Tunable bandgaps of guided waves by periodic shunting circuits in multilayered piezoelectric plates

Abstract

The multi-mode and dispersion characteristics of guided waves in plate bring great challenges to the manipulation of guided waves and controlling vibration and noise. In this study, the Stroh formalism is developed to establish a theoretical model for deriving the dispersion relations of guided waves in a multilayered piezoelectric plate. The dispersion characteristics under different electrical boundary conditions introduced by periodic shunting circuits are discussed to reveal the influences of external circuits on guided wave propagation. The proper shunting circuit is not only the key point to obtain the specific frequency of bandgap, but also the effective method to control the bandwidth. Furthermore, for the separation of symmetric and anti-symmetric modes of guided waves, the multilayered piezoelectric plate with a mirror plane is studied by using an equivalent model. Results indicate that the propagation behaviors of guided waves in multilayered piezoelectric plates can be interpreted by developed Stroh formalism, and their bandgaps can be effectively manipulated by periodically external circuits. The tunable bandgaps in this work could be helpful for designing smart devices of wave isolation based on multilayered piezoelectric plate.