The acceleration effect on the vibration frequency of thickness-shear mode of an infinite isotropic plate

With large accelerations, the mechanical vibrations of device structures can be driven to nonlinear states yielding strong variations of vibration characteristics such as frequency change and modes shape distortions. The exact equation of motion with an external acceleration of the thickness-shear vibrations of an infinite isotropic plate is approximated through the coupling in frequencies and solved with harmonics matching, and the approximate solutions of frequency and displacements due to the acceleration are obtained. The analytical solution with good accuracy is obtained and the frequency variation is evaluated with the simple relationship between deformation, acceleration, and frequency.