Dynamic properties of three-dimensional piezoelectric Kagome grids

Piezoelectric Kagome grids can be considered as a kind of functional material because they have vibration isolation performance and can transform mechanical energy to electric energy. In this study, the dynamic properties of three-dimensional (3D) piezoelectric Kagome grids without and with material defects are studied based on the frequency-domain responses. The spectral element method (SEM) is adopted to solve a 3D piezoelectric beam which contains bending components in two planes, tensional components, and torsional components. The dynamic stiffness matrix of a spectral piezoelectric beam is derived. Highly accurate solutions in the frequency-domain are obtained by solving the equation of motion of the whole structure. Compared with the results from the FEM and those in the existing literature, it can be seen that the SEM can be effectively used to study the 3D piezoelectric Kagome grids. The band-gap properties of Kagome grid and defect state properties of Kagome grid with material defects are analyzed. The effect of the piezoelectric parameter on the band-gap property is investigated further.