In-plane Band Gaps in a Periodic Plate with Piezoelectric Patches

A plate periodically bonded with piezoelectric patches on its surfaces is considered. The differential quadrature element method is used to solve the wave motion equation for the two-dimensional periodic structure. The method is very simple and easy to implement. Based on the method, band structures for in-plane wave propagating in the periodic piezoelectric plate are studied, from which the frequency band gap is then obtained. Parametric studies are also performed to highlight geometrical and physical parameters on the band gaps. It is found that the thickness of the piezoelectric patches have no effect on the upper bound frequency of the band gap. Physical mechanism is explained for the phenomena. Dynamic simulations are finally conducted to show how the band gap works for a finite quasi-periodic plate. Numerical results show that the vibration in periodic plates can be dramatically attenuated when the exciting frequency falls into the band gap.