The scattering of harmonic waves has been studied extensively for problems in quantum mechanics, acoustics, electromagnetics, and elasticity. Solutions to elastodynamic are the basis ultrasonic non-destructive evaluation measurement models. Therefore, this study, we investigate use boundary element method (BEM) frequency domain using an off-boundary technique which observation points taken insi...

This study develops a spectral theory of the interior transmission problem (ITP) for heterogeneous and anisotropic elastic solids. The importance of this subject stems from its central role in a certain class of inverse scattering theories (the so-called qualitative methods) involving penetrable scatterers. Although simply stated as a coupled pair of elastodynamic wave equations, the ITP for el...

We introduce a class of Parity-Time symmetric elastodynamic metamaterials (Ed-MetaMater) whose Hermitian counterpart exhibits frequency spectrum with unfolding (fractal) symmetries. Our study reveals scale-free formation exceptional points (EP) density is dictated by the fractal dimension their spectra. Demonstrated in quasi-periodic Aubry-Harper, geometric H-tree-fractal, and an aperiodic Fibo...

The principle underlying cloaking theory is the transformation method whereby the material properties of the cloak are defined by a (singular) spatial transformation. For elastodynamics, Milton et al. [1] concluded that the transformed materials are described by the Willis model, involving coupling between stress and velocity, in addition to anisotropic inertia. For a restricted transformation,...

In the context of numerical simulations of elastodynamic ruptures, we compare friction laws, including the linear slip-weakening (SW) law, the Dieterich-Ruina (DR) law, and the Free Volume (FV) law. The FV law is based on microscopic physics, incorporating Shear Transformation Zone (STZ) Theory which describes local, non-affine rearrangements within the granular fault gouge. A dynamic state var...

Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity representation theorems for 3D inhomogeneous PT-symmetric materials indicate some applications. We start a unified matrix-vector equation which accounts acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric seis...

Response of a transversely isotropic 3-D half-space subjected to a surface time-harmonic excitation is presented in analytical form. The derivation of the fundamental solutions expressed in terms of displacements is based on the prefect series of displacement potential functions that have been obtained in the companion paper by the authors. First the governing equations are uncoupled in the cyl...