  The operating frequency range of passive topological phononic crystals is
generally fixed and narrow, limiting their practical applications. To overcome
this difficulty, here we design and investigate a one-dimensional soft
dielectric phononic crystal (PC) plate system with actively tunable topological
interface states via the mechanical and electric loads. We use nonlinear
electroelasticity theory and linearized incremental theory to derive the
governing equations. First we determine the nonlinear static response of the
soft dielectric PC plate subjected to a combination of axial force and electric
voltage. Then we study the motion of superimposed incremental bending waves. By
adopting the Spectral Element Method, we obtain the dispersion relation for the
infinite PC plate and the transmission coefficient for the finite PC plate
waveguide. Numerical results show that the low-frequency topological interface
state exists at the interface of the finite phononic plate waveguide with two
topologically different elements. By simply adjusting the axial force or the
electric voltage, an increase or decrease in the frequency of the topological
interface state can be realized. Furthermore, applying the electric voltage
separately on different elements of the PC plate waveguide is a flexible and
smart method to tune the topological interface state in a wide range. These
results provide guidance for designing soft smart wave devices with
low-frequency tunable topological interface states.
