Optimal Design Of Low Frequency Vibration Reduction Of Multi-resonators Coupled Periodic Superstructure

A variety of periodic superstructures coupled with different local resonators are proposed,and the bandgap mechanism,bandgap law,vibration reduction optimization design and practical application are studied by means of theoretical research,numerical analysis and experimental verification.The optimized periodic superstructures with low-frequency and broad bandgap characteristics are obtained,and they are comprehensively applied to the metro vehicles floor for low-frequency and broad bandgap vibration reduction.The bandgap mechanism and characteristics of different hybrid series/parallel coupled periodic superstructures are studied.Based on single resonator periodic superstructure,one-dimensional series,parallel and hybrid coupling resonators periodic superstructure are proposed by increasing the number of resonator and changing the configuration of resonators.The low frequency bandgap characteristic and mechanism of periodic superstructures are studied from three aspects: theoretical research,numerical analysis and experimental verification.The dispersion relation of periodic superstructure is calculated by the lumped mass method.In the passband and bandgap frequency range,the displacement magnitude and direction of each mass in unit cell of periodic superstructures are studied to clarify the bandgap mechanism,and the parameter analysis is carried out to further study the key factors affecting the bandgap.The bandgap characteristics of three kinds of periodic superstructures with different resonator configurations are compared with the single resonator periodic superstructure.The bandgap of Hybrid Series MODEL Ⅱ achieves 14.5% lower and 81% wider while the bandgap of Hybrid Parallel MODEL Ⅱ achieves 163% wider than that of single resonator periodic superstructure with the same mass and stiffness.The innovative windmill-like periodic superstructures with multiple resonators is proposed to open the multiple low-frequency bandgaps.The bandgap forming mechanism is explored by dispersion curves and eigenmodes.Then,the bandgap structures of the windmill-like periodic superstructures with different number,symmetry and structural parameters of resonators with the same total mass are compared.Finally,the symmetrical and chiral windmill-like periodic superstructures are proposed.The bandgap starting frequency of chiral windmill-like periodic superstructures is 23.08% lower than that of symmetric windmill-like periodic superstructures.The total bandgap width of chiral windmill-like periodic superstructures is 50% wider than that of symmetric windmill-like periodic superstructures.The application of two-dimensional symmetrical windmill-like periodic superstructure in low-frequency vibration reduction of metro vehicles is preliminarily explored.Through numerical analysis and vibration experiment,it is concluded that the symmetrical windmill-like periodic superstructure can suppress the low-frequency vibration below 200 Hz in a broad frequency bandgap.The present studies have further benefit for the application of periodic superstructure in low frequency vibration reduction.