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.     

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.     

Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media

Elasto-dynamical equations for transversely isotropic solids have been employed to investigate the general theory of transversely isotropic magneto-elastic interface waves in conducting media under initial hydrostatic tension or compression. Particular cases of interface waves such as Rayleigh, Love and Stoneley waves have been investigated in details. In all cases, the wave velocity equations have been deduced which are in complete agreement with the corresponding results of classical surface waves of the same types where magnetic fields and initial stresses are absent. Results obtained in this paper may be considered as more general and important in the sense that the corresponding results of classical surface waves due to Rayleigh, Love and Stoneley can readily be deduced from our results as special cases. Numerical calculations and graphs have been presented in the case of Love waves and conclusions are drawn.     

Analysis of surface wave behavior in corrugated piezomagnetic layer resting on inhomogeneous half-space

This paper deals with propagation of Love type waves in a Piezomagnetic layer with corrugated boundaries overlying an inhomogeneous half-space. Inhomogeneity of elastic half-space is caused due to exponential variations in elastic parameters. Dispersion relations are obtained for magnetically open and short cases. Prominent effects of inhomogeneity, layer's width and corrugation on the phase velocity of considered wave are illustrated through graphs. Some particular cases are derived and exhibited through graphs. Also the influence of undulation parameter, elastic parameter, and piezomagnetic coefficient on phase velocity of considered wave has been marked separately. The present study finds its applications in designing and optimization of Love wave sensors and Seismic Acoustic Wave (SAW) devices. Findings may also be used for analytical study of wave propagation in piezomagnetic coupled structures.     

Magneto-visco-elastic surface waves in stressed conducting media

The present paper is concerned with magneto-visco-elastic surface waves in conducting media involving time rate of strain and stress of first order, the media being under an initial stress of hydrostatic tension or compression. The theory of magneto-visco-elastic surface waves in a conducting medium involving time rate of strain and stress of first order is derived under an initial stress. The above general theory is then employed to characterise Rayleigh, Love and Stoneley waves. Results obtained in the above cases reduce to well-known classical results when viscosity and magnetic field are absent.     

Effect of gravity on visco-elastic surface waves in solids involving time rate of strain and stress of first order

The aim of the present paper is to study the effect of gravity on visco-elastic surface waves in solids. The wave velocity equations are deduced from Biot’s theory of initial stress on the assumption that gravity creates a type of initial stress — hydrostatic in nature. Resulting equations are used to investigate surface waves of the Rayleigh, Love and Stoneley types. Results are in good agreement with corresponding classical results when gravity and viscosity are neglected.     

The propagation of Love waves in a fluid-saturated porous anisotropic layer

Summary The paper concerns the propagation of Love waves in a transverse-isotropic fluid-saturated porous layer overlaying an elastic nonhomogeneous half-space. Using the Biot's theory for the porous layer and the theory of elasticity for the lower medium, the dispersion equation has been derived. This complex transcendental equation that relates frequency, phase velocity, anisotropy factor of the layer and the inhomogeneity character of the half-space has been solved with the aid of successive approximation method. The effect of anisotropy and heterogeneity has been shown graphically.With 2 Figures     

Surface waves in fiber-reinforced anisotropic general viscoelastic media of higher orders with voids,rotation, and electromagnetic field

In this article, we investigated an effect of external magnetic field on the propagation of surface waves in a perfect electrically conducting fiber-reinforced anisotropic general viscoelastic media of rational and higher orders with voids in a rotating medium. The general surface wave speed is derived to investigate effect of electromagnetic field and rotation on surface waves in the presence of voids and viscosity. Boundary conditions are applied to obtain the secular equation for generalized types of waves. Particular cases of Stoneley, Love and Rayleigh waves are derived. The results obtained are more general in the sense that some earlier published results are obtained from our result as special cases. In the absence of voids, the results for viscoelasticity of order zero are in good agreement with the fiber-reinforced materials. Also by neglecting the reinforced elastic parameters, the results reduce to a well-known isotropic medium. It is observed that surface waves cannot propagate in a strong initially applied electromagnetic field and rotation. Numerical results for particular cases have been obtained and displayed graphically. The results indicate that the effects of voids, anisotropic, fiber-reinforcement, rotation and electromagnetic field are very pronounced and applicable for the phenomena.     

