Using kinetic and strain energies of mindlin plates for vibration mode identification

Abstract

In the study of vibrations of quartz crystal resonators, one important requirement is that the analysis of coupled vibrations, which is closely related to the identification of optimal functioning mode for the design. Vibration modes can be identified through displacement patterns by plotting vibration amplitude of coupled modes. If there is a large set of data, especially with the finite element method, the mode identification process will become time consuming. We propose a new method by using strain and kinetic energy to identify vibration modes. Through calculating the kinetic and strain energies of plates within a given frequency range, the energy concentration in each vibration mode is calculated. At peaks of energy distribution, we can designate the mode with the highest energy concentration at a specific mode as the dominant mode. This energy approach will be utilized in the finite element analysis for vibration mode identification without plotting and comparison vibration amplitudes.