A thermodynamic design methodology for achieving ultra-high frequency–quality product of microresonators. (September 2021) - Fu, Yu; Li, Li; Duan, Ke; Hu, Yujin
Abstract: Microresonators have recently emerged as ubiquitous devices in various fields. Frequency and quality factor play, respectively, a very important role in the sensitivity and resolution of a microresonator and have, however, a competitive relation. A thermodynamic design methodology is proposed herein for optimizing the overall performance (frequency–quality product) of microresonators in the framework of thermodynamics. A definition of optimization problem is formulated for achieving ultra-high frequency–quality product of microresonators. A three-dimensional 8-node thermoelastic hexahedral element is developed to predict the frequency–quality product of microresonators with complex geometric substructures. By using the three-dimensional finite element method, we formulate the thermoelastic eigenproblem of microresonators whose eigenvalues are complex. The dominated frequency (working frequency in a microresonator) can be achieved from the real part of the first-order eigenvalue, and the quality factor can be evaluated by using the ratio of the real part of the first-order eigenvalue to its imaginary part. With the help of the numerical solution technique, a topology optimization method is developed to solve the optimization problem by tailoring the substructures of microresonators. By using the developed thermodynamic design methodology, some numerical examples with different boundary conditions are discussed. Numeric examples demonstrate that a very good improvement of the frequency–quality product can be achieved for beam- and plate-type microresonators. Therefore, the proposed thermodynamic design methodology has the capability to enlarge the overall performance of microresonators by tailoring their substructures, regardless of the competitive relation between frequency and quality factor. Highlights: An optimization problem is defined for designing ultra-high frequency–quality product of microresonators. A 3D 8-node element is developed to analyze the dynamics of microresonators with complex geometric substructures. A topology optimization method is developed to solve the optimization problem by tailoring the substructures of microresonators. The proposed thermodynamic design methodology has the capability to enlarge the overall performance of microresonators.