In this study, we intend to introduce a nonlinear dynamic theory for analyzing dynamic behavior of plate-like polypyrrole-based trilayer actuators for the first time. Within the displacement field of a first-order shear deformation plate theory and contemplating the nonlinear strain–displacement relations, nonlinear equations of motion are derived using Hamilton’s principle. The nonlinear governing equations are solved using the generalized differential quadrature method together with Newmark’s time integration scheme and the Newton–Raphson iterative method. For the assessment of the accuracy of the present theory, experimental data available in the literature are utilized. Two types of boundary conditions for both steady-state and dynamic analyses are investigated. The present results indicate the importance of considering geometric nonlinearity in the system.