Elastic waves interacting with a thin, prestressed, fiber-reinforced surface film

Elastic surface waves propagating at the interface between an isotropic substrate and a thin, transversely isotropic film are analyzed. The transverse isotropy is conferred by fibers lying parallel to the interface. A rigorous leading-order model of the thin-film/substrate interface is derived from the equations of three-dimensional elasticity for prestressed, transversely isotropic films having non- uniform properties. This is used to study Love waves.     

Wave propagation in and free vibrations of gradient elastic circular cylindrical shells

The governing equations of motion for a gradient elastic circular cylindrical thin shell are derived. The basic equations of dynamic equilibrium and strain-displacement relations due to Donnell are combined with the stress–strain equations of the gradient theory of elasticity involving one microstructural and one microinertial elastic constant in addition to the two classical elastic moduli. The shell governing equations of motion are first used to study the propagation of harmonic waves and then free vibrations for the particular case of a circular cylindrical shell simply supported at its two ends. The results of these analyses are compared against those of the classical case in order to assess the microstructural and microinertial effects on the dynamic behavior of the shell.     

Some results on finite amplitude elastic waves propagating in rotating media

Summary. Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity provides such a framework for incompressible solids. Second: how can finite amplitude exact solutions be generated? It is seen that for some finite amplitude transverse waves in rotating incompressible elastic solids with general shear response the solutions are obtained by reduction of the equations of motion to a system of ordinary differential equations equivalent to the system governing the central motion problem of classical mechanics. In the special case of circularly-polarized harmonic progressive waves, the dispersion equation is solved in closed form for a variety of shear responses, including nonlinear models for rubberlike and soft biological tissues. A fruitful analogy with the motion of a nonlinear string is pointed out.     

Higher order surface couplings in elastic ferromagnets

The “classical” theory of elastic ferromagnetic materials is extended to the case of media able to support hyperstresses (double stresses, couple stresses), so as to take account of surface effects (curvature, role played by the magnetic anisotropy on the surface, boundary layer effect and to offer a larger choice of boundary conditions as far as magnetic spins are concerned (pinning, nonzero exchange torque,…). The field equations and the associated boundary conditions are obtained by using the generalized formulation of the principle of virtual power based on the requirement of objectivity for internal forces. Constitutive equations for nonlinear thermoelastic, magnetically saturated insulators and equations linearized with respect to small deformations are established. The set of equations obtained will permit a finer study of coupled magnetoelastic surface waves and of the resulting resonance phenomena in thin ferromagnetic deformable layers.     

面波产生的地震动转动分量的试验验证

迄今为止,地面运动转动分量主要是通过弹性波动理论方法间接由平动分量获得,但并未得到证实。首次运用面波试验验证了这种求取转动分量的方法的合理性。重锤击落地面,在半无限空间弹性介质的地表附近,可产生面波(瑞利波和乐夫波),合理布置拾振器位置,测得产生面波的时程,利用两点差原理可以测得地面近似转动分量;将实测转动分量和用理论方法求得的转动分量的时程曲线以及傅立叶谱进行对比,由两种方法得到的转动分量加速度时程在振动持续时间内的开始阶段、强震阶段和衰减阶段基本一致;Fourier谱峰值、峰值点个数、峰值出现的位置以及谱曲线的形状走向是接近的。     

Elastic stress transmission in cellular systems—Analysis of wave propagation

A closely packed array of thin-walled rings constitutes an idealisation of a cellular structure. Elastic waves propagating through such structures must do so via the ring (cell) walls. A theoretical investigation into the propagation of elastic stresses in thin-walled circular rings is undertaken to examine the nature of wave transmission. Three modes of motion, corresponding to shear, extensional and flexural waves, are established and their respective velocities defined by a cubic characteristic equation. The results show that all three waves are dispersive. By neglecting extension of the centroidal axis and rotary inertia, explicit approximate solutions can be obtained for flexural waves. Employment of Love's approach for extensional waves [Love AEH. A treatise on the mathematical theory of elasticity, 4th ed. New York: Dover Publications; 1944. p. 452–3] enables approximate solutions for shear waves to be derived. The three resulting approximate solutions exhibit good agreement with the exact solutions of the characteristic equation over a wide range of wavelengths. The effects of material property, ring wall thickness and ring diameter on the three wave modes are discussed, and the results point to flexural waves as the dominant means of elastic energy transmission in such cellular structures. Wave velocities corresponding to different frequency components determined from experimental results are compared with theoretical predictions of group velocity for flexural waves and good correlation between experimental data and theory affirms this conclusion.     

