Vibration band gap properties of periodic Mindlin plate structure using the spectral element method

In this paper, vibration band gap properties of periodic Mindlin plate structure with two simply supported opposite edges are studied using the spectral element method (SEM). Based on the Mindlin plate theory (MPT), the spectral Mindlin plate stiffness matrix is deduced. The spectral equation of the whole periodic structure is further established. Frequency responses are calculated by the spectral equations to illustrate band gap properties. Compared with the results based on the classic plate theory (CPT), the effects of the shear and rotary inertia on the band gap properties are analyzed. The results are also compared with those calculated by the finite element method (FEM). It can be observed that the SEM is more accurate in high frequency ranges. Furthermore, the influences of the material properties and structure dimension on the band gap behaviors are investigated.