Forced coupling vibration analysis of FBAR based on two-dimensional equations associated with state-vector approach

In our previous work, a system of two-dimensional equations for piezoelectric thin-film acoustic wave resonators (FBAR) has been derived and then successfully applied on the free vibration analysis of a finite FBAR plate. In this paper, we analyzed the forced vibrations of FBAR with alternating voltage applied on its electrodes. The derived two dimensional equations were simplified based on straight-crested wave approximations and were rewritten into matrix formalism by state-vector approach. With the knowledge of matrix function, the state-vector equation was successfully solved. Results of admittance were obtained with the dependence on the driving frequency and the aspect ratio. The obtained figure was compared with the frequency spectra obtained in free vibration analysis. Different aspect ratios and quality factors were taken to study the effects of them on the admittance. It is shown that admittance is highly influenced by mode couplings. Thus the work in this paper will be important for the thorough understanding of the coupling vibration of FBAR and its optimization design