Dielectric elastomers (DEs) are soft electromechanical devices, which operate under a high voltage. The majority of methods for calculating the nonlinear vibration of DEs are the numerical ones. However, the analytical methods may also be capable to achieve the reliable general and specific solutions for DEs. This paper investigates the vibration of a dielectric elastomer balloon (DEB) using the method of multiple scales (MMS). The equations of motion are derived by the method of Euler-Lagrange. Using the Taylor expansion, the governing equation of motion is transformed into a general form, then the MMS is applied to solve the problem. Two cases of voltage are considered; in the first one, the balloon is under a static voltage while in the second one the balloon is under a sinusoidal voltage. When the voltage is static, the time-history responses and the phase diagrams are depicted using the MMS and the Runge-Kutta numerical integration to verify the accuracy of the proposed method. For the sinusoidal voltage, the effect of jump phenomenon and variations of pressure and electrical potential difference (Voltage) on the frequency-response curves are studied. The results show that the MMS is in a good agreement with the Runge-Kutta numerical method. Moreover, with the presentation of various values of the pressure and the electrical potential difference, the softening behavior and the jump phenomenon are observed in the frequency response curves.
