Analytical Study On Dynamic Response Of Rectangular Plates On Transversely Isotropic Elastic Foundation

This paper solves the analytical solution of transversely isotropic elastic foundation under arbitrary vertical load.Firstly,based on force general solution of Hu Hai-chang of transversely isotropic elastic foundation in the Cartesian coordinate system is got on Laplace transform.Then,by using the double Fourier transform and inverse transformation,the Laplace form solution is obtained.At last,laplace inverse transform can get its real solution.Dynamic Response of Thin Plate on Transversely Isotropic Elastic Foundation under Moving Load,The boundary conditions of the thin plate and the control equation get on Laplace transform.Then the mobile load and the unknown ground reaction get on Laplace transformation.Then,they are carried out double Fourier expansion.Introducing deformation coordination equation,we get the general solution of the Laplace form.At last,Laplace inverse transform can get its real solution.Dynamic Response of Thick Plate on Transversely Isotropic Elastic Foundation under Moving Load,obtaining The Laplace form solution with unknown roughness,introducing deformation coordination equation,we get the general solution of the Laplace form.At last,Laplace inverse transform can get its real solution.Steady state vibration problem of Thick Plate,based on force general solution of Hu Hai-chang of transversely isotropic elastic foundation in the Cartesian coordinate system get on Laplace transform.Considering the Steady vibration of Plate's Control equation,introducing deformation coordination equation,we get the general solution,proving the correctness of this article.Compiling Matlab program,calculating examples through Matlab program,comparing the results with the literature,the results are consistent with the literature.The parameters of the foundation,the parameters of the plate,and the frequency of the load on the plate deflection are investigated on plate's deflection.