  Material properties of soft electro-active (SEA) structures are significantly
sensitive to external electro-mechanical biasing fields (such as pre-stretch
and electric stimuli), which generate remarkable knock-on effects on their
dynamic characteristics. In this work, we analyze the electrostatically tunable
non-axisymmetric vibrations of an incompressible SEA cylindrical tube under the
combination of a radially applied electric voltage and an axial pre-stretch.
Following the theory of nonlinear electro-elasticity and the associated
linearized theory for superimposed perturbations, we derive the nonlinear
static response of the SEA tube to the inhomogeneous biasing fields for the
Gent ideal dielectric model. Using the State Space Method, we efficiently
obtain the frequency equations for voltage-controlled small-amplitude
three-dimensional non-axisymmetric vibrations, covering a wide range of
behaviors, from the purely radial breathing mode to torsional modes,
axisymmetric longitudinal modes, and prismatic diffuse modes. We also perform
an exhaustive numerical analysis to validate the proposed approach compared
with the conventional displacement method, as well as to elucidate the
influences of the applied voltage, axial pre-stretch, and strain-stiffening
effect on the nonlinear static response and vibration behaviors of the SEA
tube. The present study clearly indicates that manipulating electro-mechanical
biasing fields is a feasible way to tune the small-amplitude vibration
characteristics of an SEA tube. The results should benefit experimental work
on, and design of, voltage-controlled resonant devices made of SEA tubes.
