Effect of voids on the propagation of waves in an elastic layer

The present paper investigates the propagation of waves in an elastic layer containing voids. Numerical calculations and discussions indicate that the velocity of the propagation of waves decreases due to the presence of voids in the material medium of the layer and the voids cause dispersion of the general waveform.     

Propagation of low-frequency elastic waves in double-porositymedia containing viscoelastic component in the pores

A self-consistent scheme named the effective field method (EFM) is applied for the calculation of the velocities and quality factors of elastic waves propagating in double-porosity media. A double-porosity medium is considered to be a heterogeneous material composed of a matrix with primary pores and inclusions that are represent by flat (crack-like) secondary pores. The prediction of the effective viscoelastic moduli consists of two steps. First, we calculate the effective viscoelastic properties of the matrix with the primary small-scale pores (matrix homogenization). Then, the porous matrix is treated as a homogeneous isotropic host where the large-scale secondary pores are embedded. Spatial distribution of inclusions in the medium is taken into account via a special two-point correlation function. The results of the calculation of the viscoelastic properties of double-porosity media containing isotropic fields of crack-like inclusions and double-porosity media with some non-isotropic spatial distributions of crack-like inclusions are presented.     

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.     

Motion of an elliptical void in interconnects embedded in matrix under gradient stress field

We present an analytical solution for the motion of an elliptical void in representative interconnects embedded in a matrix with different line aspect (volume) ratio, under gradient stress field. An orthotropic elastic model is used to represent representative interconnects embedded in a matrix. The effects of stress gradient, stress states, an equivalent void size, the orthotropic material characteristic, and the shape parameter of the void on the motion velocity of an elliptical void are described and discussed.     

Love wave propagation in a solid with a cold-worked surface layer

In this paper, experiments show Love wave generation along the top surface of used railroad rail, where the shear wave velocity has been slightly reduced by the cold-working of wheel passage for years. The rf pulses used in the experiments have about 10 µs duration and a relatively narrow frequency spectrum. The group velocity of the Love wave is found to have a strong dependence on the carrier frequency over the tested range of 0.45–3.1 MHz. Application of the seismological one-layered model to the experimental measurements yields an NDE technique for the elastic properties and the thickness of the cold-worked surface layer. The results are interpreted on the basis of a destructive observation by micro-Vickers hardness testing.     

Numerical modelling of the scattering of elastic waves in plates

This paper describes the application of finite difference methods to the calculation of the scattering of elastic waves. The emphasis is on cracklike defects in plates, and it is shown that a common numerical technique can span a range of wavelengths from Lamb waves to ultrasonic waves with many reflections from the surfaces of the plate. Quantitative results are given for the scattering of Lamb waves and ultrasonic shear waves from surface-breaking cracks.     

具有非均匀损伤带状区域中波的传播

对弹性波在二次曲线变化的非均匀损伤介质中的传播理论进行了研究。通过非均匀损伤区两端界面处力的平衡条件和位移连续性条件对方程式进行求解，利用勒让德多项式，求出了二次曲线变化的非均匀损伤介质中波动方程的解析形式解。对带状渐增和渐减的非均匀损伤介质中波的传播进行了实例计算分析，讨论了弹性波在二次曲线变化的非均匀损伤介质中传播的一般性质。     

Effects of inhomogeneity on surface waves in anisotropic media

This paper investigates the effects of anisotropy and inhomogeneity on surface waves in elastic media. Exponential variation in properties are assumed for the elastic parameters and material density. The classical equations of motion for propagation of waves in an inhomogeneous transversely isotropic elastic solid are deduced. The equations of motion for surface waves are derived and general surface waves are investigated. This general theory is then utilized to investigate Rayleigh, Love and Stoneley waves. Results obtained in the above cases reduce to the corresponding well-known classical results when inhomogeneity and anisotropy are not present. It is seen that inhomogeneity has significant effects on dispersion characteristics. Numerical calculations are included for Love waves and some conclusions have been drawn from the above calculations.     

