Dynamics analysis and design of metamaterial beams with multiple half-sine waves

Abstract

We propose a metamaterial beam having multiple corrugated parts for broad band gaps, study its band gap properties, and investigate the potential of the proposed beam in vibration control with structural strength constraints. First, the spectral element method is used to calculate the band structure and vibration transmission of the metamaterial beam. Numerical results show that band gaps can be tuned flexibly within the low, mid, and high-frequency ranges by changing the design parameters, and demonstrate the trade-off relation between the band gap design and structural strength. Then, an emerging optimization method, the cell mapping method, is applied to study the multi-objective optimal design of the periodic beam, in order to balance low vibration amplitude and high strength. Optimization results illustrate that the Pareto set can provide more options for the design of metamaterial beams, and the optimized structures have much-improved performance for vibration control in targeted frequency bands. Modal analysis is conducted to further understand the vibration attenuation mechanism of the optimized structure, which indicates that the vibration is reduced by the strong local resonance and modal cancellation. Finally, for experimental verification, three metamaterial beams are fabricated and tested with clamped–clamped boundary conditions. Experimental results show the low vibration transmission of each optimized beam within the desired band gaps.