Synergistic effect of memory-size-microstructure on thermoelastic damping of a micro-plate

Abstract

The design of high-performance micro-mechanical resonators requires sufficiently accurate analysis of their thermoelastic damping. In this paper, a micro-resonator is modeled as a thin rectangular plate in vibration, and its thermoelastic damping is characterized in terms of the inverse quality factor Q−1. The Kirchhoff plate theory containing the memory, nonlocal, and size effects is presented, where the memory effect of heat flow is described by a convolution integral for time, its nonlocal effect is captured by the Guyer–Krumhansl model for space and the size effect for microstructures is characterized by Hadjesfandiari and Dargush’s consistent couple stress theory. The temperature field related to the deflection is solved first, and the governing equation of the transverse motion of a vibrating plate is obtained later. Two methods including the complex frequency approach and energy dissipation approach are employed to derive the analytical expression for the inverse quality factor. Emphasis is focused on the synergistic effect of non-locality, memory, and microstructure on the thermoelastic dissipation in micro-plates. Additionally, the influences of boundary conditions, vibration modes, and structural dimension on the thermoelastic damping are also analyzed. The temperature dependence of the thermoelastic damping is predicted and anelastic internal friction is elucidated.