Rational design of thermoelastic damping in microresonators with phase-lagging heat conduction law

The design of thermoelastic damping (TED) affected by the phase-lagging non-Fourier heat conduction effects becomes significant but challenging for enlarging the quality factor of widely-used microresonators operating in extreme situations, including ultra-high excitation frequency and ultra-low working temperature. However, there does not exist a rational method for designing the TED in the framework of non-Fourier heat conduction law. This work, therefore, proposes a design framework to achieve low thermoelastic dissipation of microresonators governed by the phase-lagging heat conduction law. The equation of motion and the heat conduction equation for phase-lagging TED microresonators are derived first, and then the non-Fourier TED design problem is proposed. A topology optimization-based rational design method is used to resolve the design problem. What is more, a two-dimensional (2D) plain-strain-based finite element method (FEM) is developed as a solver for the topology optimization process. Based on the suggested rational design technique, numerical instances with various phase lags are investigated. The results show that the proposed design method can remarkably reduce the dissipation of microresonators by tailoring their substructures.