Effect of electrode on the dynamics of electroactive membrane

The dynamics of the electroactive membranes are being studied extensively due to their vast application at the current time. However, the effect of the mechanical behavior of the compliant electrode needs to be addressed. This paper presents the non-linear analysis of an electrically actuated membrane, considering the inertia of the electrode. The membrane is modeled as a hyperelastic material and is assumed to be incompressible, homogeneous, and isotropic. The proposed analysis is discussed in a generalized way for both the compression and suspension phases. Since the membrane is vulnerable to pull-in instability, the conditions to prevent electromechanical instability are defined. Further, an analytical relation is established for breakdown voltage and is validated with experimental data. The analytical solution of axial vibration is presented in the form of elliptic integrals and by the use of multiple scale method in a generalised way for both the phases. The resultant motions and their various physical aspects under suspension and compression phases for general initial conditions are described through graphical results to comprehend the proposed analysis. Also, parameter values are quantified analytically, for which the system executes reverse behaviour in a given configuration.