A FINITE-ELEMENT FREE-VIBRATION ANALYSIS OF A THERMALLY STRESSED SPINNING PLATE

A Lagrangian quadratic finite element formulation is used to analyse t he free vibration problem in spinning isotropic plates exposed to a th ermal environment. The plate is oriented arbitrarily with respect to t he 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 in ertia are accounted for). In the thermo-structural interface, the inpl ane thermal forces, and subsequently the inplane thermal stresses, are evaluated. These stresses further affect the bending strain energy. T he formulation includes the effects of transverse shear deformation an d rotary inertia of the plate. In the numerical examples considered, t he effects of the speed of rotation, the hub radius and the high tempe rature gradients on the non-dimensional frequency parameter, are clear ly brought out.