The Modified Galerkin’s Solution About Bending And Steady Vibration Of Rectangular Plate With Free Edges On Two-parameter Elastic Foundation

Plates on elastic foundation have been used widely in engineering field.The key to analyze static force and dynamic problems of plate on elastic foundation is to find a suitable deflection function,and then we could figure it out with corresponding measures.According to related issues in the past,deflection function can not meet the needs for random flexural deflection of plates,boundary conditions and solution of governing equation.Also the questions which could be figured out by deflection function might be circumscribed.To solve the problem mentioned above,this paper could offer a optimized solution by introducing the modified Galerkin’s solution.At the beginning,this paper gives much description of different elastic foundations,choosing Vlazov foundation model unfolding calculation by considering it describes elastic foundation simply and adequately.And a suitable deflection function is selected which is able to describle any bending of a thick rectangular plate with free edges,by comparing with certain trial functions.However this deflection only satisfies displacement boundary condition,doesn’t meets the need of all static boundary conditions.To make up this,the modified Galerkin’s solution can be used to solve the residual force caused by unsatisfied static boundary conditions and add this force to the governing function as external force.Then make the integral of governing function’s total residual force zero in the whole plate by using Galerkin’s solution.That’s increasing accuracy and amounts to solve the problem using deflection function which satisfies displacement and static boundary conditions.The modified Galerkin’s solution of rectangular plate with free edges on two-parameter elastic foundation can be obtained by theoretical derivation and programing.Compared with relevant analysis of examples,this paper analyses accuracy and astringency of the result,then solves the steady-state vibration of the plate,and finally corresponding consequences under different frequencies could be derived.The adoptive measure is explicit and simple,also it has quicker rate of convergence.The method should be used in a number of related areas,and it has broad application prospect.