Analytical properties of secondary constants of uniform and uniformly varying mono-coupled periodic structures
Analytical properties of secondary constants of uniform and uniformly varying mono-coupled periodic structures
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DOI：
10.1016/j.ymssp.2020.106974
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发表时间：
2021
影响因子：
8.4
通讯作者：
K. Nagase;Ayato Doshita;Takuya Midoro
中科院分区：
文献类型：
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作者：
K. Nagase;Ayato Doshita;Takuya Midoro
研究了单耦合周期力学系统的波动分析与控制问题，重点研究了二次常数(传播常数和特征阻抗)的性质作为拉普拉斯变换变量S的解析函数.在一般的波形分析过程中，我们从系统动力学出发，求出了二次常数，并计算了系统在简谐激励下的稳态响应(谐波分析).这对应于计算虚轴上的点S=jω上的传递函数。如果在开右半平面上将次级常数定义为解析的，则给出了正确的答案；但是，如果存在奇点，则结果是无效的。这项研究解决了这个问题，并揭示了在开放的RHP中，二级常数实际上可以被定义为解析的，并且可以满足几个所需的性质。我们首先研究均匀情形，然后将该方法应用于非均匀情形。我们导出了一个应用于波动分析的系统条件，并证明了几个均匀变化系统的串联满足该条件。数值算例验证了阻抗匹配控制器在振动控制中的有效性。
This study considers the wave analysis and control of mono-coupled periodic mechanical systems, focusing on the properties of the secondary constants (propagation constants and characteristic impedances) as analytic functions of the Laplace transform variable s. In a general wave analysis process, we derive the secondary constants from the system dynamics, and evaluate the steady-state response for harmonic excitation (harmonic analysis). This corresponds to evaluating the transfer functions on a point on the imaginary axis s= j ω. A correct answer is provided if the secondary constants are defined as analytic in the open right-half plane (RHP); however, the result is invalid if singularities exist there. This study addresses this issue, and reveals that the secondary constants can actually be defined as analytic in the open RHP and can satisfy several required properties. We firstly investigate the uniform case, and then apply the procedure to the non-uniform case. We derive a system condition to be applied to the wave analysis, and demonstrate that series connections of several uniformly varying systems satisfy this condition. A numerical example is presented to illustrate the results and the effectiveness of the impedance matching controller for vibration control.