Herein, we present a novel method for searching anti-resonance frequencies, using an eigenvalue analysis that does not need to search every dip of amplitude in the frequency response function. The eigenvalue equation is derived by utilizing the fact that the solutions of a forced vibration equation are equal to zero at anti-resonance frequencies. The characteristics of the eigenvalue problem are analyzed with a one-dimensional (1D) bar example, and as engineering applications, four numerical examples are presented to demonstrate the computational efficiency and robustness of the proposed method.

中文翻译：

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使用新的特征值公式预测反共振频率

在这里，我们提出了一种使用特征值分析来搜索反共振频率的新颖方法，该特征值分析不需要搜索频率响应函数中每个振幅的下降。特征值方程是通过利用以下事实得出的：在反谐振频率下，强迫振动方程的解等于零。通过一维（1D）条形示例分析了特征值问题的特征，并作为工程应用，给出了四个数值示例，以证明该方法的计算效率和鲁棒性。