Research On Bandgap Characteristics And Dynamic Response Of Local Resonance Metamaterial Sla

Due to low-frequency vibration’s strong penetrating power and slow attenuation speed,it has adverse effects on the operating accuracy,service life and even the health of the operator of the equipment in engineering.These adverse effects become especially obvious for low-stiffness structures such as plates and shells.In order to solve this problem,this paper designs a locally resonant monolayer plate structure and a locally resonant sandwich-like plate structure respectively according to the principle of the formation of locally resonant bandgap of phononic crystal,and studies their vibration isolation effects in the lowfrequency bandgap range respectively.The specific research contents are as follows:Firstly,a theory by utilizing the method of differential quadrature is proposed to study the natural vibration characteristics of a rectangular uniform cross-section cantilever Lshaped beam-mass system.The natural frequencies and modes of first five order of the system are obtained by theoretical calculation.The correctness of our theory is verified by a comparative study.After discussing the influence of vibrator’s parameters on the natural frequency,several feasible optimization schemes for reducing the natural frequency of the cantilever L-shaped beam are obtained.It is found that the cantilever L-shaped beam whose natural frequency is lower than the traditional cantilever straight beam can be better applied to the internal vibrator of the locally resonant metamaterial structure,which means that cantilever L-shaped beam-mass system has a good application prospect in the field of lowfrequency vibration and noise reduction.Then,a locally resonant metamaterial sandwich-like plate structure with cantilever Lshaped beam-mass resonators is designed.After solving the natural vibration characteristics of its resonator with the equivalent theory,the dispersion equation of the locally resonant acoustic metamaterial sandwich-like plate structure is established according to the Hamilton’s principle and the thin plate theory,and a locally resonant bandgap in lowfrequency range can be obtained through theoretical calculation.After the correctness of the result is verified by comparison,the dynamic response of the sandwich-like plate under forced vibration is analyzed by using the finite element software COMSOL,and the influences of the geometry and material parameters of the vibrator and the faceplate,structural damping as well as the boundary condition of the sandwich-like plate on the bandgap characteristics are discussed in detail.At last,we design a locally resonant metamaterial monolayer plate structure with spring-buckling beam-mass quasi-zero-stiffness resonators.After solving the natural frequency of its vibrator and working out the quantitative relation between the geometric and material parameters of the vibrator that meets the quasi-zero-stiffness characteristics,the theoretical bandgap of the locally resonant plate is solved by the plane wave expansion method.Then the Galerkin discretization combined with modal superposition method was used to solve the transmissibility of transverse displacement of the substrate under forced vibration.After verifying the correctness of the theoretical bandgap range,the influences of the precompression ratio of the buckling beam,additional mass,substrate damping,vibrator damping and boundary condition of the structure on the vibration reduction characteristics of metamaterial plates is analyzed through theoretical calculation and finite element simulation by COMSOL.The research results of this paper have important guiding significance for the optimization of bandgap in locally resonant structures.Specifically,they have important reference value and application value in areas such as low-frequency bandgap,widening of bandgap range,and optimization of vibration reduction characteristics within the bandgap range.