Low-frequency vibration attenuation of metamaterial sandwich plate with lever-type inertial amplified resonators

The utilization of sandwich plate structures is widespread across diverse engineering fields owing to their advantageous high stiffness-to-weight ratio properties. However, these lightweight and thin-walled structures commonly encounter challenges related to inadequate vibration performance in the low-frequency range, imposing significant limitations on their applications. This paper thereby presents a design for a metamaterial sandwich plate that incorporates lever-type inertial amplified resonators (IA-MSP) to achieve a low-frequency bandgap and effective vibration attenuation capability. The bandgap characteristics and vibration behavior of the IA-MSP are comprehensively studied through an integrated approach involving theoretical analysis, numerical simulations, and experimental studies. The dynamic model of the IA-MSP is mathematically formulated, theoretically elucidating the underlying inertial amplification mechanism within the proposed metamaterial sandwich plates. The investigation on vibration transmission is conducted to analyze the vibration attenuation performance of the IA-MSP, utilizing both numerical simulations and experimental methods. The findings reveal that lever-type resonators amplify the mass motion, thereby enhancing the effective mass of the system and leading to a reduction in the frequency associated with the coupled mode of the bandgap. This amplification facilitates the attainment of a low-frequency bandgap without the need for utilizing the inclusion of additional centralized mass or heavy local resonators. By altering the lever ratio R of the lever-type inertial amplified resonators, precise fine-tuning and optimization of the low-frequency bandgaps are achievable. Compared with traditional metamaterial sandwich plates with local resonators (LR-MSP) featuring identical geometrical and material characteristics, the proposed IA-MSP characterized by an R-value of 2 exhibits boundary frequencies that are half of those observed in the LR-MSP. With an increase in the lever ratio R of the IA-MSP, a noticeable trend emerges a decrease in the lower boundary frequency, accompanied by a corresponding shift of the bandgap towards lower frequencies. The present study's outcomes are anticipated to hold significant promise in the realm of sandwich plate design, with a specific focus on furnishing vibration attenuation capabilities at lower frequencies.