  Acoustic metamaterials, particularly the topological insulators, exhibit
exceptional wave characteristics that have sparked considerable research
interest. The study of imperfect interfaces affect is of significant importance
for the modeling of wave propagation behavior in topological insulators. This
paper models a soft Rayleigh beam system with imperfect interfaces, and
investigates its topological phase transition process tuned by mechanical
loadings. The model reveals that the topological phase transition process can
be observed by modifying the distance between imperfect interfaces in the
system. When a uniaxial stretch is applied, the topological phase transition
points for longitudinal waves decrease within a limited frequency range, while
they increase within a larger frequency scope for transverse waves. Enhancing
the rigidity of the imperfect interfaces also enables shifting of the
topological phase transition point within a broader frequency range for
longitudinal waves and a confined range for transverse waves. The transition of
topologically protected interface modes in the transmission performance of a
twenty-cell system is verified, which include altering frequencies, switching
from interface mode to edge mode. Overall, this study provides a new approach
and guideline for controlling topological phase transition in composite and
soft phononic crystal systems.
