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Thermoelastic damping, which arises when you subject a material to cyclic stress, is an important factor when designing MEMS resonators. The stress brings about deformation, where materials heat under compressive stress and cool under tensile stress. Thus, due to the resulting heat flux, energy is lost to bring about this damping.

The magnitude of the energy loss depends on the vibrational frequency and the structure’s thermal relaxation time constant, which is the effective time that the material requires to relax after an applied constant stress or strain. Therefore, the effect of thermoelastic dissipation, and consequently the damping, is most pronounced when the vibration frequency is close to the thermal relaxation frequency.

These models show how to model thermoelastic damping in a MEMS resonator using fully coupled thermal and structural mechanics equations.