Disturbance of SH-type waves due to moving stress discontinuity in an anisotropic soil layer overlying an inhomogeneous elastic half-space

The disturbance and propagation of SH-type waves in an anisotropic soil layer overlying an inhomogeneous elastic half-space by a moving stress discontinuity is considered. Stress discontinuity moves with non-uniform velocity and is impulsive in nature. The displacements are obtained in exact form by the method due to Cagniard modified by de Hoop. The numerical result is calculated for special cases and the natures are depicted graphically.     

Surfaces of weak discontinuity for cubically anisotropic solid bodies

In the context of the general theory of characteristics, the velocities of propagation of the discontinuity surfaces in cubically anisotropic deformable media are obtained.     

Nonlinear surface waves on an elastic solid

The effect of quadratic elastic nonlinearity on the propagation of surface Rayleigh waves on an isotropic elastic solid is examined. Using the method of multiple scales an approximate solution is obtained which is uniformly valid in both spatial directions as well as in time. An arbitrary wave profile is considered and an integro-differential equation is derived for the Fourier transform of the displacement on the boundary. In the case of a quasi-monochromatic wave explicit expressions are derived for the variations of the amplitudes of the fundamental and second and third harmonics along the boundary.     

Transient waves in inhomogeneous anisotropic elastic shells

Summary This paper considers the problem of transient wave propagation in linearly elastic Cosserat shells of constant thickness that may be anisotropic and inhomogeneous. The methods of rays and of singular wave curves are combined to find and integrate the transport equations governing growth-decay behaviour of the six possible wave modes. Conditions on material parameters and wave geometry are obtained for various different uncouplings of the wave modes. Some special cases of propagation conditions and of decay equations are worked out in detail.     

Surface waves in fibre-reinforced anisotropic elastic media

The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves — Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.     

Transient waves in inhomogeneous anisotropic elastic plates

Summary This paper considers the problem of transient wave propagation in elastic Cosserat plates that may be anisotropic, inhomogeneous, or of variable thickness. The methods of rays and of singular wave curves are combined to find and integrate the transport equations governing growth-decay behaviour of the extensional and bending wave modes to derive a common general formula involving the material parameters and wave geometry. For inhomogeneous isotropic plates of variable thickness, conditions for the uncoupling of the wave modes are obtained and some special cases are worked out in detail.     

Propagation of elastic waves through a discontinuity in a medium

The work was supported by the Russian Fund of Fundamental Investigations (project code 93-05-9577).     

Scattering of elastic waves by an elastic sphere

The problem of scattering of plane compressional wave by an elastic sphere embedded in an isotropic elastic medium of different material properties is solved. Approximate formulas are derived for the displacement field, stress tensor, stress intensity factors, far-field amplitudes and the scattering cross-section. It is assumed that the wave length is large compared to the radius of the scatterer. Various elastostatic limits are also presented.     

Scattering of elastic waves by an elastic sphere

The problem of scattering of plane compressional wave by an elastic sphere embedded in an isotropic elastic medium of different material properties is solved. Approximate formulas are derived for the displacement field, stress tensor, stess intensity factors, far-field amplitudes and the scattering cross section. It is assumed that the wave length is large compared to the radius of the scatterer. Various elastostatic limits are also presented.     

Longitudinal and transverse waves in anisotropic elastic materials

Summary It is shown that a necessary and sufficient condition for a longitudinal wave to propagate in the direction n in an anisotropic elastic material is that the elastic stiffness C ₁₁ (n) is a stationary value (maximum, minimum or saddle point) at n. Explicit expressions of all n and the corresponding elastic stiffness C ₁₁ (n) for which a longitudinal wave can propagate are presented for orthotropic, tetragonal, trigonal, hexagonal and cubic materials. As to longitudinal waves in triclinic and monoclinic materials, only few explicit expressions are possible. We also present necessary and sufficient conditions for a transverse wave to propagate in the direction n. As an illustration, explicit expressions of all n, the polarization vector a and the wave speed c for which a transverse wave can propagate in cubic and hexagonal materials are given. The search for n in hexagonal materials confirms the known fact that a transverse wave can propagate in any direction. A longitudinal wave is necessarily accompanied by two transverse waves. However, a transverse wave can propagate without being accompanied by a longitudinal wave.     

斜面型厚度变化板中导波的研究

针对单一模式导波入射的情况，利用混和边界元模型计算了斜面型散射区域的反射系数和透射系数与各种入射模式、入射频率以及斜面倾角变化的关系，研究了在单一模式导波入射时导波与散射体的相互作用。文章的结果可以用来提高大量实际的无损检测工程中的检测灵敏度与能量的穿透能力，尤其是在那些发生了斜面状厚度变化波导中的情形。     

Dispersive surface waves in anisotropic linear electromagnetoelasticity

The occurrence of surface waves on a dispersive piezoelectric half-space is considered on the basis of a fully electromagnetic approach. A linear constitutive model is adopted which accounts for both dielectric and magnetic time-dispersion and a Coulomb-type gauge condition is introduced to derive a Stroh eigenvalue problem in the frequency domain. Compatibility conditions are obtained for surface modes in the ranges of quasi-acoustic and quasi-electromagnetic speeds. The propagation properties are derived having recourse to an asymptotic analysis for the transformed constitutive tensors and it is found that at most three surface waves can propagate in each range of speed. Dispersive solutions are also discussed in the quasi-static limit.     

