A finite element free vibration analysis of a thermally stressed spinning plate

Abstract

A Lagrangian quadratic finite element formulation is used to analyse the free vibration problem in spinning isotropic plates exposed to a thermal environment. The plate is oriented arbitrarily with respect to the spinning hub. The inplane component of the distributed centrifugal force produces inplane tensile stresses that add to the bending strain energy. The normal component is added to the inertia force. A finite element steady-state heat conduction analysis of the plate yields the two-dimensional temperature field (convection terms due to spinning inertia are accounted for). In the thermo-structural interface, the inplane thermal forces, and subsequently the inplane thermal stresses, are evaluated. These stresses further affect the bending strain energy. The formulation includes the effects of transverse shear deformation and rotary inertia of the plate. In the numerical examples considered, the effects of the speed of rotation, the hub radius and the high temperature gradients on the non-dimensional frequency parameter, are clearly brought out.