Study on low-frequency vibration and noise mitigation performance of a multi-bandgap locally resonant meta-plate

Low-frequency vibration and noise control remains a critical challenge in modern engineering. Traditional vibration damping measures often fail to achieve effective low-frequency and multi-band suppression, and are further constrained by high added mass and restricted installation space. This study proposes a multi-bandgap locally resonant metamaterial plate (meta-plate) that generates three low-frequency bending wave bandgaps below 300 Hz by integrating multiple cantilever-mass resonators with varying geometric parameters. A theoretical bandgap model and a finite element model (FEM) are established to calculate the bandgaps and elucidate the underlying physical mechanism. The theoretical and simulation results show excellent agreement, with center frequency errors below 7%. Subsequently, a transmission loss test is conducted on a 4 × 4 periodic meta-plate array to determine the actual attenuation ranges, thereby verifying the theoretical model and FEM results. Furthermore, impact vibration and sound radiation tests are performed on a simply supported steel plate to evaluate the vibration attenuation and noise reduction performance of the meta-plate in practical structural applications. The results indicate that after installing the meta-plate, both the vibration response and radiated sound pressure are significantly suppressed. Within the bandgap ranges, the vibration amplitude attenuation reaches 20 dB, and the peak attenuation of radiated sound exceeds 15 dB. The localized resonance of the cantilever-mass resonators is identified as the key mechanism responsible for vibration and noise reduction. This study provides a theoretical foundation and experimental evidence for low-frequency vibration and noise mitigation in engineering applications, as well as for the design and application of metamaterial structures.