Effect of Boundary Conditions on Vibration Characteristics of a Sandwich Plate with Viscoelastic Periodic Cores

The effects of boundary conditions on the vibration characteristics of a sandwich plate with viscoelastic periodic cores were examined. The tangential, vertical, transverse, and torsional springs were utilized to restrict the sandwich plate’s edge in order to model a general boundary condition, bringing the benefit that the conventional free, clamped, and simply supported boundary conditions became special cases in the proposed model as these spring constants took extreme values. A theoretical model was established to calculate the forced response and band structure of the periodic sandwich plate, providing computational support for evaluating its vibration characteristics. The correctness of the theoretical model was also validated by the finite element method. The results show that the boundary spring stiffness has a significant effect on the band-gap frequencies and band-gap width of the periodic sandwich plate. Increasing the boundary spring stiffness contributes to achieving broader band gaps. In addition, the band-gap frequencies and band-gap width are more sensitive to transverse spring stiffness than the tangential, vertical, and torsional spring stiffnesses. Therefore, changing transverse spring stiffness is more effective for adjusting the band gap property. This study may provide helpful guidance on vibration and noise reduction design in engineering.