Primary resonance of piezoelectric resonators

It is found that the nonlinear behavior of piezoelectric resonators is more complicated than that predicted by previous theories. Actually the resonators work as parametrically excited vibration systems. Mode-coupled equations are obtained by means of the boundary integration. The method of multiple scales is used to solve the equations. Finally the ordinary differential equations that govern the evolution of the amplitude and phase of the fundamental and the harmonics, respectively, are derived. The nonlinear behavior of the resonator in the vicinity of primary resonance is thoroughly studied. Experiments are conducted for thickness-vibration LiNbO₃ resonators. For comparison, the behavior at the parametrically resonant regime is also discussed