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A Novel Elastic Metamaterial with Multiple Resonators for Vibration Suppression
Advances in Condensed Matter Physics ( IF 1.5 ) Pub Date : 2021-06-02 , DOI: 10.1155/2021/3914210
Saman Ahmadi Nooraldinvand 1 , Hamid M. Sedighi 1, 2 , Amin Yaghootian 1
Affiliation  

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.

中文翻译:

一种用于抑制振动的具有多个谐振器的新型弹性超材料

在本文中,提出了包含一个和两个谐振器的两种弹性超材料模型来获得带隙,目的是提供宽带振动抑制。具有一个自由度的模型是通过组装多个单元格来构建的,其中每个单元格由作为基础结构的矩形框架和通过两侧线性弹簧连接到框架的齿轮齿条机构组成。在具有两个自由度的第二个模型中,添加了一个小质量,其中心连接到一侧小齿轮的中心,另一侧通过线性弹簧连接到矩形框架。在第一种机构中,小齿轮被视为单个谐振器,而在 2DOF 模型中,小齿轮和小质量块充当多个谐振器。通过获得每个模型中单个细胞的运动控制方程,彻底研究了两个元结构的动态行为。因此,将两种模型的运动方程写成矩阵形式,然后给出色散关系,分析系统参数对带隙起始/终止频率的影响。最后,通过MATLAB-SIMULINK和MSC-ADAMS软件对两个模型进行了成功的比较和数值模拟。借助开始/结束频率的闭合表达式,可以很容易地识别系统参数和带隙间隔之间的相关性。给出色散关系以分析系统参数对带隙起始/结束频率的影响。最后,通过MATLAB-SIMULINK和MSC-ADAMS软件对两个模型进行了成功的比较和数值模拟。借助开始/结束频率的闭合表达式,可以很容易地识别系统参数和带隙间隔之间的相关性。给出色散关系以分析系统参数对带隙起始/结束频率的影响。最后,通过MATLAB-SIMULINK和MSC-ADAMS软件对两个模型进行了成功的比较和数值模拟。借助开始/结束频率的闭合表达式,可以很容易地识别系统参数和带隙间隔之间的相关性。
更新日期:2021-06-02
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