Analysis of quasi-periodic and chaotic motion of a dielectric elastomer shell under alternating voltage

The nonlinear dynamical behaviors are investigated for the dielectric elastomer (DE) spherical shell subjected to the internal pressure and alternating voltage, where the shell is composed of the incompressible hyperelastic material described by the third-order Ogden model. Considering the initial boundary conditions, the incompressible constraint and the Euler-Lagrange equation, the governing equations describing the radially symmetric motions for the dielectric elastic spherical shell are derived. Employing the qualitative analyses and numerical calculations, the dynamical response analyses of the nonlinear system are conducted. The effects of the direct current (DC) voltage and the uniformly distributed pressure on the quasi-periodic and chaotic motion for the DE spherical shell are discussed. The results indicate that the DC voltage and internal pressure have significant effects on the nonlinear oscillation of the shell. The critical values of the DC voltage and the internal pressure are presented for the shell undergoing the chaotic motions. The changes of the DC voltage and internal pressure, the corresponding critical values will increase or decrease. The present study may provide theoretical and practical significances for the design and applications of the DE structures.