Vibro-acoustic suppression of metamaterial plates in multi-bandgaps

This paper delves into the vibration and acoustic radiation properties of a metamaterial plate integrated with grouped local resonators (GLRs). The GLRs, consisting of multiple spring-mass resonators arranged in various configurations such as series, parallel, and periodic arrangements, are shown to significantly influence the structural performance of the plate. An advanced Fourier series is implemented to articulate the displacement functions and surface acoustic pressure of the plate. By utilizing the energy principle, a vibro-acoustic coupling model is developed to describe the interaction between the metamaterial plate and the external acoustic field. The theoretical framework is rigorously validated against finite element method simulations, yielding highly congruent results. The local resonance bandgap behavior is explored, and the results reveal that the arrangement and connection strategy of the GLRs determine the stopband characteristics. Multiple resonators connected in series lead to an increased number of stopbands and more pronounced attenuation valleys, whereas multiple resonators connected in parallel or arranged in a periodic array result in an unchanged number of stopbands but a significantly wider stopband bandwidth. Furthermore, transmission characteristic assessments substantiate the vibration dampening efficacy of GLRs, and the marked suppressions in flexural wave propagation are demonstrated within the multiple merged bandgaps. These insights advance the comprehension of localized resonance phenomena in metamaterials and inform the development of sophisticated noise and vibration control strategies.