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首页> 外文会议>The 7th China-Japan-Korea joint symposium on optimization of structural and mechanical systems >Using Floquet-Bloch Theory to Research Vibration Characteristics of Composite Material with Trusslike Periodic Micro-structures
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Using Floquet-Bloch Theory to Research Vibration Characteristics of Composite Material with Trusslike Periodic Micro-structures

机译：用浮球理论研究具有桁架状周期微结构的复合材料的振动特性

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Trusslike periodic structures have been considered as a promising alternative to lightweight materials.With careful design of rod size and truss topology within the trusslike periodic unit cell, the periodic structures can also be used to control propagation of elastic waves due to their well-known band gap property. Therefore, this kind of lightweight materials can be designed not only to bear a heavy load but also to insulate vibration.Here, we address the vibration characteristics of composite materials with trusslike periodic micro-structures, i.e.micro parallelepiped unit cells.In order to enhance the effect of insulation of vibration, a kind of high damping polymer materials is filled into the trusslike periodic structures, in this way the whole trusslike periodic structures will present structure damping characteristics, which will result in temporal and spatial attenuations of the elastic waves as they propagate through the trusslike periodic structures.It should be pointed out that the computational method for analyzing the fundamental wave propagation characteristics in undamped trusslike periodic structures have been well-documented by using Floquet-Bloch theory, meanwhile, the analysis method of damped Bloch waves in periodic elastic materials has also been studied recently, which mainly considers temporal attenuations of the elastic waves regardless of spatial attenuations of the elastic waves.Focusing on the insulation of vibration, we present an algorithm for analyzing damped Bloch waves in trusslike periodic structures filled with a high damping polymer material, which mainly considers spatial attenuations of the elastic waves by extending the wave number vector from real numbers to complex numbers.As a result, the algorithm needs to iteratively solve the eigenvalue problem for natural frequencies of unit cells to find the damping coefficients or attenuation coefficients corresponding to each Bloch mode.Meanwhile, for the sake of improving the damping coefficients, drawing inspiration from a mechanical vibration absorber, we embed a heavy sphere into the center of micro parallelepiped unit cell.According to our previous studies, it has been proved that embedding a heavy sphere into the unit cells can greatly improve the damping characteristics of trusslike periodic structures. The paper aims at researching the effect of different parameters of the embedded spheres, including dimension parameters and material parameters, on the vibration characteristics of trusslike periodic structures. The results of numerical examples show when the radius and density of spheres are chosen properly, the band-gap starting and cut-off frequency can drop sharply, the band-gap range can become wider, and the effect of vibration alleviation can be improved much better within a given frequency range.
机译：桁架状的周期性结构被认为是轻质材料的一种有前途的替代品。通过精心设计杆状尺寸和桁架状的周期性晶胞内的桁架拓扑结构，由于其众所周知的频带，周期性结构也可以用于控制弹性波的传播缺口性质。因此，这种轻质材料不仅可以承受重载荷，而且还可以隔离振动。在此，我们针对具有桁架状周期性微结构的复合材料（即微平行六面体晶胞）的振动特性进行研究。在隔振的作用下，一种高阻尼聚合物材料被填充到桁架状的周期性结构中，这样整个桁架状的周期性结构将呈现出结构阻尼特性，这将导致弹性波的时空衰减。应当指出的是，利用Floquet-Bloch理论已经很好地证明了分析无阻尼桁架状周期性结构中基波传播特性的计算方法，与此同时，研究了阻尼Bloch波的分析方法。最近还研究了周期性弹性材料，其中y考虑弹性波的时间衰减而与弹性波的空间衰减无关。基于振动的绝缘性，我们提出了一种算法，用于分析填充有高阻尼聚合物材料的桁架状周期结构中的阻尼Bloch波，该算法主要考虑空间衰减因此，该算法需要迭代求解单位单元固有频率的特征值问题，以找到与每种Bloch模式相对应的阻尼系数或衰减系数。同时，为了提高阻尼系数，并从机械减振器中汲取灵感，我们将重球体嵌入到微平行六面体晶胞的中心。根据我们以前的研究，已经证明将重球体嵌入到微球体的中心。晶胞可以大大改善桁架状周期的阻尼特性ic结构。本文旨在研究嵌入球体的不同参数（包括尺寸参数和材料参数）对桁架状周期性结构振动特性的影响。数值算例结果表明，正确选择球的半径和密度，能带隙的起始和截止频率会急剧下降，能带隙的范围会变宽，减振效果会大大改善。在给定的频率范围内更好。

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