  We present a methodology to perform inverse analysis on reconfigurable
topological insulators for flexural waves in plate-like structures. First the
unit cell topology of a phononic plate is designed, which offers two-fold
degeneracy in the band structure by topology optimization. In the second step,
piezoelectric patches bonded over the substrate plate are connected to an
external circuit and used appropriately to break space inversion symmetry. The
space inversion symmetry breaking opens a topological band gap by mimicking
quantum valley Hall effect. Numerical simulations demonstrate that the
topologically protected edge state exhibits wave propagation without
backscattering and is immune to disorders. Predominantly, the proposed idea
enables real-time reconfigurability of the topological interfaces in waveguide
applications.
