Free vibration of plates with stepped variations in thickness on non-homogeneous elastic foundations

Abstract

A finite element model is presented for the analysis of the free vibration of plates with multiple stepped variations in thickness resting on non-homogeneous elastic foundations. Based on Mindlin plate theory, the model includes transverse shear deformation as well as bending-extension coupling in cases of plates with stepped sections eccentrically located with respect to the mid-planes. The section of elastic foundation under a plate element is treated as a separate foundation element. The transverse deformation of these foundation elements is made to be consistent with the deflection of plate elements being supported, resulting in a consistent stiffness matrix for the elastic foundation. Numerical results are in good agreement with the available reported results. The effect of eccentricity of the locations of stepped sections on the natural frequencies is found to be not negligible. The elastic foundations are found to have a significant effect on the fundamental natural frequencies of both uniform and stepped plates. Natural frequencies and mode shapes of rectangular plates and circular plates with multiple eccentrically stepped sections resting on non-homogeneous elastic foundations are presented.