A further study on nonlinear vibration of initially stressed plates

Abstract Numerical solutions of an arbitrary initially stressed plate based on various displacement fields under nonlinear vibration are presented. Nonlinear partial differential equations of plate vibration are formulated from Lo’s high order transverse shear and transverse normal deformation plate theory. The higher order terms for Lo’s displacement field are neglected to obtain various simpler forms of equations such as the first order theory and other higher order theories for isotropic plate. These nonlinear partial equations of different forms are then transformed by the Galerkin method to ordinary nonlinear differential equations. The Runge–Kutta method is used to obtain the ratio of nonlinear frequency to linear frequencies of vibration. By using these equations, the nonlinear vibration of simply supported initially stress plates with various plate theories are investigated. The frequency responses of nonlinear vibration are sensitive of the vibration amplitude, Poisson ratio, initial stress and plate theory. The study concludes that the surprising discrepancies exist among the various plate theories, which indicate the transverse normal strain, nonuniform shear stress and initial stress have great effect on the vibration behavior of plate under nonlinear vibration.

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