Vibration characteristics of a sandwich plate with viscoelastic periodic cores

The vibration characteristics of a sandwich plate with viscoelastic periodic cores are examined analytically and experimentally, which extends the previous research of corresponding periodic sandwich beam structure. Closed-form solutions for forced response and band structure of periodic sandwich plate are theoretically derived, providing computational support on the attenuation analysis. In the theoretical model, a new admissible displacement function for sandwich plate is proposed. Although it is used in free boundary condition in this paper, it is also suitable for clamped, simply supported, slipping, and elastic boundary conditions. The formation of the band gap is carefully studied, showing that the overall band gap is proved to be the intersection of all the cross-stream modal band gaps, which is quite different from a corresponding periodic beam structure. The parametric analysis shows further that the overall band gap could disappear when length ratio, element width, or core thickness exceeds a cut-off value, which provides a guidance in the band-gap design. The attenuation in a sandwich plate with viscoelastic periodic cores is mainly dominated by Bragg scattering mechanism in the band gap and by energy dissipation out of the band gap. Owing to the combined effect of both mechanisms, the sandwich plate with viscoelastic periodic cores provides better attenuation performance than that with a uniform viscoelastic core. This research could possibly provide useful guidance for the researches and engineers on the design of plate-type damping structures.