Dispersion of Axisymmetric Longtudinal Waves in a Pre-Strained Imperfectly Bonded Bi-Layered Hollow Cylinder

This paper studies the dispersion of the axisymmetric longitudinal wave propagation in the pre-strained hollow cylinder consisting of two-layers under the shear-spring type imperfectness of the contact conditions between these layers. The investigations are made within the framework of the piecewise homogeneous body model by utilizing the 3D linearized theory of elastic waves in elastic bodies with initial stresses. It is assumed that the layers of the cylinder are made from compressible hyper-elastic materials and their elasticity relations are given through the harmonic potential. The degree of the mentioned imperfectness is estimated by the shear-spring parameter. Numerical results on the influence of this parameter on the behavior of the dispersion curves related to the fundamental mode are presented and discussed. It is established that the considered type imperfectness of the contact conditions causes two branches of the dispersion curve related to the fundamental mode to appear: the first disappears, but the second approaches the dispersion curve obtained for the perfect interface case by decreasing the shear-spring parameter.     

Forced Vibration of the Pre-Stressed and Imperfectly Bonded Bi-Layered Plate Strip Resting on a Rigid Foundation

Within the scope of the piecewise homogeneous body model with utilizing of the three dimensional linearized theory of elastic waves in initially stressed bodies the influence of the shear-spring type imperfection of the contact conditions between the layers of the pre-stressed bi-layered plate strip resting on the rigid foundation, on the frequency response of this plate strip is investigated. The corresponding mathematical problem is solved numerically by employing FEM and numerical results illustrating the influence of the parameter characterizing the degree of the mentioned imperfectness, on the frequency response of the normal stress acting on the interface planes between the layers and between the plate and rigid foundation are presented and discussed. In particular, it is established that an increase in the value of the shear-spring parameter the absolute values of the compressed normal stress decrease, but the values of the stretched normal stress increase and this parameter has an influence also on the character of the action of the initial stresses on the frequency response under consideration.     

Velocity of shear waves in an initially stressed incompressible anisotropic medium

The paper aims at the study of propagation of shear waves in an initially stressed anisotropic medium. The velocity equation is obtained and it is seen that the velocity of propagation depends upon the direction of propagation, the anisotropic factor and also on the initial stresses. Numerical computation indicates that the initial compressive stress diminishes the velocity of a shear wave which propagates along the direction 0° to 45° but increases it along the direction 45° to 90°. The reverse effect is obtained when initial stress is tensile. The anisotropy increases the velocity and even in the absence of initial stresses the velocity of the wave depends on the direction of propagation.     

The Influence of the Imperfectness of Contact Conditions on the Critical Velocity of the Moving Load Acting in the Interior of the Cylinder Surrounded with Elastic Medium

The dynamics of the moving-with-constant-velocity internal pressure acting on the inner surface of the hollow circular cylinder surrounded by an infinite elastic medium is studied within the scope of the piecewise homogeneous body model by employing the exact field equations of the linear theory of elastodynamics. It is assumed that the internal pressure is point-located with respect to the cylinder axis and is axisymmetric in the circumferential direction. Moreover, it is assumed that shear-spring type imperfect contact conditions on the interface between the cylinder and surrounding elastic medium are satisfied. The focus is on the influence of the mentioned imperfectness on the critical velocity of the moving load and this is the main contribution and difference of the present paper the related other ones. The other difference of the present work from the related other ones is the study of the response of the interface stresses to the load moving velocity, distribution of these stresses with respect to the axial coordinates and to the time. At the same time, the present work contains detail analyses of the influence of problem parameters such as the ratio of modulus of elasticity, the ratio of the cylinder thickness to the cylinder radius, and the shear-spring type parameter which characterizes the degree of the contact imperfection on the values of the critical velocity and stress distribution. Corresponding numerical results are presented and discussed. In particular, it is established that the values of the critical velocity of the moving pressure decrease with the external radius of the cylinder under constant thickness of that.     

The influence of the third order elastic constants to the generalized Rayleigh wave dispersion in a pre-stressed stratified half-plane

Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elasticity the influence of the third order elastic constants on the velocity of the generalized Rayleigh wave propagation in a pre-stressed stratified half-plane is investigated. Between the layer and half-plane the complete contact conditions are satisfied. The concrete numerical investigations are made on the various materials for which the values of the third order elastic constants are known. The initial stresses are determined within the framework of the classical linear theory of elasticity.     

