Speed-dependent nonlinear broadband vibrations of smart functionally graded piezoelectric material plates

In this work, speed-dependent nonlinear vibrations of functionally graded piezoelectric material plates are investigated both analytically and numerically. The functionally graded piezoelectric material plates move in the longitudinal direction at a constant speed. The material properties of functionally graded piezoelectric material plates have graded distribution in the thickness direction that obeys a power law. Adopting the Kármán nonlinear geometrical relations, the transverse equation of motion is derived from d’Alembert’s principle by considering the dynamic equilibrium relationships. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. These ordinary differential equations are solved analytically by utilizing the method of harmonic balance. Then, the approximate analytical results are validated by utilizing the adaptive step-size fourth-order Runge–Kutta technique. The stability of approximate analytical solutions is also examined via the perturbation method. Nonlinear frequency-amplitude characteristics show some interesting nonlinear vibration phenomena in the smart structures. Specially, the nonlinear broadband vibration is detected in the translational functionally graded piezoelectric material plates due to the mode interaction. Finally, a parametric study is conducted to reveal the effects of system parameters on the nonlinear vibration characteristics of the translational functionally graded piezoelectric material plates.