Analytical solution on the non-linear vibration of a traveling wave ultrasonic motor

A vibration model for the stator of traveling wave type ultrasonic motors has been presented using Kirchhoff plate theory. In this model, the vibration equation influenced by electric field is established based on the geometric equations, the constitutive equations and the balanced equations for the structure. This electric field distribution is assumed based on Maxwell equation. Shearing deformation, rotary inertia and damping of the piezoelectric ceramic are been taken into account. Firstly, the dynamics of the stator is discussed. The mode of the stator is derived and validated by comparing the resonant frequencies and modal shapes with those by finite element analysis. Then, the effect of the piezoelectric ceramic damping is also discussed. Finally, The friction layer is simplified as the axial spring. Using modal shapes as the weight function, the analytic solution under the forced vibration for the stator is computed by Galerkin method. The theoretical model and its analytic solution in this paper contribute to simplifying the model for the parametric study and understanding the vibration between the stator and the rotor.