Dynamic analysis of an elastic plate on a cross-anisotropic elastic half-space under a rectangular moving load
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O R I G I NA L PA P E R
Niki D. Beskou · Edmond V. Muho
· Jiang Qian
Dynamic analysis of an elastic plate on a cross-anisotropic elastic half-space under a rectangular moving load
Received: 30 March 2020 / Revised: 16 June 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract The dynamic response of an elastic thin plate resting on a cross-anisotropic elastic half-space to a rectangular load moving on its surface with constant speed is analytically obtained. The moving load and the plate and soil displacements are expanded in double complex Fourier series involving the two horizontal coordinates x and y as well as the time and the load velocity. Thus, the plate equation of lateral motion reduces to an algebraic equation, while the soil equations of motion reduce to a system of three ordinary differential equations with respect to the vertical coordinate z, which can be easily solved. Compatibility and equilibrium at the plate–soil interface as well as employment of the boundary conditions of the system enable one to determine the solution in terms of displacements of the plate and the half-space soil medium. The solution is first verified by using it to obtain as special cases the solutions for isotropic and cross-anisotropic half-space problems and compare them against existing analytical solutions. Parametric studies are conducted to assess the effects of the degree of cross-anisotropy on the plate and soil responses in conjunction with the effects of other important parameters, such as the speed of the moving load.
1 Introduction A considerable amount of research has been conducted during the last twenty years or so on the dynamic analysis of flexible and rigid pavements under moving vehicles with the goal of developing accurate and efficient response prediction methods for assessing pavement behavior and improving pavement design. A rather recent review paper by Beskou and Theodorakopoulos [1] on the subject of pavement dynamics provides a fairly comprehensive description of both analytical and numerical methods for predicting pavement response to moving loads. Even though numerical methods, such as the finite element method (FEM), can provide realistic solutions by successfully treating complicated geometries and material behaviors, analytical methods of solution, which are restricted to simple geometries and linear elastic material behavior, are very useful because they: (i) can easily provide a physical insight into the problem, (ii) can easily study the effect of various parameters on the response via parametric studies and (iii) can serve as benchmarks for assessing the accuracy of numerical methods of solution. In this paper, the effect of soil cross-anisotropy on the dynamic response of rigid pavements to moving loads is studied analytically by employing a simple model consisting of an elastic plate resting on an elastic cross-anisotropic half-space. The cross-anisotropic or transversely isotropic soil has one axis of symmetry (the N. D. Beskou Department of Civil Engineering,
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