Dynamical behavior of a particle_doped multi-segment dielectric elastomer minimal energy structure

The dynamic behavior of dielectric elastomers (DEs) has significant influence on their performance. The present study investigates the nonlinear dynamics of particle_doped multi-segmented DE minimum energy structures (DEMESs). To simulate the multi-segment DEMES, we consider each segment as a combination of hyperelastic film and elastic beam and obtain the ordinary differential equations governing the system dynamics based on the Euler–Lagrange equations. Due to the difficulty in measuring various physical parameters of DEs in practice, we utilize experimental data from a single-segment DE and employ a physics-informed neural network to predict the unknown parameters of the DE and the framework, such as stiffness K _bb and doping volume fraction ϕ. Based on these predictions, nonlinear analysis is performed for the multi-segment system. Stability analyses of the motion equations reveal that the system exhibits a supercritical pitchfork bifurcation with hyperelastic thin film pre-stretching as the bifurcation parameter. For the three-segment DEMES, there are eight stable modes, but only four are illustrated in the bifurcation diagram due to the identical parameter settings for each segment. The amplitude-frequency curves under different AC voltage loads indicate the presence of harmonic, superharmonic, and subharmonic resonances in the system, with varying frequencies and magnitudes depending on the applied load. The Poincaré maps of the time response demonstrate that the system response is predominantly quasiperiodic. Under low voltage loads, the system exhibits periodic oscillations, while under certain high voltage loads, chaotic behavior emerges, characterized by strong nonlinearity in the time-dependent curves and non-periodicity in the Poincaré maps. This study provides insights into the present mathematical model in the motion control of DEMES.