Nonlinear vibration of an initially stressed plate based on a modified plate theory

Nonlinear partial differential equations for the vibrating motion of a plat e based on a modified higher order plate theory with seven kinematic variab les are derived. The present seven-variable modified higher order plate the ory satisfies the stress-free boundary conditions. Using these derived gove rning equations, the large amplitude vibrations of a simply supported thick plate subjected to initial stresses are studied. The Galerkin method is us ed to transform the governing nonlinear partial differential equations to o rdinary nonlinear differential equations and the Runge-Kutta method is used to obtain the ratio of linear to nonlinear frequencies. Frequency ratios o btained by the present theory are compared with the Mindlin plate theory re sults and Lo's 11-variable higher order plate theory results. It can be con cluded that present modified plate theory predicts frequency ratios very ac curately. Also, the benefit of significant simplification can be observed a s compared with the Lo's higher order plate theory. The effects of initial stress and other factors on frequency ratio are investigated. (C) 2001 Publ ished by Elsevier Science Ltd.