NONLINEAR DYNAMIC ANALYSIS OF PIEZOELECTRIC LAMINATED DISK UNDER STANDING WAVE VIBRATION

Considering the quadratic stiffness in nonlinear constitutive relations of piezoelectric materials, a nonlinear dynamic model of laminated disk affixed with piezoelectric materials is established using Hamilton’s principle and the Rayleigh-Ritz method. Applying the method of multiple scales, the second-order approximation of the primary resonance under standing wave vibration of the laminated disk is investigated. The results show that the second-order primary resonance includes not only the quadratic harmonic but also the direct current components. The second-order approximation can be single or multiple when the excitation frequency changes. The realization of primary resonance lies on the stability conditions and initial conditions. Numerical analysis verifies the feasibility of the analytical analysis.