Dynamic analysis of a piezothermoelastic resonator with various shapes

The resonator is stimulated by piezoelectric ceramics to produce oscillations with frequencies in the ultrasonic region for the ultrasonic motor application. The steady-state temperature rise due to the heat generated by this actuation and its effects on the dynamic behavior of the resonator are investigated. The effect of three different geometry shapes of the resonator is also studied for the resonator design. The piezothermoelasticity theory is applied to model the complex coupled phenomenon of interaction among the mechanical deformation, electric field and temperature distribution. The extended Hamilton's principle is used for formulation and the finite element method is used to approximate the governing equations for numerical simulation. It is found that the resonator expands axially due to this temperature rise and thus the trajectory of the resonator tip has an offset, which is large compared to the axially moving range of the tip trajectory. The shape of the resonator can change a little bit of the temperature distribution in the resonator, but it has large impact on the natural frequencies of the resonator. [S0739-3717(oo)01003-5].