Axisymmetric Nonlinear Vibration Analysis Of Annular Sandwich Plate

Sandwich plate is widely used in engineering because of its good physical and mechanical properties,and there are many related research work.However,due to its nonlinearity and structural complexity,the related research work on the large amplitude vibration of annular sandwich plate is limited.Therefore,in this paper,the large amplitude axisymmetric nonlinear vibration of annular sandwich plate is mainly studied.In this paper the axisymmetric bending of annular sandwich plate is analyzed.The fundamental equations and boundary conditional expressions of the problem are derived by the potential energy principle of deformed body.And then the preceding fundamental equations without flexural rigidity of the surface plates are simplified considerably.And the large amplitude axisymmetric nonlinear free vibration of annular sandwich plate is analyzed.The fundamental equations and boundary conditional expressions of the problem are derived by Hamilton principle.And the preceding fundamental equations without flexural rigidity of the surface plates are also simplified considerably.The large amplitude axisymmetric nonlinear free vibration of annular sandwich plate with fixed internal boundary and free external boundary conditions which without considering the flexural rigidity of the surface plates is studied.In the process of analysis,the expression of vibration differential equation and boundary condition is dimensionless treated.Then the dimensionless system of nonlinear differential equations is solved by modified iteration method.Based on the results,the influence of characteristic parameters and radius ratio on vibration characteristics of annular sandwich plate is analyzed.After that,the large amplitude axisymmetric nonlinear free vibration of annular sandwich plate considering the flexural rigidity of upper and lower surface plates is analyzed.The results are compared with those of the previous studies.Then the influence of each parameter on the vibration results of annular sandwich plate is analyzed,whether the flexural rigidity of surface plates is considered or not.Basing on the foregoing study,the governing equations of static problems of annular sandwich plate subjected to in-plane uniform radial pressure loads on the outer boundary are derived.Then the analytic solution of the problem is obtained by using the power series method.Next,the governing equations and boundary condition expressions of the nonlinear vibration of annular sandwich plate which based on this static problem are derived.Then the expression of the characteristic relation between amplitude-frequency and load is obtained by solving the equations.And the characteristic relation curves are drawn.The influence of pressure load on the nonlinear vibration characteristics of annular sandwich plate is discussed.