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.

具有大的弹性变形能力以及优异的机电耦合特性的软电活性材料（SEAM）在力学和相关工程学科领域引起了越来越多的关注。基于电弹性的非线性理论及其对增量场的线性化形式，我们推导了在静态偏置场作用下大预变形下SEAM圆板在小幅自由振动下的状态空间公式。然后，通过对圆边界处具有弹性简单支撑的板采用有限的汉克尔变换，即可获得精确的三维解。各向同性线性弹性圆形板的精确解可以作为一种特殊且退化的情况来获得。在数值模拟中考虑了广义的新霍克可压缩材料模型。已经发现，固有频率虽然取决于板的固有参数（例如，初始厚度和机电耦合系数），但是可以通过外部因素（例如，预拉伸和偏置电位移）有效地控制。结果进一步表明，在偏置电位移和预拉伸的某种组合下，欧拉的不稳定性将发生，当人们打算通过外部载荷来调整板的动态特性时，欧拉的不稳定性将具有实际意义。可以通过外部因素（例如，预拉伸和偏置电位移）有效地进行控制。结果还表明，在偏置电位移和预拉伸的一定组合下，会发生欧拉不稳定性，当人们打算通过外部载荷来调整板的动态特性时，欧拉的不稳定性将具有实际意义。可以通过外部因素（例如，预拉伸和偏置电位移）有效地进行控制。结果还表明，在偏置电位移和预拉伸的一定组合下，会发生欧拉不稳定性，当人们打算通过外部载荷来调整板的动态特性时，欧拉的不稳定性将具有实际意义。