Abstract
In this paper, two models of elastic metamaterial containing one and two resonators are proposed to obtain the bandgaps with the aim of providing broadband vibration suppression. The model with one DOF is built by assembling several unite cells in which each unite cell consists of a rectangular frame as the base structure and a rack-and-pinion mechanism that is joined to the frame with a linear spring on both sides. In the second model with two DOF, a small mass is added while its center is attached to the center of the pinion on one side and the other side is connected to the rectangular frame via a linear spring. In the first mechanism, the pinion is considered as the single resonator, and in the 2DOF model, on the other hand, the pinion and small mass acted as multiple resonators. By obtaining the governing equations of motion for a single cell in each model, the dynamic behavior of two metastructures is thoroughly investigated. Therefore, the equations of motion for the two models are written in matrix form, and then, the dispersion relations are presented to analyze the influences of system parameters on the bandgaps’ starting/ending frequencies. Finally, two models are successfully compared and then numerically simulated via MATLAB-SIMULINK and MSC-ADAMS software. With the aid of closed-form expressions for starting/ending frequencies, the correlation between the system parameters and bandgap intervals can be readily recognized.
Highlights
Metamaterials are referred to the types of advanced materials that are synthetically made including small substructures which generally behave like a continuous material. e frequency bands at which acoustic and elastic waves cannot propagate are called bandgap, which is the most prominent feature of metamaterials. e propagation of waves of different wavelengths is controlled by the low/high-frequency bandgaps generated by the metamaterials
A model of two degrees of freedom of elastic metamaterials (EMM) is presented. is model is an extended model of the first model discussed in the previous section. e unite cell of the model is made of rectangular frames with a rackand-pinion inside it connected to a concentrated mass
At first, a new model of elastic metamaterials (1DOF model) involving a rack-and-pinion mechanism was presented. en, by adding a concentrated mass, the model was modified by converting to a novel metastructure with multiple resonators in which more broadband bandgaps were produced
Summary
Two models of elastic metamaterial containing one and two resonators are proposed to obtain the bandgaps with the aim of providing broadband vibration suppression. e model with one DOF is built by assembling several unite cells in which each unite cell consists of a rectangular frame as the base structure and a rack-and-pinion mechanism that is joined to the frame with a linear spring on both sides. E model with one DOF is built by assembling several unite cells in which each unite cell consists of a rectangular frame as the base structure and a rack-and-pinion mechanism that is joined to the frame with a linear spring on both sides. In the second model with two DOF, a small mass is added while its center is attached to the center of the pinion on one side and the other side is connected to the rectangular frame via a linear spring. The pinion is considered as the single resonator, and in the 2DOF model, on the other hand, the pinion and small mass acted as multiple resonators. Erefore, the equations of motion for the two models are written in matrix form, and the dispersion relations are presented to analyze the influences of system parameters on the bandgaps’ starting/ending frequencies. With the aid of closed-form expressions for starting/ending frequencies, the correlation between the system parameters and bandgap intervals can be readily recognized
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