The Dynamics Research Of Piezoelectric Cantilever Beam

Because piezoelectric material has unique piezoelectric effect, it is often used inenergy collector. Based on the piezoelectric cantilever beam, the nonlinearcharacteristics of piezoelectric structure are studied. Double crystal cantilever beamstructure is adopted, considering geometric nonlinearity and the inverse piezoelectriceffect. Under the influence of nonlinear factors, complex nonlinear dynamics behaviorwill be appeared, this kind of random vibration can cause failure behavior such asfatigue and buckling, thus affects its power output.When the piezoelectric structure is simplified into a bimorph cantilever beammodel, the geometrical nonlinearity and piezoelectric constitutive relationship areconsidered in the modeling process. The nonlinear governing equation is derived byHamilton principle, and the averaged equation is obtained through Galerkin methodand the asymptotic perturbation method. The numerical analysis is given based on theaveraged equation of the piezoelectric cantilever beam. The content of this paper canbe summarized as following chapters.(1) First, the piezoelectric structure is simplified into a bimorph Euler-Bernoullicantilever beam. The nonlinear dynamical equation of the piezoelectric cantileverbeam is conducted. The nonlinear geometrical deformation and piezoelectricconstitutive relationship are considered. The harmonic translation is subjected at thebase of the beam, and a proof mass is presented at the end. The nonlinear governingequation of the transverse vibrations of the piezoelectric beam is derived byHamilton principle and the Galerkin method.(2) Frequency response behavior of the piezoelectric cantilever beam is studied,after the averaged equation of the transverse vibrations of the piezoelectric beam isderived by the asymptotic perturbation method. The numerical simulation which thevibration amplitude, vibration frequency, damping and piezoelectric parameter areselected as controlling parameter. The stability analysis is delivered based on thefrequency response curve of the system. The results show that system may havemultiple solutions, and shows soft spring characteristics or hard spring characteristics.(3) The chaos dynamic analysis is investigated for the case of1:2internalresonance. The averaged equations of the piezoelectric beam are obtained by theasymptotic perturbation method. The numerical simulation which the vibrationamplitude, vibration frequency, damping and piezoelectric parameter are selected ascontrolling parameter, Phase portrait, wave form and Poincare section are given in thenumerical simulation. Numerical results show that the periodic motion and chaoticmotion system can appear alternately.(4) The modal and harmonic analysis are obtained by using the finite element method, the first four order resonance frequency are derived under the differentstructural dimensions and material parameters, the influence of these factors on thepiezoelectric Resonance frequencies, vibration modes and the output voltage arestudied. As Supplement for previous theory analysis, certain references are providedabout the relationship between the energy output and the mechanics properties of thestructure by using the finite element simulation.