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

Abstract

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.

Vibration and Buckling of Shear Deformable Functionally Graded Nanoporous Metal Foam Nanoshells

“…Functionally graded materials (FGMs) have a continuous and smooth graded distribution of material properties in the spatial field. Due to their superior properties and advantages, FGMs have been successfully extended to various engineering applications and received much attention [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ]. Recently, a breakthrough made it possible to realize desired structural properties by adjusting the local density of structures, thereby developing novel functionally graded (FG) porous structures composed of metal foams having graded density [ 25 , 26 , 27 , 28 ].…”

A widespread internal resonance phenomenon in functionally graded material plates with longitudinal speed

“…12 studied nonlinear dynamics of FGM plates using pseudo-arc-length continuation technique. Wang and Zu 13 presented broadband vibration of traveling piezoelectric FGM plates. Zhang et al .…”