Axisymmetric Free Vibration of Soft Electroactive Circular Plates under Biasing Fields

Soft electroactive materials (SEAMs) with large elastic deformation capacity as well as excellent electromechanical coupling characteristic have attracted increasing attention in the fields of mechanics and related engineering disciplines. Based on the nonlinear theory of electroelasticity and its linearized version for incremental fields, we derive the state-space formulations for small-amplitude free vibrations of an SEAM circular plate under large pre-deformation due to static biasing fields. An exact three-dimensional solution is then obtained by adopting the finite Hankel transform for the plate with an elastic simple support at the circular boundary. The exact solution for an isotropic linear elastic circular plate can be obtained as a particular and degenerated case. The model of generalized neo-Hookean compressible material is considered in numerical simulations. It is found that the natural frequency, while depending on the intrinsic parameters of the plate (e.g., initial thickness and electromechanical coupling coefficients), can be controlled effectively by the extrinsic factors (e.g., pre-stretch and biasing electric displacement). Results further indicate that Euler's instability will occur under a certain combination of the biasing electric displacement and pre-stretch, which should be of practical importance when one intends to tune the dynamic characteristics of a plate by means of external loading.