FREE-VIBRATION OF PLATES WITH STEPPED VARIATIONS IN THICKNESS ON NONHOMOGENEOUS ELASTIC FOUNDATIONS

A finite element model is presented for the analysis of the free vibra tion of plates with multiple stepped variations in thickness resting o n non-homogeneous elastic foundations. Based on Mindlin plate theory, the model includes transverse shear deformation as well as bending-ext ension coupling in cases of plates with stepped sections eccentrically located with respect to the mid-planes. The section of elastic founda tion under a plate element is treated as a separate foundation element . The transverse deformation of these foundation elements is made to b e consistent with the deflection of plate elements being supported, re sulting in a consistent stiffness matrix for the elastic foundation. N umerical results are in good agreement with the available reported res ults. 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 freque ncies and mode shapes of rectangular plates and circular plates with m ultiple eccentrically stepped sections resting on non-homogeneous elas tic foundations are presented.