Band gap property analysis of periodic plate structures under general boundary conditions using spectral-dynamic stiffness method

Vibration band gap properties of periodic rectangular plate structures with general boundary conditions are studied using the spectral-dynamic stiffness method (S-DSM). Material and dimensional properties are assumed to vary periodically in the whole plate structure. In the S-DSM, the general solution governing each unit plate is firstly derived with the aid of spectral method and then the dynamic stiffness matrix is established by substituting the general solution into corresponding boundary equations. Finally, the global spectral dynamic matrix for the whole periodic plate structure is assembled in a similar way to the finite element method (FEM). The harmonic responses are calculated to illustrate the band gap properties of the periodic structures. By comparing the results obtained by the FEM, it can be verified that the S-DSM is of superior accuracy and convergence rate. A parametric study is also conducted to investigate the effects of the material properties, geometrical parameters and structural damping on the vibration band gap behaviors of the periodic structures.