Study On The Primary Resonance Of Laminated Piezoelectric Rectangular Plates

Researches on the vibration of laminated piezoelectric plates have been hot issues and one difficult issue in research process is the vibration under the excited electric field.In this paper the nonlinear behaviors of the piezoelectric material are considered and the vibration characteristics are investigated,then expressions of the response and frequency at the primary resonance are derived and compared with the experiment results to verify the validity.The paper also gives influence factors of the response and frequency.The main contents of this paper are shown as follows:(1) Based on Hamilton's principle and Rayleigh-Ritz method,model of a nonlinear dynamic laminated piezoelectric rectangular plate is established and the governing equations are derived and solved for the thin plate model.The response of the rectangular plate at the primary resonance is investigated with the use of the method of multiple scales.Furthermore,influence factors of the response are derived.(2) The response of laminated piezoelectric rectangular plate at the primary resonance is investigated for the thick plate model.Solutions within the two models are compared and the limitation of the thin plate model is analyzed.(3) The resonance frequency of the laminated piezoelectric rectangular plate is investigated for the thin plate model with the use of mechanics equations.Relationship between the fundamental resonance frequency of the plate and the electric field is given and influence factors of the response frequency are derived.