Effect of loosely bonded undulated boundary surfaces of doubly layered half-space on the propagation of torsional wave

This paper investigates the propagation of torsional wave in an initially stressed poroelastic layer with corrugated as well as loosely bonded boundary surfaces, sandwiched between a corrugated fiber-reinforced layer and a viscoelastic half-space under initial stress. The velocity equation has been obtained in closed form analytically and the substantial effect of affecting parameters on the phase velocity of torsional surface wave has been demonstrated numerically and graphically. Comparative study has been made to observe the effect of flatness parameter, reinforcement, viscoelasticity and porosity on the phase velocity, meticulously. Some particular cases have also been discussed and it is found that velocity equation is in well-agreement to the classical Love wave equation. Moreover, some remarkable observation has been made through numerical computation and graphical demonstration for fiber-reinforced layer of carbon fiber-epoxy resin, poroelastic layer of sandstone and a viscoelastic half-space.     

Propagation of torsional waves in an inhomogeneous layer over an inhomogeneous half-space

The present paper is concerned with the study of propagation of torsional waves in an inhomogeneous isotropic layer whose material properties vary harmonically with a space variable, lying over a semi-infinite inhomogeneous isotropic half-space. The closed form solutions for the displacement in the layer and half-space are obtained separately. The dimensionless phase velocity has been plotted against dimensionless wave number and scaled wave number for different values of inhomogeneity parameters. The effects of inhomogeneity have been shown in the dispersion curves using 2D and 3D plot.     

SH-waves in viscoelastic heterogeneous layer over half-space with self-weight

The effect of gravity, heterogeneity and internal friction on propagation of SH-waves (horizontally polarised shear waves) in viscoelastic layer over a half-space has been studied. Using the method of separation of variables, dispersion equation has been obtained and used to recover the damped velocity of SH-waves. Both the real and imaginary parts of dispersion equation are in well agreement with the classical Love wave equation. It has been observed that heterogeneity of the medium affects the velocity profile of SH-wave significantly. Some other peculiarities have been observed and discussed in our study.     

Effect of rigid boundary on the propagation of torsional waves in a homogeneous layer over a heterogeneous half-space

In the present paper we study the effect of rigid boundary on the propagation of torsional waves in a homogeneous layer over a semi-infinite heterogeneous half-space, where the heterogeneity is both in rigidity and density. The present study demonstrates that torsional waves can propagate in the layer. The velocities of torsional waves have been calculated numerically as a functions of KH, (where K is the wave number and H is the thickness of the layer) and are presented in a number of graphs. It is also observed that, for a layer over a homogeneous half-space, the velocity of torsional waves does not coincide with that of Love waves in the presence of the rigid boundary whereas it does at the free boundary.     

Torsional surface waves in heterogeneous anisotropic half-space under initial stress

The present paper is concerned with the propagation of torsional surface waves in a heterogeneous anisotropic half-space under the initial compressive stress. The heterogeneity in the half-space is caused by the linear variation in rigidity, initial compressive stress and density. The solution part of the problem involves the use of Whittaker function. The dispersion equation has been obtained in a closed form, which shows the variation of phase velocity with corresponding wave number. Effects of anisotropy and initial stress have been shown by the means of graphs for different anisotropic materials. It has found that the phase velocity of torsional waves decreases with increment in initial stress and inhomogeneity. Obtained phase velocity of torsional surface wave is found to be less than the shear wave velocity, which agrees with the standard result.     

Love wave propagation in heterogeneous micropolar media

The present paper framed to study the impact of heterogeneity on propagation of Love wave in a heterogeneous micropolar layer over an elastic inhomogeneous stratum, when both rigidity and density are assumed to vary linearly with depth. The equations of motion have been formulated separately for layer and half-space under suitable boundary conditions. Analytical solution for the dispersion equation has been obtained using method of separation of variables by means of the Airy function and Whittaker function. Some particular cases have also been investigated. Further, as a special case the velocity equation for isotropic layer over a homogeneous half-space coincides with the standard result of Love wave. Numerical calculations of frequency relation have been performed and depicted by means of graphs to exhibit the substantial impact of heterogeneity, micropolar parameters and wave number on the phase velocity of Love wave. The wave velocity is strongly influenced by these parameters.     

