FLEXURAL VIBRATION AND DAMPING OF THERMOELASTIC THIN PLATES

Recent interest in thermoelasticity of vibrating structures is motivated by the unavoidable fact that ther-moelastic damping remains after all other sources of dissipation are removed, e.g. mounting losses, or crystal imperfection. Thus, carefully controlled experiments on silicon MEMS oscillators [1] have demon-strated that the dominant loss mechanism is thermoelastic (TE). Further reduction in TE damping of MEMS resonators, with applications to next generation RF devices, requires understanding this limiting effect. The talk reviews recent theoretical developments starting from a general procedure for calculating thermoelastic damping in structures [2]. The main idea is to take advantage of the fact that coupling between elastic and thermal fields is weak, and consequently TE damping can be found the purely elastic lossless solution by regular perturbation. The talk emphasizes new results for TE damping in flexural vibration of thin structures. The procedure generalizes the original Zener [3] theory for beams, though for thin plate situation is more interesting by virtue of the two dimensional nature which introduces the possibility of flexure in two directions, coupling the kinematics and the thermal diffusion. The latter is due to the alternating compression and extension on opposite faces of the thin structure, causing the instantaneous or isentropic bending stiffness of the plate to relax to its isothermal value. It can be shown that the lateral (in-plane) diffusion of heat is negligible. The net effect for thin plates in flexure is to modify the equation relating bending moment M and curvature κ to M = D(0)κ−∆Dg ∗ κ, where D(0) is the instantaneous or adiabatic bending stiffness, ∆D =