Non-linear vibration of circular plates with transverse shear and rotatory inertia

Abstract

This study is an analytical investigation of large amplitude flexural vibrations of clamped circular plates with stress-free and immovable edges. The effects of transverse shear deformation and rotatory inertia are included in the governing equations. Solutions are formulated on the basis of Galerkin's method and calculated by using the Runge-Kutta numerical procedure. An excellent agreement is found between the present results and those reported earlier for non-linear static and dynamic cases. Numerical results indicate that the effects of transverse shear deformation and rotatory inertia are usually neligible in the non-linear dynamic analysis of circular plates, but can be significant for moderately thick plates with a radius-to-thickness ratio less than 10.