Wave Propagation in L-Shape Beams with Piezoelectric Shunting Arrays

Piezoelectric shunting arrays are employed to control the elastic wave propagation in L-shape beams. Unlike straight beams where longitudinal and flexural waves usually propagate independently, these waves are coupled in an L-shape beam. Based on transfer matrix method and Bloch theorem, dispersion curves and vibration transmissibility are evaluated and analyzed. A locally resonant gap is produced on the flexural and longitudinal waves, respectively, whose locations are nonoverlapped if the shunt damping is void. However, the longitudinal wave band gap can be completely overlaid by the flexural one when a proper shunting resistance is involved. With the decreasing of shunting inductance, the locations of longitudinal and flexural wave gaps both go up to higher frequencies which agree with the variation of resonant frequencies, but they are less affected by shunting resistance. As the resistance increases, the width of the band gaps grows, whereas the attainable maximum attenuation within the band gaps shows a significant decrease. Also, finite element simulations are performed to validate the numerical predictions, which demonstrate that the resulting transmissibility of displacements agree well with the band gaps.