Nonlinear Vibration and Chaos Analysis of Hyperelastic Combined Cantilever Plates

In this work, the nonlinear forced vibration response of a hyperelastic combined cantilever plate is investigated. The plate consists of two irregular quadrilaterals and is under a uniformly distributed load perpendicular to the midplane. First, two irregular quadrilateral regions are projected into two rectangular regions by the iso-parametric element transformation. Then the nonlinear ordinary differential governing equations is obtained by the thin-plate theory, and Lagrange variational principle. In addition, the chaotic behavior is analyzed by the bifurcation diagram, Poincaré map, phase diagram, and maximum Lyapunov exponent. The results indicate that the amplitude and frequency of the external excitation have a significant effect on the nonlinear vibration, each of which can excite the chaotic response. Furthermore, it is found that the varying geometric parameters generate a larger chaotic region compared to the varying external excitation parameters. In summary, this study provides theoretical references for the excitation strategy and structural design of hyperelastic combined cantilever plates.