Nonlinear dynamics and bifurcation behavior of a sandwiched micro-beam resonator consist of hyper-elastic dielectric film

Abstract

Dielectric elastomers (DEs) are applied in a wide variety of applications at micro electro-mechanical systems (MEMSs). In this study, oscillations and bifurcation of a sandwiched micro-beam resonator, consist of a dielectric hyperelastic core and two layers of elastic electrodes is studied. Free and forced nonlinear vibrations with large amplitudes have been investigated. Material nonlinearity is modeled with the Yeoh hyper-elastic material theory. The governing equation of motion is formulated by means of Hamilton’s principle and then truncated into a reduced-order model through Galerkin’s technique. Approximate analytical solution in the primary resonant case is obtained using multiple time scales (MTS) method. The stabilities of steady-state responses in the vicinity of the equilibrium states and critical buckling voltage are analyzed. Moreover, the bifurcation phenomenon has been studied according to the different values of some control parameters such as the applied DC voltage, the frequency detuning parameter, and the amplitude of the excitation force. The results have been compared with those of some previous studies and can provide a better understanding of the design of dielectric elastomer resonators, which are designed in the form of micro-beam structure.