A semi-analytical method for vibration localization of plates integrated with low-frequency plate-type resonators

Abstract

A plate-type local resonator with varying free boundaries is integrated within the plate to transform the initial low-order global vibration modes into localized vibration modes. A novel semi-analytical method is proposed to analyze the free vibration of the plate with discontinuities in thickness and displacement. The host plate and the resonator are modeled separately and coupled by the condition of displacement compatibility, based on the geometry configuration. A set of local admissible functions, consisting of global and local parts in the resonator domain, is proposed to describe the vibration localization and displacement discontinuity. The Ritz method with the proposed admissible functions is employed to investigate the effect of geometry parameters and boundary conditions on the vibration characteristics of the plates. The lack of orthogonality between the global and localized modes is determined using the analytic mode functions obtained by the proposed method and can be altered by the free boundary conditions of the resonator. The results demonstrate that by applying free boundary conditions to a resonator, the low-order localized vibration frequencies can be significantly reduced by up to 90 %, with negligible effect on low-order global frequencies. An original and exciting finding is that the global modes can be assimilated by the corresponding localized vibration modes with close frequencies.