Análisis de Vibración de Platos Anulares con Soporte Elástico

Abstract

This research consists of a mechanical model of bending and tension-compression springs to analyze the change in natural frequencies and modal shapes with respect to the rigidities in the supported disc. The clamped fastening of a real mechanical system is commonly modeled as an ideal fastening that totally re-stricts the moments and forces, which commonly does not exist in real systems. This limitation motivates the development of the present model that allows considering the elasticity of the fastening that exists in the annular disc. The free vibration of an annular plate with outer free edge is modeled by different stiffness boundary conditions at the inner edge and solved analytically by the Bessel functions. The natural fre-quency parameters γ2 are tabulated for the clamped and the elastic support for different internal-external radius ratios, modes of vibration and stiffnesses at the inner edge. It is observed that as the rigidities of the flexible support increase, the values of the parameters γ2 converge to the classical clamped supported disk. Modal shapes change differently with respect to changes in stress-compression stiffness and with respect to changes in flexural stiffness.