  We investigate the nonlinear vibrations of a functionally graded dielectric
elastomer plate subjected to electromechanical loads. We focus on local and
global dynamics in the system. We employ the Gent strain energy function to
model the dielectric elastomer. The functionally graded parameters are the
shear modulus, mass density, and permittivity of the elastomer, which are
formulated by a common through-thickness power-law scheme. We derive the
equation of motion using the Euler-Lagrange equations and solve it numerically
with the Runge-Kutta method and a continuation-based method. We investigate the
influence of the functionally graded parameters on equilibrium points, natural
frequencies, and static/dynamic instability. We also establish a Hamiltonian
energy method to detect safe regions of operating gradient parameters.
Furthermore, we explore the effect of the functionally graded parameters on
chaos and resonance by plotting several numerical diagrams, including time
histories, phase portraits, Poincar\'e maps, largest Lyapunov exponent
criteria, bifurcation diagram of Poincar\'e maps, and frequency-stretch curves.
The results provide a benchmark for developing functionally graded soft smart
materials.
