Vibration band-gap properties of three-dimensional Kagome lattices using the spectral element method

The spectral element method (SEM) is extended to investigate the vibration band-gap properties of three-dimensional (3D) Kagome lattices. The dynamic stiffness matrix of the 3D element which contains bending, tensional and torsional components is derived. The spectral equations of motion of the whole 3D Kagome lattice are then established. Comparing with frequency-domain solutions calculated by the finite element method (FEM), the accuracy and the feasibility of the SEM solutions are verified. It can be shown that the SEM is suitable for analyzing the vibration band-gap properties. Due to the band-gap characteristics, the periodic 3D Kagome lattice has the performance of vibration isolation. The influences of the structural and material parameters on the vibration band-gaps are discussed and a new type of 3D Kagome lattice is designed to obtain the improved vibration isolation capability.