Free Vibration And Buckling Analysis Of Orthotropic Rectangular Plates Resting On Elastic Foundations By Using DTM

Based on the classic thin plate theory,free vibration of orthotropic rectangular plates with variable thickness resting on Winkler elastic foundations is solved by using the balance relation of force and differential trasnformation method(DTM),free vibration and buckling analysis of compressed orthotropic rectangular plates resting on Winkler-Pasternak foundations is solved by using Hamilton principle and DTM.The results of the third chapter are reduced to constant thickness or variable thickness orthotropic rectangular plates which are compared with the extend Kantorovich method and the modified Fourier series method.The results of the forth chapter are reduced to the isotropic rectangular plates which are compared with quintic spline techinque(QST)and differential quadrature method(DQM).The convergence of non-dimensional natural frequency,the influence of different parameters on dimensionless natural frequency and the critical buckling loads and vibration mode shapes for different boundary boundary conditions are investigated by using DTM.The results show that DTM presents high accuracy,strong applicability and fast convergence for solving the frequency and the critical buckling load parameters.For the lower order vibration mode and the weaker restrained boundary conditions,the convergence of frequency is faster.Free vibration frequency increases with increasing Winkler foundation parameter,Pasternak foundation parameter and aspect ratio.When the aspect ratio is relatively small,the influence of loading parameter on frequency is neglected.The influence of increasing the aspect ratio on the frequency is obvious and frequency parameter increases with increasing the aspect ratio.For stronger restrained boundary conditions,free vibration frequency parameter becomes heavy and increases more easily with increasing varied thickness parameter.However,frequency parameter decreases and changes to zero with increasing the intensity of compressed force which is substituted by the critical buckling load.The critical buckling load increases with increasing Winkler foundation parameter and Pasternak foundation parameter.In particular,for ?=1.5,2,as the orthotropic rectangular plate is subjected to compressed and tensile forces simultaneously and hence two values of critical buckling loads(one positive,one negative)are presented which is similar to the isotropic plate.