Voltage‐Controlled Vibrations in Bending‐Deformed Soft Electro‐Active Slabs

The material properties of soft electro‐active (SEA) structures exhibit remarkable sensitivity to external electro‐mechanical biasing fields, such as pre‐stretch and electric stimuli, significantly influencing their dynamic characteristics. This study explores the electrostatically tunable vibrations of an incompressible SEA slab under bending deformation, considering the combined action of radial voltage and axial pre‐stretch. Employing the theoretical framework of nonlinear electro‐elasticity and its linearized perturbation theory, the nonlinear static response of the bending‐deformed SEA slab to applied biasing fields is established, applicable to a general class of energy functions. By using the State‐Space Method, we derive the frequency characteristic equations governing voltage‐controlled small‐amplitude three‐dimensional vibrations. These frequency equations capture a wide spectrum of vibrational modes, ranging from breathing modes to axisymmetric, prismatic diffuse, and non‐axisymmetric vibration modes. Convergence analysis and a finite element analysis are performed to validate the proposed methodology, supplemented by additional numerical investigations that elucidate the effects of applied voltage and axial pre‐stretch on the tunable vibration characteristics of the bending‐deformed SEA slab. This study comprehensively guides the design of tunable cylindrical panel resonators via biasing fields and the utilization of vibration behaviors to characterize the stability of bending‐deformed SEA slabs.