Thermoelastic damping effect of the micro-ring resonator with irregular mass and stiffness

Fundamentally, vibration characteristic is a main factor for the stability of structures. In this regard, the irregularity of mass and stiffness distributions for the structure have been an interesting issue for many years. Recently, the Micro Electro Mechanical Systems (MEMS) are developed for various applications such as gyro sensors. In the present work, in-plane vibration of micro-ring structure with multiple finite-sized imperfections is investigated. Then, the unbalance of the structure is represented using Heaviside Step Function for the inextensional modeling of the ring. Also, thermoelastic damping (TED) due to internal friction is studied based on Fourier׳s one-dimensional heat conduction equation using Laplace Transform. To obtain the quality-factors (Q-factors) for imperfect micro-ring, analytical solutions are calculated from governing equations of motion with TED. And then, the natural frequencies and the Q-factors are observed to separate into lower and higher modes. Additionally, the vibration mode shapes are presented, and the frequency trimming concept due to attached imperfections is investigated.