Electrostatically tunable axisymmetric vibrations of soft electro-active tubes

Due to their unique electromechanical coupling properties, soft electro-active (SEA) resonators are actively tunable, extremely suitable, and practically important for designing the next-generation acoustic and vibration treatment devices. In this paper, we investigate the electrostatically tunable axisymmetric vibrations of SEA tubes with different geometric sizes. We consider both axisymmetric torsional and longitudinal vibrations for an incompressible SEA cylindrical tube under inhomogeneous biasing fields induced by radial electric voltage and axial pre-stretch. We then employ the state-space method, which combines the state-space formalism in cylindrical coordinates with the approximate laminate technique, to derive the frequency equations for two separate classes of axisymmetric vibration of the tube subjected to appropriate boundary conditions. We perform numerical calculations to validate the convergence and accuracy of the state-space method and to illuminate that the axisymmetric vibration characteristics of SEA tubes may be tuned significantly by adjusting the electromechanical biasing fields as well as altering the tube geometry. The reported results provide a solid guidance for the proper design of tunable resonant devices composed of SEA tubes.