Vibration localization and reduction of double-plate structures

A thin plate-type resonator is attached to a host-stepped plate to achieve vibration localization and reduction in initial low-order global vibration modes. A semi-analytical method is proposed to analyze the free and forced vibrations of the double-plate structure, considering the geometric configuration's heterogeneity and discontinuity. The double plate structure is divided into several sub-plates for individual modeling, with admissible functions constructed for the displacements of each subdomain. These subdomains are then combined into a unified whole through displacement compatibility conditions. The no-orthogonality between global vibration and localized modes is determined using analytic mode functions obtained by the Ritz method with special admissible functions, which is crucial for suppressing the multiple resonance peaks of global vibration using the integrated plate-type resonator. An intriguing finding is that at the frequency veering point of global vibration modes and localized modes, the non-orthogonality can lead to two coupled global-localized modes that are similar to the initial localized mode, and the vibration of initial global modes can be mainly concentrated in the resonator region outside the plate during free vibration. For force vibration of the double plate, the initial resonance peak splits from one into two smaller resonance peaks due to the two coupled global-localized modes. Furthermore, the coupled global-localized mode allows for a substantial reduction in the host plate vibration while making a negligible impact on the total mass and global vibration frequency. This study presents a promising approach for reducing multimodal vibrations in lightweight structures.