Surface waves at the interface between an inviscid fluid and a dipolar gradient solid

This paper is about the dispersion analysis of surface waves propagating at the interface between an inviscid fluid and a higher gradient homogeneous elastic solid modelled as a dipolar gradient continuum. In order to compare the results, a second gradient model is also evaluated. The analysis is carried out by finding the roots of the secular equation, and by carefully studying their physical meaning. As it is well known, higher gradient continua are dispersive, i.e. phase and group velocities are frequency dependent. As a consequence, the existence of surface waves will indeed depend on frequency. In order to investigate the behaviour of surface waves in this specific fluid–solid configuration, a complete dispersion analysis is performed, with a particular focus on the frequency range in which the phase velocity of shear waves is lower than the speed of waves of the fluid. Surface waves of the type Leaky Rayleigh and Scholte–Stoneley are observed in this frequency range. This work extends the knowledge on surface waves in the case of higher gradient solids and applications of these results can be found in the field of non-destructive damage evaluation in micro structured materials, composites, metamaterials and biological tissues.     

Reflection and transmission of elastic waves through a couple-stress elastic slab sandwiched between two half-spaces

The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then, the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave (P wave) and incident transverse wave (SV wave) are both considered. The influences of the couple-stress are mainly discussed based on the numerical results. It is found that the couple-stress mainly influences the transverse modes of elastic waves.     

Reflection and transmission of plane waves between two different fluid-saturated porous half-spaces

The present study deals with reflection and transmission of plane waves between two different fluid-saturated porous half-spaces, where longitudinal and transversal waves impinge obliquely onto the interface. Amplitude ratios of various reflected and transmitted waves are obtained. Variations of amplitude ratios with the angle of incidence are depicted graphically. A particular case of reflection at the free surface of the fluid-saturated porous half-spaces is discussed.     

Effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces

The effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces are studied in this paper. First, the secular equations in the traverse isotropic piezoelectric half space are derived from the general dynamic equation with initial stress taken into consideration. Then, the interface conditions that displacement, stress, electric potential, and electric displacement are continuous across interface are required to be satisfied by three sets of coupled waves, namely, quasi-longitudinal wave, quasi-transverse wave and the electric–acoustic wave. The algebraic equations resulting from the interface conditions are solved to obtain the amplitude ratio of various waves and furthermore the energy reflection and transmission coefficients of various waves. The numerical results are shown graphically and the effects of initial stress are discussed.     

Size effects on strength, toughness and fatigue crack growth of gradient elastic solids

The present study investigates the microstructural size effect on the strength of a bar under axial loading, and on the toughness and crack growth of a beam under three-point bending within the framework of strain gradient elasticity. The gradient responses have been found considerably tougher as compared to the classical theory predictions and the observed deviation increases with increasing values of the non-dimensional parameter g/L (microstructural length over structural length). Based on the analytical solution of the strain energy release rate for the three-point bending case, a new, simple and universal, strain gradient elasticity, brittle fracture criterion and a new, size adjusted fatigue crack growth law have been established. Finally, the analytical predictions of the current modeling compare well with previous experimental data, based on three-point bending tests on single-edge notched concrete beams.     

Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids

Wave propagation in a porous elastic medium saturated by two immiscible fluids is investigated. It is shown that there exist three dilatational waves and one transverse wave propagating with different velocities. It is found that the velocities of all the three longitudinal waves are influenced by the capillary pressure, while the velocity of transverse wave does not at all. The problem of reflection and refraction phenomena due to longitudinal and transverse wave incident obliquely at a plane interface between uniform elastic solid half-space and porous elastic half-space saturated by two immiscible fluids has been analyzed. The amplitude ratios of various reflected and refracted waves are found to be continuous functions of the angle of incidence. Expression of energy ratios of various reflected and refracted waves are derived in closed form. The amplitude ratios and energy ratios have been computed numerically for a particular model and the results obtained are depicted graphically. It is verified that during transmission there is no dissipation of energy at the interface. Some particular cases have also been reduced from the present formulation.     

波在双孔隙与单孔隙介质界面上的反射与透射

基于Biot理论和双重孔隙介质理论研究了弹性波在双重孔隙介质与流体饱和单一孔隙介质 界面的反射和透射问题,在界面上假定裂缝孔隙流体相对于固体骨架的位移为零,推导了反 射系数和透射系数的计算公式,数值讨论了反射系数和透射系数随入射角和频率的变化关 系. 同时,讨论了双重孔隙介质中3种压缩波(P-1, P-2和P-3波)和一种剪切波(S波) 的频散和衰减特性.     

