Do Xuan Tung

This paper investigates the reflection and transmission of inhomogeneous plane waves at a planar interface separating two transversely isotropic thermoelastic diffusive half‐spaces. The mixed specification of the complex slowness vector is employed to describe the incident inhomogeneous wave, while the component specification is used for reflected and transmitted waves. The governing field equations are solved to obtain the characteristic equation, which yields four complex wave modes: quasi‐elastodiffusive, quasi‐mass diffusive, quasi‐thermodiffusive and quasi‐transverse. Closed‐form expressions for the amplitude and energy reflection/transmission coefficients are derived, including the necessary interference contributions to ensure energy conservation. Numerical simulations were performed using copper‐like material parameters. Key findings include a frequency threshold ( Hz) below which homogeneous waves cannot propagate; propagation angles are significantly smaller than the corresponding attenuation angles for all reflected/transmitted waves; the sum of all energy ratios (including interference terms) equals unity, confirming energy conservation. The present results provide new physical insights into inhomogeneous wave propagation in dissipative anisotropic media and may serve as benchmarks for experimental validation in geophysical exploration and non‐destructive testing.

The effects of prestress on the reflection and transmission waves at the imperfect interface between two orthotropic elastic half‐spaces are studied in this paper. First, the characteristic equation in the orthotropic half‐space is derived from the general dynamic equation with prestress taken into consideration. The form of the incident, reflected, and transmitted waves is derived. Then, from the interface conditions for two cases (perfect and imperfect interface), the displacement and stress are required to be satisfied. The algebraic equations resulting from the interface conditions are solved to obtain the amplitude ratio of various waves. To validate these findings, energy partitions of reflected and transmitted waves are computed, demonstrating adherence to the Law of Conservation of Energy. Numerical examples are provided to illustrate the effect of the imperfect interface, prestress, and incident angle on the reflection and transmission coefficients, energy ratios, reflection, and transmission angles of waves.

This paper investigates plane wave propagation in orthotropic micropolar media using nonlocal strain gradient theory. We derive the characteristic equation for surface wave existence, which reduces to classical gradient strain, nonlocal, and classical elasticity theories as special cases. Dispersion equation for the propagation of Rayleigh-type waves at the free surface has been derived. Moreover, it is found that the dimensionless wave velocities demonstrate either stiffness-softening or stiffness-hardening behavior, depending on the relative values of the nonlocal parameter and material length scale.

The phenomenon of reflection and transmission of shear wave (horizontally polarized) at an imperfect interface between two different transversely isotropic elastic half-spaces is investigated in this paper. First, the characteristic equation in the transversely isotropic half-space is derived. The forms of the incident, reflected, and transmitted waves are derived. Then, from the interface conditions for two cases (perfect and imperfect interfaces), the displacement and stress are required to be satisfied. The reflection and transmission coefficients in terms of the amplitude ratio of various waves are calculated using interface continuous conditions. The energy ratios of reflected and transmitted waves of the structures have been computed and shown to observe the law of conservation of energy. Numerical examples are shown graphically to exhibit the effects of initial stress as well as the imperfect interface on the phase velocity, phase angles, and reflection and transmission coefficients.

The present article deals with the propagation of inhomogeneous waves in an orthotropic viscoelastic medium. For chosen directions of propagation and a real finite inhomogeneity parameter, a complex slowness vector is specified to define the propagation of an inhomogeneous incident wave. Then, the reflection and transmission of plane waves at a plane interface between two orthotropic viscoelastic half-spaces are discussed. In this incidence, horizontal slowness determines the slowness vectors for all reflected and transmitted waves. For each reflected and transmitted wave, the corresponding slowness vector is resolved to define its phase direction, phase velocity and attenuation angle. Appropriate boundary conditions on this wave field determine the amplitude ratios for reflected and transmitted waves relative to the incident wave. The numerical examples are provided to show the effect of the inhomogeneity of the incident wave on the propagation characteristic as well as the reflection and transmission coefficients. The existence of homogeneous, inhomogeneous incident waves also is investigated.

This paper deals with propagation of Rayleigh-type waves in nonlocal inhomogeneous transversely isotropic half-space. From the characteristic equation of wave for the nonlocal inhomogeneous transversely isotropic medium, the existence of the number of surface waves depends on the inhomogeneity of the medium through the number of solutions satisfying the damping condition of the characteristic equation discussed. It has also been concluded that there exist cut-off frequency and escape frequency for the wave propagating in size-dependent materials based on the nonlocal theory. Dispersion equation for the propagation of Rayleigh-type surface waves at the free surface has been derived. Based on the obtained dispersion equation, the effects of the inhomogeneity of material and nonlocality parameter on the Rayleigh wave propagation are considered through some numerical examples.

The purpose of this research is to study the propagation of surface waves in transversely isotropic piezoelastic medium based on nonlocal strain gradient theory. A characteristics equation for the existence of surface waves is discussed. This equation could be easily reduced to the ones of the gradient strain theory, nonlocal theory, and classical theory. It has also been concluded that there exist cut-off frequency for the wave propagating in size-dependent materials based on the nonlocal strain gradient theory. The dispersion equation which surface wave speed satisfies is derived from the free traction condition on the surface of half-space with consideration of electrically open circuit conditions. The effect of the nonlocal parameter, the strain gradient parameter on the existence of surface waves as well as the Rayleigh wave propagation is illustrated through some numerical examples.