  Soft electroactive materials can undergo large deformation subjected to
either mechanical or electrical stimulus, and hence they can be excellent
candidates for designing extremely flexible and adaptive structures and
devices. This paper proposes a simple one-dimensional soft phononic crystal
cylinder made of dielectric elastomer to show how large deformation and
electric field can be used jointly to tune the longitudinal waves propagating
in the PC. A series of soft electrodes are placed periodically along the
dielectric elastomer cylinder, and hence the material can be regarded as
uniform in the undeformed state. This is also the case for the uniformly
pre-stretched state induced by a static axial force only. The effective
periodicity of the structure is then achieved through two loading paths, i.e.
by maintaining the longitudinal stretch and applying an electric voltage over
any two neighbouring electrodes, or by holding the axial force and applying the
voltage. All physical field variables for both configurations can be determined
exactly based on the nonlinear theory of electroelasticity. An infinitesimal
wave motion is further superimposed on the pre-deformed configurations and the
corresponding dispersion equations are derived analytically by invoking the
linearized theory for incremental motions. Numerical examples are finally
considered to show the tunability of wave propagation behavior in the soft PC
cylinder. The outstanding performance regarding the band gap (BG) property of
the proposed soft dielectric PC is clearly demonstrated by comparing with the
conventional design adopting the hard piezoelectric material. Note that soft
dielectric PCs are susceptible to various kinds of failure (buckling,
electromechanical instability, electric breakdown, etc.), imposing
corresponding limits on the external stimuli.
