The Bending And Vibration Of Orthotropic Rectangular Thin Plates On An Elastic Half-space

In this paper,the double trigonometrical sine series with supplementary terms were used to analyze the bending or vibration problems of orthotropic rectangular thin plates on an elastic half-space,the general analytic solution of an orthotropic rectangular thin plate with arbitrary edges on an elastic half-space loaded with arbitrary vertical force was given by combining with an integral transform solution of an elastic half-space loaded with arbitrary vertical force.First,the bending problem was researched in the paper.Based on the integral transform solution of an elastic half-space loaded with arbitrary vertical force,the general analytic solution of an orthotropic rectangular thin plate with arbitrary edges on an elastic half-space loaded with vertical force was given by an Fourier series expansion method,including the deflection and internal force of the plate,the subgrade reaction. At last,some numerical examples were calculated by using the Matlab programming, the results were compared with numerical method.At the same time,the variation regularity of the deflection and subgrade reaction along the different ratio of the thickness and length of plate,the different ratio of the elastic modulus of foundation and plate was analyzed.Second,the vibration problem was researched in the paper.Based on the analytic solution of steady vibration of an elastic half-space loaded with arbitrary vertical harmonic load,the general analytic solution of an orthotropic rectangular thin plate with arbitrary edges on an elastic half-space loaded with arbitrary vertical harmonic load was given by an Fourier series expansion method,including the amplitude of deflection and internal force of the plate,the amplitude of subgrade reaction.At last,some numerical examples were calculated by using the Matlab programming,the results were compared with existing calculation results.At the same time,the variation regularity of the amplitude of deflection and subgrade reaction along the different ratio of the thickness and length of plate,the different ratio of the elastic modulus of foundation and plate was analyzed.This new method would be feasible in practical applications.In this paper,no hypothesis was done about subgrade reaction.Under this premise, the deflection and internal force of the plate,the subgrade reaction(or the amplitude of deflection and internal force of the plate,the amplitude of subgrade reaction) were given which proved that this new method having several theoretical and practical meanings.