Love wave dispersion in pre-stressed homogeneous medium over a porous half-space with irregular boundary surfaces

The paper investigates the existence of Love wave propagation in an initially stressed homogeneous layer over a porous half-space with irregular boundary surfaces. The method of separation of variables has been adopted to get an analytical solution for the dispersion equation and thus dispersion equations have been obtained in several particular cases. Propagation of Love wave is influenced by initial stress parameters, corrugation parameter and porosity of half-space. Velocity of Love waves have been plotted in several figures to study the effect of various parameters and found that the velocity of wave decreases with increases of non-dimensional wave number. It has been observed that the phase velocity decreases with increase of initial stress parameters and porosity of half-space.     

Influence of partial constrained layer damping on the bending wave propagation in an impacted viscoelastic sandwich

This paper presents a parametric model to study the transient bending wave propagation in a viscoelastic sandwich plate due to impact loading. The effect of partial constrained layer damping (PCLD) geometry on wave propagation is investigated by comparing with propagation in single layer elastic plate. Several boundary conditions are also considered, and their effect on wave propagation is highlighted.The equation of motion is obtained from Lagrange’s equations. For the single layer plate, the governing equation is solved in time domain using Newman and Wilson method. For the plate with PCLD, the frequency dependant viscoelastic behavior of the core is represented by Prony series; the equation of motion is converted into frequency domain using Fourier transform the displacement is obtained in the frequency domain and is converted into time domain with the Inverse Fast Fourier Transform.The model was validated in our previous paper (Khalfi and Ross (2013)) with experimental results, additional validation is carried in this paper with literature, and good agreement is recorded. The results show that the plate covered with PCLD remains a dispersive medium. The shape of the wave is mainly related to the sandwich stiffness while the viscoelastic layer contributes in reducing the amplitude and speed of propagation. The particularity of this transient model lies in its ability to follow the shape of the bending wave at all times to observe formation, propagation and disappearance. With this model, the influence of any structural input parameters on the bending wave can be studied. The findings presented will also serve as a research base for more advanced horizons.     

Effect of rigid boundary on propagation of torsional surface waves in porous elastic layer

The paper presents the effect of a rigid boundary on the propagation of torsional surface waves in a porous elastic layer over a porous elastic half-space using the mechanics of the medium derived by Cowin and Nunziato (Cowin, S. C. and Nunziato, J. W. Linear elastic materials with voids. Journal of Elasticity, 13(2), 125–147 (1983)). The velocity equation is derived, and the results are discussed. It is observed that there may be two torsional surface wave fronts in the medium whereas three wave fronts of torsional surface waves in the absence of the rigid boundary plane given by Dey et al. (Dey, S., Gupta, S., Gupta, A. K., Kar, S. K., and De, P. K. Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores. Tamkang Journal of Science and Engineering, 6(4), 241–249 (2003)). The results also reveal that in the porous layer, the Love wave is also available along with the torsional surface waves. It is remarkable that the phase speed of the Love wave in a porous layer with a rigid surface is different from that in a porous layer with a free surface. The torsional waves are observed to be dispersive in nature, and the velocity decreases as the oscillation frequency increases.     

SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media

The present paper studies the propagation of shear waves (SH-type waves) in an homogeneous isotropic medium sandwiched between two semi infinite media. The upper half-space is considered as orthotropic medium under initial stress and lower half-space considered as heterogeneous medium. We have obtained the dispersion equation of phase velocity for SH-type waves. The propagation of SH-type waves are influenced by inhomogeneity parameters and initial stress parameter. The velocity of SH-type wave has been computed for different cases. We have also obtained the dispersion equation of phase velocity in homogeneous media in the absence of initial stress. The velocities of SH-type waves are calculated numerically as a function of kH (non-dimensional wave number) and presented in a number of graphs. To study the effect of inhomogeneity parameters and initial stress parameter we have plotted the velocity of SH-type wave in several figure. We have observed that the velocity of wave increases with the increase inhomogeneity parameters. We found that in both homogeneous and inhomogeneous media the velocity of SH-type wave increases with the increase of initial stress parameter. The results may be useful for the study of seismic waves propagation during any earthquake and artificial explosions.     

Effect of irregularity on the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer

The paper studies the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface. The irregularity is taken in the half space in the form of a rectangle. It is observed that torsional surface waves propagate in this assumed medium. In the absence of the irregularity, the velocity equation of the torsional surface wave is also obtained. For a layer over a homogeneous half space, the velocity of torsional surface waves coincides with that of the Love waves.     

Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer

This paper presents the wave propagation in a cylinder coated with a thin piezoelectric layer. The piezoelectric coupling effects are fully modeled in the mechanics model for this piezoelectric coupled cylindrical shell with bending resistance. The decoupled torsional wave velocity and the dispersion curves for the two- mode shell model are obtained theoretically. The cut-off frequency and phase velocities at limit wave number are also derived. The numerical simulations are conducted to present the results of wave propagation in this cylindrical shell and as well as to compare the results by the current bending theory and the membrane shell theory. From the comparisons, the results display obvious deference of wave propagations in terms of dispersion characteristics by different shell theories when thicker piezoelectric layer are used and when higher wave number is considered. The results of this paper can serve as a reference for future study on wave propagation in coupled structures as well as in the design of smart structures incorporating piezoelectric materials.     

Influence of linearly varying density and rigidity on torsional surface waves in inhomogeneous crustal layer

The present work deals with the possibility of propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. The layer has inhomogeneity which varies linearly with depth whereas the inhomogeneous half space exhibits inhomogeneity of three types, namely, exponential, quadratic, and hyperbolic discussed separately. The dispersion equation is deduced for each case in a closed form. For a layer over a homogeneous half space, the dispersion equation agrees with the equation of the classical case. It is observed that the inhomogeneity factor due to linear variation in density in the inhomogeneous crustal layer decreases as the phase velocity increases, while the inhomogeneity factor in rigidity has the reverse effect on the phase velocity.     

Wave propagation through mangrove forests in the presence of a viscoelastic bed

The influence of viscoelastic ocean beds on the characteristics of surface waves passing through mangrove forests is analyzed under the assumption of linearized water wave theory in two dimensions. The trunks of the mangroves are assumed to be in the upper-layer inviscid fluid domain, whilst the roots are inside the viscoelastic bed. The associated equation of motion is obtained by coupling the Voigt’s model for flow within the viscoelastic medium with the equation of motion in the presence of mangroves. The modified dynamic conditions are coupled with the kinematic conditions to obtain the boundary condition at the free surface and the interface of the two fluids consisting of the upper layer inviscid fluid and the viscoelastic fluid bed. To understand the effects of bed viscosity as well as elasticity on energy dissipation, the complex dispersion relation associated with the plane progressive wave is derived and analyzed. Effect of physical parameters associated with mangroves and viscoelastic bed on wave motion in surface and internal modes are computed and analyzed to understand their roles in attenuating wave effects. The present model will be useful in the better understanding of wave propagation through mangroves in the coastal zone having muddy seabed.     

Propagation of SH waves in an irregular monoclinic crustal layer

The present paper discusses the dispersion equation for SH waves in a monoclinic layer over a semi-infinite elastic medium with an irregularity. In the absence of the irregularity, the dispersion equation reduces to standard dispersion equation for SH waves in a monoclinic layer over an isotropic semi-infinite medium. The dispersion curves for different size of the irregularity are computed and compared for the half-space without any irregularity. It can be seen that the phase velocity is strongly influenced by the wave number and the depth of the irregularity.     

