Abstract 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.

中文翻译：

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均匀和均匀变化的单耦合周期结构的二次常数的解析性质

摘要 本研究考虑单耦合周期机械系统的波动分析和控制，重点关注作为拉普拉斯变换变量 s 解析函数的次级常数（传播常数和特征阻抗）的性质。在一般的波浪分析过程中，我们从系统动力学中推导出二次常数，并评估谐波激励的稳态响应（谐波分析）。这对应于在虚轴 s = j ω 上的一个点上评估传递函数。如果二次常数定义为开右半平面 (RHP) 中的解析常数，则提供正确答案；然而，如果奇点存在，则结果无效。本研究针对这个问题，并揭示了二次常数实际上可以定义为开放 RHP 中的解析常数，并且可以满足几个所需的属性。我们首先调查统一案例，然后将程序应用于非统一案例。我们推导出一个应用于波浪分析的系统条件，并证明几个均匀变化系统的串联连接满足这个条件。给出了一个数值例子来说明阻抗匹配控制器用于振动控制的结果和有效性。