Effect of temperature dependent material properties on thermoelastic damping in thin beams

Accurate analysis and control of thermoelastic damping in thin beams are crucial for the design of high-performance components such as interferometric gravitational-wave detectors and micro- and nanomechanical resonators. The nonlinear thermoelasticity due to temperature dependent material properties may be the dominant source of energy dissipation and thermal noise in some cases. In this paper, the effect of temperature dependent material properties on thermoelastic damping is investigated. Governing equations for nonlinear coupled thermoelasticity in a thin beam with temperature dependent material properties are described and the perturbation method is used to treat the governing equations. An analytical model of thermoelastic damping is derived from the definition of thermoelastic damping, and a coefficient ξ is introduced into the analytical model to represent the effect of temperature dependent material properties. Numerical results of the coefficient ξ in a silicon thin beam with temperature dependent material properties are presented and validated by the experimental results. From the obtained numerical results, one can suppress the effect of temperature dependent material properties by reducing the initial amplitude, cooling the beam and selecting suitable boundary conditions and mode shapes.