应力波在杆形部件中的传播与反演设计

应用矩阵方法,研究了应力波在弹性杆形部件中的传输特性。推导了以顺波、逆波为状态向量的应力波传播方程和杆形部件的作用力、速度传播的特征矩阵;探讨了特征矩阵及各元素的表达形式和特性;定义了部件透射率和反射率。基于给定部件的特征矩阵,采用多项式根的替换方法,反演递推求解出给定部件等透射率的部件设计方案;从设计方案的多项式根的分布状态和部件外部形态等方面探讨了设计方案数与离散单元数的关系。     

Coupled Tamm waves guided by an isotropic and homogeneous dielectric layer in a rugate filter

The propagation of Tamm waves (also known as Bloch surface waves) guided by a layer of homogeneous dielectric material in a rugate filter was studied theoretically. A canonical boundary-value problem was set up and a dispersion equation was obtained. The solution of the dispersion equation indicated the existence of coupled modes of Tamm waves that were absent when the homogeneous dielectric material was taken to occupy a half space. The spatial profiles of the electric and magnetic fields of Tamm waves showed that Tamm waves propagate localized to either one or both interfaces. Multiple Tamm waves may lead to multi-analyte chemical sensors and multi-channel communication.     

Propagation of elastic waves in honeycomb panels for application to rapid inspection techniques

This paper considers the properties of elastic waves guided by an aluminum plate bonded to a honeycomb core for application to rapid inspection of honeycomb panels. Current acoustic inspection techniques involve the transmission of a signal between a pair of small transducers located on opposite sides of the panel. Scanning the transducers in raster fashion results in a high resolution inspection of the panel, but is very time consuming. An alternative technique would simultaneously inspect all points along a line between two widely spaced transducers located on the same side of the panel. Scanning the pair once over the panel permits rapid inspection, although with decreased resolution. Studies presented here indicate that such a method of inspection is feasible and that the flexural mode is probably the most useful.     

Boundary integral equation analysis for radiation and scattering of elastic waves in three dimensions

Abstract

In this paper, the boundary integral equation (BIE) method is employed to investigate the radiation and scattering of time‐harmonic elastic waves by obstacles of arbitrary shape embedded in an infinite medium. Based on the vector BIE, entirely free of Cauchy principal value integrals, an efficient numerical scheme using quadratic isoparametric boundary elements is proposed. Furthermore, the difficulty of non‐uniquess of a solution inherent with BIE formulations for exterior elastodynamic problems is studied numerically and analytically. The counterparts of the combined Helmholtz integral formulation method for elastodynamics together with the least‐square or Lagrange‐multiplier technique are derived and applied to overcome this difficulty successfully. In addition, the elastic‐wave fields radiated or scattered by either a spherical cavity or a rigid sphere in an infinite medium are calculated and the results are compared with the analytical solutions to demonstrate the accuracy and versatility of the proposed numerical scheme.     

Propagation of Rayleigh surface waves with small wavelengths in nonlocal visco-elastic solids

This paper investigates Rayleigh waves, propagating on the surface of a visco-elastic solid under the linear theory of nonlocal elasticity. Dispersion relations are obtained. It is observed that the waves are dispersive in nature for small wavelengths. Numerical calculations and discussions presented in this paper lead us to some important conclusions.     

Diffraction of elastic waves by defects in plates: Calculated arrival strengths for point force and thermoelastic sources of ultrasound

This paper applies geometrical ray theory to the calculation of the surface displacements generated by point force and thermoelastic sources of ultrasound in plates containing planar defects. The calculation includes direct wave arrivals, waves undergoing back-wall reflection with or without mode conversion, and waves diffracted by the crack-tip. Ultrasonic B-scan data are also simulated so that comparison can be made with experimental data. It is shown that the thermoelastic source, which can be generated by a pulsed laser, is particularly well suited to defect detection by the ultrasonic time-of-flight technique.     

地基含倾斜界面时Love波弥散特性

利用有限元法及解析法相结合的方法建立了地基含有倾斜层时Ｌｏｖｅ波弥散特征方程和位移计算公式。利用这一方法研究了该类地基Ｌｏｖｅ波弥散特性，并与水平成层地基（α＝０°）进行比较     

弹性支撑条件下一维声子晶体结构振动特性研究

为了开展弹性支撑环境下一维声子晶体结构弯曲波振动特性的研究,采用回传射线矩阵法对其频率响应函数曲线进行计算,并开展相应的参数化研究.通过与有限元法比较可以发现,二者的吻合程度较好,证明该计算方法的正确性.为了进一步分析几何参数与多种条件下弹性刚度对于弹性支撑下一维声子晶体振动特性的影响规律,对不同情况下带隙的起始频率、...     

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.     

Solution of a three-dimensional problem of the elasticity theory in terms of displacements for an isotropic elastic layer

A new method is proposed for solving a three-dimensional problem of the elasticity theory for a layer in terms of displacements. It is much easier to satisfy the boundary conditions within the framework of this approach than with the known methods. An example brought to numerical results is considered. __________ Translated from Problemy Prochnosti, No. 3, pp. 38–46, May–June, 2008.