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.     

Modeling and evaluating the scattering of Rayleigh waves by a linear distribution of surface cracks

A numerical evaluation model of the reflection coefficient of Rayleigh waves for a linear distribution of surface cracks is developed using the weight function estimation method. The numerical evaluation of the reflection coefficients varying with respect to the crack depth ratios, frequencies, and the number of the cracks for several commonly used engineering materials is performed. The results show that the model can effectively be used to evaluate the reflection coefficient for a linear distribution of the cracks. The crack depth which can be evaluated has been extended substantially and the evaluation results have been improved.     

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.     

A new point contact surface acoustic wave transducer for measurement of acoustoelastic effect of polymethylmethacrylate

A new acoustic transducer and measurement method have been developed for precise measurement of surface wave velocity. This measurement method is used to investigate the acoustoelastic effects for waves propagating on the surface of a polymethylmethacrylate (PMMA) sample. The transducer uses two miniature conical PZT elements for acoustic wave transmitter and receiver on the sample surface; hence, it can be viewed as a point- source/point-receiver transducer. Acoustic waves are excited and detected with the PZT elements, and the wave velocity can be accurately determined with a cross-correlation waveform comparison method. The transducer and its measurement method are particularly sensitive and accurate in determining small changes in wave velocity; therefore, they are applied to the measurement of acoustoelastic effects in PMMA materials. Both the surface skimming longitudinal wave and Rayleigh surface wave can be simultaneously excited and measured. With a uniaxial-loaded PMMA sample, both acoustoelastic effects for surface skimming longitudinal wave and Rayleigh waves of PMMA are measured. The acoustoelastic coefficients for both types of surface wave motions are simultaneously determined. The transducer and its measurement method provide a practical way for measuring surface stresses nondestructively.     

Propagation of boundary acoustic waves along a ZnO layer between two materials

Theoretical and experimental results on boundary acoustic waves propagated along a ZnO layer sandwiched between two materials are presented. It is shown that boundary acoustic waves can exist only when the material constants of the three materials satisfy the particular conditions obtained here. Experiments on SiO(2)/ZnO/SiO(2 ) were performed to verify the theoretical prediction of the existence of boundary waves. Boundary waves were excited and received by interdigital transducers and propagated along the ZnO layer. Propagation loss was practically the same as for Rayleigh waves, indicating a proper mode of the system. The results suggest that future SAW (surface acoustic wave) devices can be made without any package.     

Laser-Generated Rayleigh Waves Propagating in Transparent Viscoelastic Adhesive Coating/Metal Substrate Systems

We have established numerical models for simulating laser-generated Rayleigh waves in coating/substrate systems by a finite element method and investigated the propagation characteristics of Rayleigh waves in systems concerning the viscoelasticity and transparency of adhesive coatings. In this way, we have studied the influence of the mechanical properties of the coating, such as the elastic moduli, viscoelastic moduli, coating thickness, transparency, and coating material, on the propagation characteristics of the Rayleigh waves. The results show that the propagation characteristics of the Rayleigh waves can be divided into low- and high-frequency parts. The high-frequency propagation characteristics of the Rayleigh wave are closely related to the properties of the adhesive coating.     

声表面波滤波器的离散Green函数分析法

日本学者Hashimoto提出栅格有效介电常数和离散Green函数,并结合有限元方法分析了短路金属栅阵中声表面波的传输特性。由此开发了相应的Fortran应用程序。国际上许多从事声表面波器件的研发公司都使用该程序设计他们的产品。以Rayleigh波在128°YX-LiNbO3基片、铝金属栅中传播为例,给出根据Hashimoto程序运算的结果,读取禁带下边缘和禁带上边缘所对应的相对频率的数值,代入COM理论色散关系的数学表达式中,该表达式的图形就是由COM理论色散关系而确定的波数色散曲线,以提取耦合模参数。     

Numerical calculations of elastic wave propagation in anisotropic thin films deposited on substrates

In this work, we present a generalized numerical model to study the dispersion curves of elastic waves in anisotropic thin layer/substrate systems. Dispersion curves as a function of wave frequency for different propagation angles are calculated. The nature of the mode (Rayleigh or Love) is identified by analyzing the polarization of the three-dimensional displacement field. This numerical model has been applied to the system Au(0 0 1)/Ni(0 0 1).     

Body to Rayleigh wave mode-conversion at steps and slots

The efficient excitation of Rayleigh waves at surface discontinuities due to body wave incidence has potential as a method for the detection and sizing of surface breaking defects. In this paper, the mode-conversion phenomenon at several types of surface features is studied in detail, using numerical models which employ finite-difference methods. The emphasis is on examining the spectral content of the Rayleigh wave field in order to arrive at a method for relating the spectral information to the defect dimensions. The numerical results are backed up by experimental observations.     

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.     