Reflection and transmission of elastic waves by the spatially periodic interface between two solids (Theory of the integral-equation method)

The linear theory of two-dimensional reflection and transmission of time-harmonic, elastic waves by the spatially periodic interface between two perfectly elastic media is developed. A given phase progression of the incident wave in the direction of periodicity induces a modal structure in the elastodynamic field and leads to the introduction of the so-called spectral orders. The main tools in the analysis are the elastodynamic Green-type integral relations. They follow from the two-dimensional form of the elastodynamic field reciprocity theorem, where in the latter a Green state adjusted to the periodicity of the structure at hand is used. One of these relations is a vectorial integral equation from which the elastodynamic field quantities can be determined.

The consequences of field reciprocity in the structure and of the conservation of energy are developed in view of their serving as a check on numercal results to be obtained from the relevant integral equations.

The formalism thus developed applies to profiles, if periodic, of arbitrary shape and size and can without too serious difficulties be implemented on a computer. The major difficulty in this respect is the relevant Green function, the series representation of it being slowly convergent. Its evaluation becomes tractable after an appropriate technique for accelerating the convergence. The only practical limitations are then put by the speed of the computer and its storage capacity.     

Reflection and transmission of elastic waves by the spatially periodic interface between two solids (Numerical results for the sinusoidal interface)

The integral-equation method for calculating the reflection and transmission of elastic waves by the spatially periodic interface between two solids, developed in a previous paper, is applied to a sinusoidal interface, and numerical results are presented. The computations have been carried out for four different heights of the profile (the plane interface included), a single frequency of operation, two combinations of elastic solids, and the four types of excitation. We have considered the interface between granite and slate, the interface between copper and flint glass, and P- as well as SV-wave incidence in either of the media.A peaked behaviour of the reflection and transmission factor occurs at angles of incidence where an elastodynamic spectral mode changes from propagating to evanescent and vice versa. An additional anomaly occurs in cases where the horizontal wave number of one of the spectral orders coincides with the horizontal wave number of a Stoneley wave along the corresponding plane interface. The latter phenomenon is the more pronounced, the shallower the corrugation of the interface is.     

Response of loose bonding on reflection and transmission of elastic waves at interface between elastic solid and micropolar porous cubic crystal

The problem of reflection and transmission of plane periodic waves incident on the interface between the loosely bonded elastic solid and micropolar porous cubic crystal half spaces is investigated. This is done by assuming that the interface behaves like a dislocation, which preserves the continuity of traction while allowing a finite amount of slip. Amplitude ratios of various reflected and transmitted waves have been depicted graphically. Some special cases of interest have been deduced from the present investigation.     

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids.The propagation of three longitudinal waves is represented through three scalar potential functions.The lone transverse wave is presented by a vector potential function.The displacements of particles in different phases of the aggregate are defined in terms of these potential functions.It is shown that there exist three longitudinal waves and one transverse wave.The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated.For the presence of viscosity in pore-fluids,the waves refracted to the porous medium attenuate in the direction normal to the interface.The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations.These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave.The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model.The conservation of the energy across the interface is verified.The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.     

两微极磁热弹性固体分界面上波的反射与折射

给出了磁场、热场和弹性场多场耦合作用下微极广义热弹性固体的一般控制方程.该方 程既包含了磁场、热场和弹性场的耦合作用,又在其广义热传导方程中涵盖了耦合热弹理论 (C-D)及其5类推广(L-S理论,G-L理论,G-N(II,III)理论和C-T理论).运用该微极广义磁热 弹性控制方程,研究了在定常磁场作用下, 具有均匀初始温度的两理想接触微极弹性介质平面分界面上磁热弹性波的反射和折射现象.给出了分别在缺少磁场、热场作用或不同广义热传 导理论下反射或折射热波、纵向位移波、耦合横向和微旋转波与入射纵向位移波的振幅比随 入射角变化的关系曲线.对缺少磁、热和微极性以及热松弛时间时对应的反射、折射系数进 行了对比.结果表明磁、热和微极性以及热松弛时间对振幅比均有不同程度的影 响,与磁、热和微极性一样,热松弛时间对不同类型波的影响能力差别明显,但对同 一类型的反射波和折射波的影响相似.