Metamaterial beams with graded two-stage inertial amplification and elastic foundation

Abstract

In this study, a novel local resonant metamaterial (LRM) beam with elastic foundation is proposed by introducing grounded local resonators based on the two-stage inertial amplification structure with adjustable large inertia. The complex band structure is calculated by using the extended plane wave expansion method, and it is found that bandgaps of the novel LRM beam are lower and wider than that of the existing inertant LRM beam. The formation mechanisms of such bandgaps are revealed, and the effects of structural parameters on bandgap characteristics are discussed. Numerical analysis and experimental measurement of vibration transmission characteristics of finite beam structure verify the accuracy of the theoretical results. Furthermore, three kinds of bandgap widening methods based on the structure tunability of local resonator are proposed by setting graded structural parameters. The regularities of bandgap variation with different parameter spacings are given, and the effectiveness of the method is verified by numerical analysis of the finite graded LRM beam under different boundary conditions. These results are expected to provide certain guidance for low and ultra-low frequency broadband flexural waves and vibration control.