Nonlinear Dynamics of a Cantilever Beam Actuated by Piezoelectric Layers Available to Purchase

The nonlinear equations of motion for a silicon cantilever beam, covered symmetrically by piezoelectric ZnO layers are derived for voltage excitation. Starting with the nonlinear description of the strain distribution in the beam for finite displacement, the Lagrangeian of the system is obtained from the electric enthalpy density. By application of Hamilton’s principle, the nonlinear equations of motion are consistently derived and truncated to third order for perturbation analysis. The evolution equations are obtained by the multiple scales method and periodic solutions to the equations of motion are determined and discussed with respect to the influence of geometric nonlinearities and nonlinear properties of the piezoelectric layer.