封闭空间爆炸载荷特性研究

封闭空间爆炸载荷主要包含瞬态冲击波和持续时间较长的准静态超压。为了研究封闭空间爆炸载荷特性,基于FORTRAN平台,采用三阶WENO有限差分格式编写了爆炸波高精度三维数值计算程序。应用Sod激波管、双爆轰波碰撞等经典算例验证了所开发数值程序的可靠性。在封闭空间内炸药爆炸波数值计算的基础上,基于冲量等效原则提出封闭空间内爆炸载荷简化模型,理论推导给出准静态超压峰值计算公式并通过数值计算结果验证了该公式的可靠性。开发的高精度爆炸波三维数值计算程序及提出的简化载荷模型可用于封闭空间内爆炸载荷的快速计算,为工程抗爆结构设计提供载荷输入。     

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.     

Elastodynamic Doppler effects

Summary The Doppler effect is discussed for flexure waves in beam and plate, three body waves (P, SV, SH) in an infinite solid, modal SH waves in a thick plate and a Rayleigh wave on the surface of a semi-infinite solid. The exact closed form solution for each elasto-dynamic problem is obtained and the simple equation for the Doppler frequency shift is derived for all waves. It is shown that the Doppler frequency shift takes place continuously in the 2D plane problems, and that the most sensible wave for the Doppler frequency shift is the non-dispersion wave, such as the body wave and Rayleigh wave. The flexural and modal waves, which have the dispersion nature, are less sensible. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

爆破地震波在岩石介质中传播特性与数值计算研究

通过从不同角度对大量的深孔爆破地震动测试数据的分析 ,得到了岩石中爆破地震波传播的频率、幅值和持续时间等主要参数的变化规律以及它们的影响因素 ,并通过二元回归法 ,拟合出计算爆破地震波加速度幅值的经验公式。在此基础上 ,建立了爆破地震波传播过程的计算模型 ,编制了有限元计算程序。数值模拟仅考虑弹性区域 ,爆炸波对岩石介质的作用经粉碎区、破裂区衰减后成为输入荷载。计算结果与实测结果基本相符 ,证明该模型与方法可用于一般岩石介质中爆破地震波传播的数值模拟。研究结果为深孔爆破地震控制措施的制订提供了依据 ,对其它类似问题的研究也有一定的参考作用     

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.     

Dispersion and characteristic surfaces of waves in hybrid multilayered piezoelectric circular cylinders

The frequency and group velocity dispersion behaviors, and characteristic surfaces of waves in a hybrid multilayered piezoelectric circular cylinder are investigated. The associated frequency dispersion equation is developed using an analytical-numerical method. In this method, the cylinder is modeled using the three-nodal-line layer element; the coupling between the elastic field and the electric field is considered in each element. A system of governing differential equations of each layer element is obtained following the Hamilton Principle. The phase velocity and slowness as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces, e.g. the phase velocity, slowness and wave surfaces as well as the group velocity, slowness and wave surfaces, are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. A corresponding program code is developed and numerical examples are presented for hybrid multilayered piezoelectric circular cylinders with two ratios of radius to thickness.     

浅海沉积层中界面波的传播以及掩埋目标的回波

根据地声界面波的相关理论,采用时域有限差分法建立浅海沉积层中界面波传播模型。以沉积层中掩埋小目标为例,计算界面波对空腔掩埋物和实心掩埋物的不同作用结果。根据运动方程和应力应变关系采用中心差分网格建立声场的有限差分模型,计算了声场瞬态情况和质点振动的时间序列结果,从不同角度比较分析了地声界面波对掩埋目标的作用。根据浅海沉积层的性质计算了界面波的传播损失和对掩埋物体的目标强度,由于界面波传播衰减主要由沉积层的能量耗散引起,其规律接近横波的传播衰减,在高频情况下界面波在沉积层中传播的距离不远。文章试图建立一种对浅海沉积层中掩埋小尺度目标的探测新方法。通过一些典型模型的分析,从理论角度证明地声界面波对目标探测的可行性。     

A new DRBEM model for wave refraction and diffraction

A numerical model using the dual reciprocity boundary element method (DRBEM) is developed to study the combined refraction and diffraction of water waves propagating around islands or solid offshore structures over a seabed with a variable depth. Based on the well-known mild-slope equation, the model has been validated by comparison with both analytical solutions and standard numerical solutions available in the literature. The results show that a considerable improvement in terms of numerical efficiency has been achieved with the adoption of the DRBEM and the model has a great potential to be used in engineering practice to solve wave refraction and diffraction problems.     

利用瑞利波速度弥散特性反演地基参数

文献[1]利用有限元与半无限元相结合的方法已能精确有效地计算成层地基R波速度的理论弥散曲线.在此基础上,本文利用阻尼最小二乘法推导了R面波法反分析成层地基土的有关参数的公式,给出了应用实测的R波弥散曲线反演土层参数的方法,并编制了相应的计算机程序.最后,通过计算实例验证了本文方法的可靠性和实用性.