Research on the low frequency band gap properties of periodically composite stiffened thin-plate with fillers

In this paper, a new composite stiffened thin-plate (CSTP) is developed, the filler is distributed periodically in the viscoelastic damping material (VDM), and the simplified-super-finite-element (SSFM) is employed in the analysis. According to the periodical properties of the CSTP, a primitive cell is extracted, which is divided into six parts according to n-order Lagrangian element (LgE). After each parts' mass, stiffness and damping matrices are obtained, the global matrices are assembled by standard direct stiffness method (SDSM). The filler's mass is considered as lump mass loaded on the defined LgE's nodes, and the filler's number is determined by the LgE's order. Then, the element matrices are simplified and compressed by Bloch's theorem. Finally, the band gap properties of the CSTP are determined according to the eigenvalues problems, and the parameters of the structures (such as the filler's mass, the VDM's damping ratio and the lattice constant, etc.) which affect the band gaps are examined thoroughly. The results show the existence of full band gap (FBG) in low frequency. Meanwhile, the results are validated by the finite element method (FEM), which show good consistency.