On the Rayleigh surface waves on an anisotropic homogeneous thermoelastic half space

In this paper, we consider the propagation of surface waves in half spaces made of anisotropic homogeneous thermoelastic materials. When the thermal dissipative properties of a half space are taken into consideration, the undamped characteristic features of Rayleigh waves do not remain valid. Then, the process is irreversible and the Rayleigh waves are damped in time and dispersive. Here, we show that the Stroh formulation of the problem leads to a first-order linear partial differential system with constant coefficients. The associated characteristic equation (the propagation condition) is an eight degree equation with complex coefficients and, therefore, its solutions are complex numbers. Consequently, the secular equation results to be with complex coefficients, and therefore, the surface wave is damped in time and dispersed. The results are illustrated for the case of an orthotropic homogeneous thermoelastic half space, when an explicit bicubic form of the characteristic equation with complex coefficients is obtained. The analysis of these Rayleigh waves in a homogeneous orthotropic half space is numerically exemplified. Further, in the case of an isotropic homogeneous thermoelastic material, the characteristic equation is solved exactly and the general solution of the first-order differential system follows. On this basis, the Rayleigh-type surface waves are studied, and the dispersion condition is found.     

Resonance scattering of elastic waves by an elastic inclusion in an elastic matrix. Numerical calculations

The scattering of an incident plane ultrasonic (longitudinal) wave by an elastic spherical inhomogeneity contained within an elastic matrix is studied. The emphasis is on the computation and analysis of basic multiple cases that result when different material behaviours are present in the matrix and in the inclusion. These calculations are useful in underwater acoustic applications. The behaviors are dominated by the soft or rigid backgrounds of the resonance scattering theory (RST). The first three multiple coefficients appearing in the expansions for the total elastodynamic fields developed around the inhomogeneity during the scattering process have been calculated in suitable frequency bands in all the cases considered. The examination of modulus, the real parts, and the imaginary parts of these (complex) coefficients under the RST approach allows the quantitative assessment of the conditions under which monopole or dipole resonances will occur and their relative magnitudes. The decomposition of the multiple coefficients into their resonance and background portions shows that it is the upward frequency shift of the background curves that controls the dominance of either radial (monopole) or translation (dipole) oscillations of the inclusion. This has an effect on the dispersion curves of the composite, which develop optical as well as acoustical branches. The real and imaginary parts of the multiple coefficients are respectively proportional to the attenuation and the effective wave speed in this simple inhomogeneous composite.     

A note on surface waves in anisotropic media

Summary An examination of possible forms of traction free surface wave in anisotropic elastic materials is undertaken. The results yield some interesting features of a certain arbitrariness which exists in displacement waves on a traction free surface in anisotropic media.     

Electromagnetic instability of surface waves in semiconductor superlattices

It is shown that in semiconductor superlattices surface electromagnetic waves traveling in the direction parallel to the external static electric field may become unstable. This instability manifests itself in the emission of electromagnetic waves. The instability criteria are derived, and the frequency as well as the growth increment and the direction of the emitted waves are determined.     

Effect of surface stresses on surface waves in elastic solids

This paper deals with the propagation of surface waves in homogeneous, elastic solid media whose free surfaces or interfaces of separation are capable of supporting their own stress fields. The general theory for the propagation of surface waves in a medium which supports surface stresses is first deduced, and then this theory is employed to investigate the particular cases of surface waves, viz. (a) Rayleigh waves, (b) Love waves and (c) Stoneley waves. It is seen that the Rayleigh waves become dispersive in nature; and, in case of low frequency with residual surface tension, a critical wavelength exists, below which the propagation of Rayleigh waves is not possible. This critical wave length is directly proportional to the surface tension. Some numerical calculations have been made in the case of Love waves and conclusions have been drawn.     

Diffraction of elastic waves by an elliptic crack

The integral equation method is used to obtain the scattered field of a normally incident plane wave from an elliptic crack embedded in an isotropic elastic medium. It is shown that the determination of the diffracted field depends on the solution of integro-differential equation. A formal power series solution, in the low frequency limit, is obtained. Expressions are derived for the scattered amplitudes and the dynamic stress intensity factor.     

Effects of inhomogeneity on surface waves in anisotropic media

This paper investigates the effects of anisotropy and inhomogeneity on surface waves in elastic media. Exponential variation in properties are assumed for the elastic parameters and material density. The classical equations of motion for propagation of waves in an inhomogeneous transversely isotropic elastic solid are deduced. The equations of motion for surface waves are derived and general surface waves are investigated. This general theory is then utilized to investigate Rayleigh, Love and Stoneley waves. Results obtained in the above cases reduce to the corresponding well-known classical results when inhomogeneity and anisotropy are not present. It is seen that inhomogeneity has significant effects on dispersion characteristics. Numerical calculations are included for Love waves and some conclusions have been drawn from the above calculations.