Structure of weak shock waves in 2-D layered material systems

Shock waves in homogeneous materials in the absence of phase transitions are understood to have a one-wave structure. However, upon loading of a layered heterogeneous material system a two-wave structure is obtained––a leading shock front followed by a complex pattern that varies with time. This dual shock-wave pattern can be attributed to material architecture through which the shock wave propagates, i.e. the impedance (and geometric) mismatch present at various length scales, and nonlinearities arising from material inelasticity and failure.The objective of the present paper is to provide a better understanding of the role of material architecture in determining the structure of weak shock waves in 2-D layered material systems. Normal plate-impact experiments are conducted on 2-D layered material targets to obtain both the precursor decay and the late-time dispersion. The particle velocity at the free surface of the target plate is measured by using a multi-beam VALYN VISAR. In order to understand the effects of layer thickness and the distance of wave propagation on elastic precursor decay and late-time dispersion several different targets with various layer and target thicknesses are employed. Moreover, in order to understand the effects of material inelasticity both elastic–elastic and elastic–viscoelastic bilaminates are utilized.The results of these experiments are interpreted by using asymptotic techniques to analyze propagation of acceleration waves in 2-D layered material systems. The analysis makes use of the Laplace transform and Floquet theory for ODE’s with periodic coefficients [Asymptotic solutions for wave propagation in elastic and viscoelastic bilaminates. In: Developments in Mechanics, Proceedings of the 14th Mid-Eastern Mechanics Conference, vol. 26, no. 8, pp. 399–417]. Both wave-front and late-time solutions for step-pulse loading on layered half-space are compared with the experimental observations. The results of the study indicate that the structure of acceleration waves is strongly influenced by impedance mismatch of the layers constituting the laminates, density of interfaces, distance of wave propagation, and the material inelasticity.     

Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space

The paper studies the propagation of Love waves in a non-homogeneous substratum over an initially stressed heterogeneous half-space. The dispersion equation of phase velocity is derived. The velocities of Love waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. The case of Gibson’s half-space is also considered. It is observed that the speed of Love waves is finite in the vicinity of the surface of the half-space and vanishes as the depth increases for a particular wave number. It is also observed that an increase in compressive initial stresses causes decreases of Love waves velocity for the same frequency, and the tensile initial stress of small magnitude in the half-space causes increase of the velocity.     

Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave propagation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano’s and Ferrari’s methods are deployed to estimate the roots of differential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.     

波能耗散的结构阻尼损耗因子度量方法

根据波动理论,用Timoshenko梁理论在高频范围内分析能量的耗散,通过重建作为频率函数的色散关系曲线,得到动力粘弹性模量及材料的损失因子。根据动力系统的固有特征方程与材料弹性特性的关系,研究利用阻尼损耗因子定量描述在高频情况下,波在结构中传播时的能量耗散效应以及结构阻尼损耗因子的表示方法,并通过实验利用波的色散关系估计结构的动力粘弹性模量,理论分析和实验结果表明了这种方法的可行性。     

非饱和土中弹性支承桩的扭转振动响应分析

基于已建立的非饱和土中的波动方程,对均质非饱和滞回阻尼土层中的弹性支承桩扭转振动特性进行了分析.首先利用拉普拉斯变换,在拉氏交换域中求得了土体振动位移形式解,依据桩土接触面处的衔接条件将该解耦合进桩身动力平衡方程,求解桩的动力平衡方程,得到了桩顶速度导纳的频域响应解析解和半正弦脉冲激励作用下桩顶时域响应的半解析解,并分析了主要参数对振动特性的影响.结果表明,桩底支承刚度因子影响较大,土滞回材料阻尼有一定的影响,而土底支承剐度因子基本没有影响.