On guided circumferential waves in soft electroactive tubes under radially inhomogeneous biasing fields

Soft electroactive (EA) tube actuators and many other cylindrical devices have been proposed recently in literature, which show great advantages over those made from conventional hard solid materials. However, their practical applications may be limited because these soft EA devices are prone to various failure modes. In this paper, we present an analysis of the guided circumferential elastic waves in soft EA tube actuators, which has potential applications in the in-situ nondestructive evaluation (NDE) or online structural health monitoring (SHM) to detect structural defects or fatigue cracks in soft EA tube actuators and in the self-sensing of soft EA tube actuators based on the concept of guided circumferential elastic waves. Both circumferential SH and Lamb-type waves in an incompressible soft EA cylindrical tube under inhomogeneous biasing fields are considered. The biasing fields, induced by the application of an electric voltage difference to the electrodes on the inner and outer cylindrical surfaces of the EA tube in addition to an axial pre-stretch, are inhomogeneous in the radial direction. Dorfmann and Ogden's theory of nonlinear electroelasticity and the associated linear theory for small incremental motion constitute the basis of our analysis. By means of the state-space formalism for the incremental wave motion along with the approximate laminate technique, dispersion relations are derived in a particularly efficient way. For a neo-Hookean ideal dielectric model, the proposed approach is first validated numerically. Numerical examples are then given to show that the guided circumferential wave propagation characteristics are significantly affected by the inhomogeneous biasing fields and the geometrical parameters. Some particular phenomena such as the frequency veering and the nonlinear dependence of the phase velocity on the radial electric voltage are discussed. Our numerical findings demonstrate that it is feasible to use guided circumferential elastic waves for the ultrasonic non-destructive online SHM to detect interior structural defects or fatigue cracks and for the self-sensing of the actual state of the soft EA tube actuator.