Dynamic Response Analysis of Viscoelastic Multilayered Foundation in the Cartesian Coordinate System
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摘要: 基于直角坐标系下黏弹性力学的基本控制方程,运用Fourier-Laplace积分变换、解耦变换、微分方程组理论和矩阵理论,推导轴对称动荷载及非轴对称动荷载作用时黏弹性地基三维空间问题积分变换域内的解析单元刚度矩阵;根据边界条件和层间连续条件集成总刚度矩阵;求解含有总刚度矩阵方程的代数方程,得到积分变换域内相应问题的解;利用Fourier-Laplace积分逆变换得到真实物理域内的解.编制相应程序计算黏弹性层状地基动力响应与已有解答进行对比,验证了提出方法的正确性.Abstract: Based on the governing viscoelastic equations in the Cartesian coordinate system, the analytical element stiffness matrices in the integral transform domain of 3D problems of viscoelastic foundation under axisymmetric and non-axisymmetric dynamic loads were derived with the Fourier-Laplace transform, the decoupling transformation, the differential equations theory and the matrix theory. The global stiffness matrix was assembled in view of the boundary conditions and the continuity between adjacent layers, the solution in the integral transform domain was obtained from the algebraic equations involving the global stiffness matrix, and the solution in the physical domain was acquired through the inverse Fourier-Laplace transform. Through a corresponding computer program, comparison of the dynamic responses of viscoelastic multilayered foundation between the proposed algorithm and the existing method proves the validity of the former.
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