Nonlinear free vibration analysis of generic coupled induced strain actuated piezo-laminated beams
Piezo-laminated thin beams have been analyzed with induced strain actuation using Kirchhoff’s hypothesis and von Kármán strain displacement relations. Extremizing the Lagrangian of the system derives the governing nonlinear partial differential equations for the beam. Eliminating the in-plane displacement, an integro-partial differential equation of motion is obtained in terms of the transverse displacement. A deflection function that satisfies the simply supported boundary conditions is assumed to get the system equation as a nonlinear second order ordinary differential equation in time, which is of Duffing’s type. The solution of the problem is obtained through exact integration. Results are presented for frequency and amplitude for surface bonded PZT-5A layer in composite beams with various stacking sequences.