  Topological insulators, which allow edge or interface waves but forbid bulk
waves, have revolutionized our scientific cognition of acoustic/elastic
systems. Due to their nontrivial topological characteristics, edge
(interface)waves are topologically protected against defects and disorders.
This superior and unique characteristic could lead to a wealth of new
opportunities in applications of quantum and acoustic/elastic information
processing. However, current acoustic/elastic topological insulators are still
at an infancy stage where the theory and prediction only work in laboratories
and there are still many problems left open before promoting their practical
applications. One of the apparent disadvantages is their narrow working
frequency range, which is the main concern in this paper. We design a
one-dimensional phononic beam system made of a homogeneous epoxy central beam
sandwiched by two homogeneous piezoelectric beams, and covered with extremely
thin electrodes, periodically and separately placed. These electrodes are
connected to external electric circuits with negative capacitors. We show that
a topological phase transition can be induced and tuned by changing the values
of the negative capacitors. It follows that the working frequency of the
topologically protected interface mode can be widely changed, such that the
working frequency range of the topological insulator can be considerably
`broadened'. This intelligent topological device may also find wide
applications in intelligent technologies that need controllable information
processing of high precision.
