Energy-based nonlinear dynamical modeling of dielectric elastomer transducer systems suspended by elastic structures

This paper presents the Hamilton principle approach to model, design and control mechatronic systems using dielectric elastomer transducers (DET) suspended with elastic structures. An overall dynamical modeling approach for dielectric elastomer-based actuators is presented, taking into account the dynamical effects, e.g., electrical input quantities, inertia, viscous effects, and the nonlinear behavior of DETs and elastic structures. Energy-based techniques are used to obtain a coherent modeling of the electrical and mechanical domains. Based on the variational principle and using the Rayleigh–Ritz method to approximate the field variable, a nonlinear state space model is derived considering various geometric deformations and boundary conditions. The presented approach leads to a set of ordinary differential equations that can be used for control and engineering applications. The proposed method is finally applied to a multilayer DET coupled with a nonlinear buckled beam structure and analyzed based on analytical considerations and numerical simulations.