Acoustoelastic effect in stressed heterostructures

Mechanical stresses influence the phase velocity of acoustic waves, known as the AE (acoustoelastic) effect. In order to calculate the AE effect of biaxially stressed layered systems, we extended the transfer matrix method for acoustic wave propagation by considering the change of the density, the influence of residual stress, and the modification of the elastic stiffness tensor by residual strain and by third-order constants. The generalized method is applied to the calculation of the angular dispersion of the AE effect for transverse bulk modes and surface acoustic waves on Ge(001). Our calculations reveal that the AE effect significantly depends on the propagation direction and can even change sign. The maximal velocity change occurs for transversally polarized waves propagating parallel to the [110] direction. For the layered Ge/Si(001) system, the AE effect is investigated for Love modes propagating in the [100] and [110] directions. The AE effect increases rapidly with increasing layer thickness and almost reaches its maximal value when the wave still penetrates into the unstressed substrate     

Torsional Wave Propagation in the Finitely Pre-Stretched Hollow Bi-Material Compound Circular Cylinder

This paper studies the torsional wave dispersion in the hollow bi-material compounded cylinder with finite initial strains. The investigations are carried out within the scope of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies. The mechanical relations of the materials of the cylinders are described through the harmonic potential. The numerical results on the influence of the initial stretching or compression of the cylinders along the torsional wave propagation direction are presented and discussed     

On dispersion relations of Rayleigh waves in a functionally graded piezoelectric material (FGPM) half-space

For propagation of Rayleigh surface waves in a transversely isotropic graded piezoelectric half-space with material properties varying continuously along depth direction, the Wentzel–Kramers–Brillouin (WKB) technique is employed for the asymptotic analytical derivations. The phase velocity equations for both the electrically open and shorted cases at the free surface are obtained. Influences of piezoelectric material parameters graded variations on Rayleigh wave dispersion relations, particles’ displacements magnitude and corresponding decay properties are discussed. Results obtained indicate that coupled Rayleigh waves can propagate at the surface of the graded piezoelectric half-space, and their dispersion relations and the particles displacements ellipticity at the free surface are dependent upon the graded variation tendency of the material parameters. By the Rayleigh surface waves phase velocities relative changing values combined with the relationship between the wave number and the material graded coefficient, a theoretical foundation can be provided for the graded material characterization by experimental measurement.     

Effect of An Initial Stress on SH-Type GuidedWaves Propagating in a Piezoelectric Layer Bonded on A Piezomagnetic Substrate

Propagation of SH-type guided waves in a layered structure with an invariant initial stress is studied, where a piezoelectric thin layer is perfectly bonded on a piezomagnetic substrate. Both the layer and the substrate possess transversely isotropic property. The dispersion relations of SH waves are obtained for four kinds of different electro-magnetic boundary conditions. The effects of initial stress, thickness ratio and electro-magnetic boundary conditions on the propagation behaviors are analyzed in detail. The numerical results show that: 1) The positive initial stresses make the phase velocity increasing, while the negative initial stresses decrease the phase velocity; 2) The smaller the thickness ratio of a piezoelectric layer to a piezomagnetic substrate, the larger the phase velocity of SH-type guided wave propagating in the corresponding layered structure; 3) The electrical boundary conditions play a dominant role in the propagating characteristics. Moreover the phase velocities for the electrically shorted surface are smaller than that for the open case. The obtained results are useful for understanding and design of the electromagnetic acoustic wave and microwave devices.     

Surface wave propagation in a fluid-saturated incompressible porous medium

A study of surface wave propagation in a fluid-saturated incompressible porous half-space lying under a uniform layer of liquid is presented. The dispersion relation connecting the phase velocity with wave number is derived. The variation of phase velocity and attenuation coefficients with wave number is presented graphically and discussed. As a particular case, the propagation of Rayleigh type surface waves at the free surface of an incompressible porous half-space is also deduced and discussed.     

