The Analytical Study On Dynamic Response Of Rectangular Plate On The Elastic Half Space Foundation Under The Moving Load

Firstly, basing on the three-dimensional elasticity theory and making the Laplace transform to the dynamic equations described by displacement. And then using the double Fourier transform to obtain the Laplace form displacement integral solution of the elastic half space foundation under arbitrary dynamic loading under the Cartesian coordinates.Making Laplace transform to the dynamic boundary value problem of the limited large rectangular thin plate based on Kirchhoff theory laid on foundation to obtain the Laplace form deflection analytical solution of the plate with unknown ground reaction force. Then, combined with the deformation compatibility condition of plate and foundation to fully get Laplace form analytical solution of plate on the elastic half space foundation under the moving load, and then adopting Laplace inverse transform method developed by Durbin to obtain its true solution.Making Laplace transform to the dynamic boundary value problem of the limited large rectangular middle thick plate based on Hu Haichang's bending theory of flat plate with extensive three-displacement laid on foundation to obtain the Laplace form deflection analytical solution of the plate with unknown ground reaction force. Then, combined with the deformation compatibility condition of plate and foundation to fully get Laplace form analytical solution of plate on the elastic half space foundation under the moving load, and then adopting Laplace inverse transform method developed by Durbin to obtain its true solution.Establishing the method to calculate the dynamic response coefficient, which is infinite integral function with singularity and oscillatory, and writing Matlab program to calculate it. When comparing the results of this paper with the literature, we can find out they agree well with each other. It proves the correctness of theoretical derivation and the feasibility of the research methods. Meanwhile,using the method of this paper to accurately analyze the dynamic characteristics of the substrate in four load conditions.