nonlinear free vibrations analysis of a piezoelectric bimorph nanoactuator using nonlocal elasticity theory

In this paper, the nonlinear free vibrations of a bimorph piezoelectric nanoactuator is studied based on nonlocal elasticity. The Euler-Bernoulli beam theory and Hamilton’s principle are used to derive the equation of motion of the actuator. In order to obtain the reduced-order form of equations, the Galerkin method is used. The mode shapes of a multi-span beam are used for a faster convergence. The nonlinear natural frequencies are obtained by using He’s variational approach. Equations are solved for clamped-clamped boundary conditions, and the effects of values of DC voltage, actuator length and thickness, length of piezoelectric layers and nonlocal parameter on the nonlinear natural frequencies are studied. The results show that applying a DC voltage induces a static deflection and an increase in the stiffness of the actuator. Therefore, the natural frequency increases. Moreover, increasing the nonlocal parameter decreases the rate of change in frequency variation. An increase in the nonlocal parameter or the length of the actuator increases the nonlinear to nonlinear natural frequency ratio. Finally, the effect of the middle layer material of the actuator on the frequency ratio is studied.