Micro-mechanical modelling of granular material. Part 2: Plane wave propagation in infinite media

Summary This paper discusses the propagation of plane body waves through a second-gradient micropolar elastic continuum. In an accompanying paper, this macroscopic constitutive law has been derived from the micro-level particle characteristics, which are the inter-particle stiffness, the particle size and the package density. As a result of incorporating the micro-scale effects, the body waves propagate in a dispersive manner, where dispersion becomes more prominent when the wavelength of the generated body waves reaches the order of magnitude of the particle size. After successively deriving the equations of motion and the dispersion relations for plane body wave propagation, the compressional wave properties for the second-gradient micro-polar model are compared to those for the Born-Karman lattice structure. Furthermore, distinguished features of the second-gradient micro-polar model are exhibited by comparing the dispersion relations of the coupled propagation of the shear wave and the micro-rotational wave with those of more simple constitutive models. The paper ends with a parameter study, where the effect by the translational particle contact stiffness and the rotational particle contact stiffness is examined.     

Rayleigh surface wave propagation in an orthotropic rotating magneto-thermoelastic medium subjected to gravity and initial stress

Abstract

The prime objective of the present article is to analyze the effects of rotation and initial stress on the propagation of Rayleigh surface waves in a homogeneous, orthotropic magneto-thermoelastic half space subjected to gravity field. The frequency equations in closed form are derived and the amplitude ratios of surface displacements, temperature change during the Rayleigh wave propagation on the surface of half space have been computed analytically. The highlights of this study are the effects of different parameters (rotation, magnetic field, initial stress, and gravity) on the velocity of Rayleigh waves. Variation in phase velocity of Rayleigh waves against a wave number is shown graphically. Some particular cases have been deduced. Also, the classical Rayleigh wave equation is obtained as a special case of the present study. Numerical example has been carried out and represented by the means of graphs. Impacts of various involved parameters appearing in the solutions are carefully analyzed. In fact, in the absence of various parameters, these equations are in agreement with the results for isotropic medium.     

Rayleigh waves at the boundary surface of modified couple stress generalized thermoelastic with mass diffusion

In this problem, we have studied propagation of Rayleigh waves in an homogeneous isotropic modified couple stress generalized thermoelastic with mass diffusion solid half space in the context of Lord–Shulman (L-S), Green–Lindsay (G-L) theories of thermoelasticity. Secular equations are derived mathematically by using appropriate boundary conditions. The values of determinant of secular equation, Rayleigh wave velocity and attenuation coefficient with respect to angular velocity for different values of wave number and relaxation times in the absence and presence of mass diffusion, are computed numerically. The numerical simulated results are depicted graphically for copper material.     

Rayleigh waves in a thermoelastic solid half space using dual-phase-lag model

The present paper deals with the study of Rayleigh waves in a thermoelastic homogeneous isotropic solid half space in the context of dual-phase-lag model. The medium is subjected to stress free, thermally insulated, boundary conditions. The equation for the phase velocity of Rayleigh waves and the analytical expressions for the amplitudes of the displacements, temperature and thermal stresses have been derived. The expressions are obtained for a wave traveling along the free surface. The results discussed numerically and illustrated graphically to show effect of the coupling parameter and phase-lags.     

Effects of surface stresses and voids on rayleigh waves in an elastic solid

Rayleigh waves propagating at the plane material boundary of an elastic half-space containing a distribution of voids (vacuous pores) are considered. It is found that the waves are generally dispersive and that the dispersion is caused by both the surface stresses exerted by the boundary and the voids inside. If the body is incompressible, voids have no influence on the motion. In the case of small frequency, the effect of the voids is just to modify the speed of propagation. If the frequency is small and surface stresses are due to a residual surface tension, there exists a critical wavelength at which waves propagate with the speed of pure shear waves and below which the motion is not possible. The critical wave length varies directly with the surface tension and the effect of the voids is to widen the range of wavelengths for which the waves exist.     

