摘要
A three-dimensional state space method has been developed for the calculation of dynamic response of plates with two free edges and two simply supported edges.A complex damping model was introduced, then the exact solutions which satisfy all the governing equations and boundary conditions were obtained.In order to overcome the difficulty of satisfying all the stress conditions at free edges, the displacement functions of free edges were assumed.The boundary conditions were strictly satisfied when the convergence rate was good.The computing time was evidently less than that of finite element method.The comparison of the solution with those of finite element method show that there is an excellent agreement for displacements.When the imaginary parts of normal stress deviated, the finite element results showed existence of shear stresses at top and bottom surfaces, and the boundary conditions of FEM model were not strictly satisfied.
A three-dimensional state space method has been developed for the calculation of dynamic response of plates with two free edges and two simply supported edges. A complex damping model was introduced, then the exact solutions which satisfy all the governing equations and boundary conditions were obtained. In order to overcome the difficulty of satisfying all the stress conditions at free edges, the displacement functions of free edges were assumed. The boundary conditions were strictly satisfied when the convergence rate was good. The computing time was evidently less than that of finite element method. The comparison of the solution with those of finite element method show that there is an excellent agreement for displacements. When the imaginary parts of normal stress deviated, the finite element results showed existence of shear stresses at top and bottom surfaces, and the boundary conditions of FEM model were not strictly satisfied.
