The Cauchy Problem for a Class of Semilinear Wave Equations with Piecewise Constants Data

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弹性介质中圆柱壳动力响应研究的现状和展望

一、引言在地震动情况下,地下结构与地面结构相比较其动力响应是十分不同的。以桥梁和水堤为例,对这类结构的设计,水平惯性力是一个极为重要的因素。可是,对于地下结构,以埋管为例,惯性荷载主要由其周围的土介质所承受。地下管道系统的地震破坏,     

小波基方法在波传问题中的应用

基于多尺度分析理论，引入哈密顿体系和插值小波变换，分别构造了适合于求解复杂域波传问题的快速自适应方法——多尺度辛格式和插值小波配点格式，利用小波基的局部性与消失矩等特性改善计算效率，并将插值小波应用到波动方程的多尺度反演问题中。讨论了其优缺点并提出几点展望。     

Numerical study of wave processes in a pressure-wave refrigerator

The paper provides some results concerning the numerical study of the strongly transient gasdynamic processes in a pressure-wave refrigerator (PWR). A hierarchical set of numerical models from the simplest one-dimensional to a fully three-dimensional formulation is introduced. The computations show that one-dimensional solutions give a reasonable foundation for the understanding of PWR operational principles but cannot satisfactorily predict the refrigeration efficiency. Good agreement with experiment is achieved by considering two- and three-dimensional effects of gas mixing by overlap of rotating nozzles and expansion tubes. Received Received 14 February 1996 / Accepted 1 June 1996     

Testing Aluminum Alloy from Quasi-static to Dynamic Strain-rates with a Modified Split Hopkinson Bar Method

An aluminum alloy¹ was tested at quasi-static to dynamic strain-rates (from 10⁻¹ to 5 10³ s⁻¹), using a single measuring device, a modified Split Hopkinson Bar. A wave separation technique [Bussac et al., J Mech Phys Solids 50:321–350, 2002] based on the maximum likelihood method was applied to process the strain and velocity measurements recorded at various points on each bar. With this method, it is possible to compute the stress, strain, displacement and velocity at any point on the bar. Since the measurement time is unlimited, the maximum strain measured in a given specimen no longer decreases with the strain-rate, as occurs with the classical Split Hopkinson Bar method. ¹The authors wish to thank the automobile manufacturer who provided samples of the alloy used in this study. For reasons of commercial and industrial confidentiality, we were not informed about the composition of this alloy.     

Wave propagation in carbon nanotubes embedded in an elastic matrix

This paper reports the results of an investigation into the characteristics of wave propagation in carbon nanotubes embedded in an elastic matrix, based on an exact shell model. Each of the concentric tubes of multi-walled carbon nanotubes is considered as an individual elastic shell and coupled together through the van der Waals forces between two adjacent tubes. The matrix surrounding carbon nanotubes is described as a spring element defined by the Winkler model. The effects of rotatory inertia and elastic matrix on the wave velocity, the critical frequency, and the amplitude ratio between two adjacent tubes are described and discussed through numerical examples. The results obtained show that wave propagation in carbon nanotubes may appear in a critical frequency at which the wave velocity changes suddenly; the elastic matrix surrounding carbon nanotubes debases the critical frequency and the wave velocity, and changes the vibration modes between two adjacent tubes; the rotatory inertia based on an exact shell model obviously influences the wave velocity at some wave modes. Finally, a comparison of dispersion solutions from different shell models is given. The present work may serve as a useful reference for the application and the design of nano-electronic and nano-drive devices, nano-oscillators, and nano-sensors, in which carbon nanotubes act as basic elements.     

Two-dimensional transient dynamic response of orthotropic layered media

In this study, two-dimensional transient dynamic response of orthotropic plane layered media is investigated. The plane multilayered media consist of N different generally orthotropic, homogeneous and linearly elastic layers with different ply angles. In the generally orthotropic layer, representing a ply reinforced by unidirectional fibers with an arbitrary orientation angle, the principal material directions do not coincide with body coordinate axes. The solution is obtained by employing a numerical technique which combines the use of Fourier transform with the method of characteristics. The numerical results are displayed in curves denoting the variations of stress and displacement components with time at different locations. These curves clearly reveal, in wave profiles, the scattering effects caused by the reflections and refractions of waves at the boundaries and at the interfaces of the layers, and also the effects of anisotropy caused by fiber orientation angle. The curves properly predict the sharp variations in the response at the neighborhood of the wave fronts, which shows the power of the numerical technique employed in the study. By suitably adjusting the elastic constants, the results for multilayered media with transversely isotropic layers, or layers with cubic symmetry, or isotropic layers can easily be obtained from the general formulation. Furthermore, solutions for some special cases, including Lamb’s problem for an elastic half-space, are obtained and compared with the available solutions in the literature and very good agreement is found. Preliminary version presented at the Second International Congress on Mechatronics (MECH2K3), Graz, Austria, July 14-17, 2003.     

Propogation of waves in a linear elastic fluid

The non-classical symmetry method is used to determine particular forms of the arbitrary velocity and forcing terms in a linear wave equation used to model the propogation of waves in a linear elastic fluid. The behaviour of solutions derived using the non-classical symmetry method are discussed. Solutions satisfy a given initial profile and wave velocity. For some solutions the arbitrary forcing terms and wave velocity can be written in terms of the initial wave profile. Relationships between the arbitrary forcing, arbitrary velocity and the solution are derived.     

Linear interactions affecting the propogation of waves in a linear elastic fluid

Small linear interactions affecting the propogation of waves in a linear elastic fluid are investigated. These linear interactions may occur as a result of impurities on the surface of a linear elastic fluid. These interactions are imposed on the linear wave equations which were investigated in Momoniat (Propogation of waves in a linear elastic fluid, submitted for publication) using the non-classical contact symmetry method. The occurrence of a small parameter in the wave equations under consideration in this paper makes the problem ideal for analysis using an approximate non-classical contact symmetry method. Approximate contact symmetries and approximate solutions are determined and discussed for the problems under consideration. Comparisons are made with the case of no interaction.     

Application of transparent boundary conditions to high-order finite-difference schemes for the wave equation in waveguides

We propose a method for generating finite-difference approximations of transparent boundary conditions (TBCs) with the fourth and sixth order in space. It is based on the wave equation solution continuation extra two or three layers of grid points outside the computational domain to use them in central-difference operators on approaching the boundary. We present the theoretical background of the method, give estimates of computational resources, and discuss accuracy and stability results of numerical tests in 1D and 2D cases.