Dynamical (time-harmonic) axisymmetric interface stress field in the finite pre-strained half-space covered with the finite pre-stretched layer

Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), the dynamical (time-harmonic) stress field in the initially finite strained half-space covered with an initially and finitely stretched layer is investigated. It is assumed that on the upper free face of the covering layer the point located force which acts is harmonic with respect to time. The corresponding boundary contact problem is solved by employing the Hankel integral transformation. Moreover, it is assumed that the material of the layer and half-space are incompressible and elastic relations for those are given through the Treloar’s potential. In the case where the initial strains are absent in the layer and half-space the considered problem formulation and solution to that coincide with the corresponding ones of the classical linear theory of elasticity for an incompressible body. The algorithm for obtaining numerical results is proposed. The numerical results regarding the stresses acting on the interface plane are presented. These results are obtained for the case where the stiffness (distortion wave velocity) of the covering layer material is less (greater) than that for the half-space material. In this case, the main attention is focused on the dependencies between the values of the stresses and frequency of the external force and also the influence of the initial strains on these dependencies. In particular, it is established that the “resonance” values of the frequency of the external force increase, but the absolute maximum values of the stresses decrease significantly with the amount of the initial tension of the covering layer.     

初始应力对瑞利波无损评价45钢表层应力的影响

基于瑞利波声弹效应理论,在瑞利波无损表征45钢表层应力的基础上分析了45钢表层初始应力状态对应力评价结果的影响。采用声程固定不变中心频率为5MHz的双瑞利波探头对45钢表层应力进行评价,在归一化互相关函数基础上计算了应力引起的瑞利波信号间时间差。结果表明:初始应力不会影响瑞利波在45钢表层中传播速度随拉伸应力的变化规律,即随拉伸应力的增加,瑞利波在45钢表层中的传播速度基本呈线性规律增加,当应力达到一定值时,再随应力的增加,瑞利波传播速度不再呈线性规律变化;但初始应力和去应力退火状态45钢的名义瑞利波声弹性系数不同,分别为0.838和1.041,最大时间差对应的应力值也不同,去应力退火前后应力评价结果的误差约为22%。     

Effects of thermal relaxation time on plane wave propagation under two-temperature thermoelasticity

The present paper is concerned with an in-depth investigation of the propagation of harmonic plane waves in elastic media in the context of the linear theory of two-temperature generalized thermoelasticity. The exact dispersion relation solutions for the longitudinal plane wave are determined analytically. Asymptotic expansions of several characterizations of the wave field, like phase velocity, specific loss and penetration depth of the dilatational waves, are obtained for both the high frequency as well as low frequency values. The effects of thermal relaxation parameter on the plane wave is analyzed in details by comparing the theoretical as well as numerical results of the present work with the corresponding results in the context of classical two-temperature thermoelasticity theory as reported earlier.     

Behavior of Rayleigh surface waves in an anisotropic media lying over a prestressed orthotropic half-space

The present paper discusses the propagation of Rayleigh waves in an anisotropic layer with finite thickness lying over a prestressed orthotropic half-space. An anisotropic media and orthotropic media are supposed for the upper layer and lower half-space, respectively. Dispersion equation and displacement components are computed in a compact form considering the case that the displacement and stress are continuous at the interface and stress vanishes on a free surface. Graphs are sketched to represent the effect of density, initial stress and height of the layer on wave velocity. The graphs are also configured to exhibit the mode of propagation of Rayleigh waves. This paper is an attempt to explain the nature of Rayleigh waves mathematically.     

Effects of the initial stress on the propagation and localization properties of Rayleigh waves in randomly disordered layered piezoelectric phononic crystals

In this paper, the effects of the initial stress on the propagation and localization properties of the Rayleigh surface waves in randomly disordered layered piezoelectric phononic crystals are studied. Due to different mechanical properties between the piezoelectric material and the polymer, different initial stresses in these two layers satisfying the equilibrium condition and interfacial compatibility are considered, which is more suitable for the practical cases. The transfer matrix between two consecutive piezoelectric unit cells is derived according to the continuity conditions. The expression of the localization factor is presented, and the wave localization properties are analyzed. Numerical calculations for the PVDF/PZT–2 periodic composites with the initial stress are performed. The band gap characteristics are studied taking the mechanical and electrical coupling into account. It is found that the localization degree can be influenced by the piezoelectric constants. With the increase in the piezoelectric constant, the stop band regions are enlarged for the ordered structures, and the localization properties of Rayleigh waves are strengthened for the disordered systems. The Rayleigh waves will be localized in mistuned periodic piezoelectric composites. The characteristics of band gaps and wave localization in ordered and disordered piezoelectric phononic crystals can be significantly changed by tuning the initial stress.