayered medium subjected to nonaxisymmetric dynamic loadings. The wave field is decomposed into two parts; one is the P-SV system of waves and the other is the SH system, each of which propagates independently in a horizontally layered medium. A simple relationship between solutions of two- and three-dimensional problems in the Fourier transform domain is also presented. A matrix solution in the triple transform domain is obtained by Brownwich expansion and the inverse transform is inverted by Cagniard’s method. The matrix representation of the solution can be easily used to calculate the transient response of the multilayered medium without tracing the ray path manually. The formulas presented in this study enable us to calculate the long-time transient responses of the multilayered medium for three-dimensional configuration. The theoretical transient solution for a layer overlaying a half-space subjected to an arbitrarily oriented point force is presented in detail. The numerical calculations are compared with experimental measurements for the surface displacement response on a plate and a layer overlaying a half-space subjected to an axisymmetric point force. The numerical investigation is also carried out for nonaxisymmetric loading problem of a layer overlaying a half-space.

In elastic wave systems, combining the powerful concepts of resonance and spatial grading within structured surface arrays enable resonant metasurfaces to exhibit broadband wave trapping, mode conversion from surface (Rayleigh) waves to bulk (shear) waves, and spatial frequency selection. Devices built around these concepts allow for precise control of surface waves, often with structures that are subwavelength, and utilise Rainbow trapping that separates the signal spatially by frequency. Rainbow trapping yields large amplifications of displacement at the resonator positions where each frequency component accumulates. We investigate whether this amplification, and the associated control, can be used to create energy harvesting devices; the potential advantages and disadvantages of using graded resonant devices as energy harvesters is considered. We concentrate upon elastic plate models for which the A0 mode dominates, and take advantage of the large displacement amplitudes in graded resonant arrays of rods, to design innovative metasurfaces that trap waves for enhanced piezoelectric energy harvesting. Numerical simulation allows us to identify the advantages of such graded metasurface devices and quantify its efficiency, we also develop accurate models of the phenomena and extend our analysis to that of an elastic half-space and Rayleigh surface waves.

The concept of topology has attracted tremendous attention in classical wave systems in the past decade. The robust and chiral properties of topological system provide fantastic toolkits to control the wave behaviors. In this work, an alternative method has been proposed to construct edge states in phononic crystal (PnC) plates without requiring topological phase transition. These edge states are realized by shifting part of the valley topological PnC plate, and are called as abnormal edge states. These abnormal edge states are demonstrated to be robust against sample defects such as cavity, disorder and sharp bend. By using these abnormal edge states, frequency dependent wave routes also have been built up, in which the elastic waves can be guided to different ports at different frequencies. These results enrich the design of topological PnC devices.

Ultra-wideband valley transmission on elastic topological phononic crystals

The term microseisms applies to all elastic wave systems which are propagated along the surface of the earth and which, on the one hand, are not caused by earthquakes and, on the other hand, are not purely local man-made disturbances due to traffic or industrial activity. We may also exclude from present consideration the more or less irregular local vibrations produced by natural causes, such as varying pressure of the wind on a particular structure, wind friction on a landscape, freezing and thawing of the ground, jerky movements due to cooling of structures or of hills or other topographic features, although these are often referred to in the literature as a class of microseisms. We are thus restricting our attention to elastic surface waves which are propagated in the earth’s crust over appreciable distances. These microseisms seem to be of different types and to appear in discontinuous frequency bands rather than in a continuous spectrum.

The existence of multimodes is a unique characteristic of various elastic wave systems, including elastic metasurfaces. Nevertheless, most of the previous research on elastic metasurfaces has focused on a single mode only, so the related physics is largely unknown and noise is generated by the undesired incident wave mode. Here, we present a mode-selective elastic metasurface that can tailor the target wave mode while filtering out the undesired wave mode. To this end, analytical investigation is carried out for an elastic metasurface with multimode incidence such that the metasurface can operate for both longitudinal and shear wave modes. After that, the mode-selective elastic metasurface is designed and validated numerically and experimentally. With our research, it is now possible to explicitly design an elastic metasurface for the multimode incidence case. Furthermore, since the noise caused by the undesired wave mode is barely generated with the proposed mode-selective metasurface, various elastic wave devices and physical findings are expected from the current research.