Steady Vibration Analytic Solutions Of Anisotropic Rectangular Plates On Transversely Isotropic Elastic Foundation

In this paper, we selected the more extensive transversely isotropic semi-infinite elastic foundation model, and did not make any assumption for the reaction force of foundation, to analyze the dynamic characteristics of the anisotropic plates under any load. Firstly, based on the force general solution of Hu Hai-chang(which includes two displacement function) of transversely isotropic elastic foundation in the Cartesian coordinate system, we combined the Mankind Methods and Computer Methods, used Fourier transform techniques to analyze and get the steady vibration analytic solutions of transversely isotropic elastic foundation. And then we simplified the solutions to comparison with the researches of literatures for proving them. It combines the governing equation of steady vibration of anisotropic rectangular thin plate with four free edges on the elastic foundation with deformation compatibility equation of the plate and foundation which are based on static integral transform solution of the steady vibration analytic solutions on the transversely isotropic elastic half-space loaded with arbitrary vertical loads. According to symmetrical decomposition(Decompose deflection, foundation reaction force and load symmetrically to two parts called central symmetry and central anti symmetry generally) and using triangular series method, we obtained the analytical vibration analytic solution of anisotropic rectangular thin plate with four free edges on the transversely isotropic elastic half-space. That is, the analytical expression of the foundation reaction force, deflection of the plate and the internal force of the plate was derived. We used Gaussian integration technology, Regularization Tools and the MATLAB software to analyze the steady vibration analytic Solutions of transversely isotropic elastic foundation.To overcome the drawbacks of numerical method, cancel the Winkler foundation model or double parameter foundation model assumptions, thus obtained plate foundation pressure and internal force of more reasonable, more accurate distribution. Finally, the numerical example was analyzed and the results were compared with those from literatures. The agreement was found to be satisfactory which proved the method in this paper would be feasible in practical application and correct in theoretical derivation.We obtained how vibration frequency of load、Ratio of Elastic Modulus xE of the plate and 1E of the foundation、q of Ratio of Elastic Modulus xE of the plate to main direction and positive direction of axis x、Ratio of Elastic Modulus of the foundation, those factors affected the deflection,foundation reaction force and the like.