Diffraction of Elastic Waves by a Spherical Inclusion with an Anisotropic Graded Interfacial Layer and Dynamic Stress Concentrations

Scattering of compressional waves in multiphase metal matrix composites containing spherical particles with spherically isotropic graded interfacial layers is investigated using a state-space approach. A continuous transition from the particle to the matrix with the change of volume fraction of one of the constituents is assumed to exist across the thickness of the interphase zone. A simplified multilayer model for the interphase complications including both anisotropy and inhomogeneity is considered. Taylor’s expansion theorem is employed to solve a modal state equation leading to a global transfer matrix that directly links the boundary conditions at the outer surface of the interface layer to those at the inner surface. Numerical calculations reveal the important effects of interphase anisotropy and inhomogeneity on the total scattering cross section and dynamic stress concentrations for a moderately wide range of frequencies and interface layer thicknesses.     

Comments on “surface waves in fibre-reinforced anisotropic elastic media” by Sengupta and Nath [Sādhanā 26: 363–370 (2001)]

In the paper under discussion, the problem of surface waves in fibrereinforced anisotropic elastic media has been studied. The authors express the plane strain displacement components in terms of two scalar potentials to decouple the plane motion into P and SV waves. In the present note, we show that, for wave propagation in fibre-reinforced anisotropic media, this decoupling cannot be achieved by the introduction of the displacement potentials. In fact, the expressions for the displacement potentials used by the authors do not satisfy one of the equations of motion. Consequently, most of the equations and results of the subject paper are either irrelevant or incorrect     

Nonlinear capillary-gravity waves under an edge condition

The objective of this paper is to investigate the forced motion of nonlinear capillary-gravity waves in a waterfilled circular basin by a harmonic vibration applied to its side wall under Evans's or Hocking's edge condition at a contact line. The forcing frequency is near a resonance frequency under the classical edge condition of the basin. Two complex-amplitude equations for the excited eigenmode at the resonance frequency corresponding to these two edge conditions are derived. The solutions to these equations display quite different behavior and an edge condition indeed has a great influence on the excited surface waves.     

Three‐dimensional BEM for scattering of elastic waves in general anisotropic media

Based on the full‐space Green's functions, a three‐dimensional time‐harmonic boundary element method is presented for the scattering of elastic waves in a triclinic full space. The boundary integral equations for incident, scattered and total wave fields are given. An efficient numerical method is proposed to calculate the free terms for any geometry. The discretization of the boundary integral equation is achieved by using a linear triangular element. Applications are discussed for scattering of elastic waves by a spherical cavity in a 3D triclinic medium. The method has been tested by comparing the numerical results with the existing analytical solutions for an isotropic problem. The results show that, in addition to the frequency of the incident waves, the scattered waves strongly depend on the anisotropy of the media. Copyright © 2003 John Wiley & Sons, Ltd.     

正交各向异性弹性层/压磁半空间结构中Love波的传播

分析了正交各向异性弹性层/压磁半空间结构中Love波的传播特性,得到了Love波传播时的解析解,基于推导的频散方程,数值分析了正交各向异性层的切割角度对Love波频散关系的影响,结果显示相速度对切割角度有很大的依赖性。     

On the Theory of Acoustic Tomography of Stresses in Solids

We consider a mathematical model of propagation of weak elastic perturbations in acoustically inhomogeneous solids. The acoustic inhomogeneity and anisotropy of the body are induced by a field of initial strains. A linearized system of dynamic equations obtained for the Murnagan cubic potential of elasticity includes coefficients depending on the components of initial strains. An iterative approach proposed for the solution of this system of equations whose coefficients depend on space coordinates enables us to reduce the problem to the solution of a sequence of inhomogeneous wave equations with constant coefficients. Even in the zero-order approximation, this approach enables us to establish relations connecting the mean phase velocities of plane monochromatic waves of various types with linear integrals of the components of strains for arbitrary directions of propagation of waves. The corresponding relations are presented for the case of plane deformation.