Nonlinearities in Langevin transducers

At frequencies close to resonance, Langevin transducers exhibit strong nonlinearities at low voltage levels. First, characteristic phenomena of a nonlinear behavior, such as the resonance frequency shift and the hysteresis effect, appear. Moreover, these nonlinearities result in an electrical and mechanical energy spreading over a discrete spectrum. Experimental results for current and tail mass displacement are given for power piezomaterial. They show a saturation of the fundamental amplitude due to the increase of the overtones amplitudes. To interpret these experimental results, a nonlinear oscillator model, based on nonlinear piezoelectric relationships, has been developed. A numerical solution of this nonlinear Langevin equation is given. Simulations and experimental results are in good agreement