Structural dynamic modification is a popular approach to obtain desire frequencies and dynamic characteristics. It has been observed that reanalyzing the modified structure usually involves complicated calculations when modifications are concerned with numerous degrees of freedom (DOFs), especially adding substructures to these DOFs. This paper proposed a method to reanalyze the frequency response functions (FRFs) of structures with multiple co-ordinates modifications. Two different cases are taken into consideration in the modifications, including adding (or decreasing) masses, stiffness, and damping, as well as adding spring-mass substructures, which makes the method more practical. This method is developed by employing Sherman–Morrison and Woodbury (SMW) formula based on the FRFs related to the modifications coordinates of the original system. The advantage of this method is that neither a physical model nor a modal model is required; instead, it needs only the FRFs, which can be directly measured by experimental modal testing. Another salient feature of this proposed strategy is that the FRFs of the modified structure can be calculated in only one step. Validation of this proposed method is demonstrated using various numerical examples. It is shown that the method is very effective and can be considered for real applications.

中文翻译：

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基于谢尔曼-莫里森-伍德伯里公式的基于频响函数的结构再分析

结构动态修改是一种获得所需频率和动态特性的流行方法。已经观察到，当修改涉及多个自由度（DOF）时，尤其是向这些DOF添加子结构时，重新分析修改后的结构通常涉及复杂的计算。本文提出了一种重新分析具有多个坐标修改的结构的频率响应函数（FRF）的方法。修改中考虑了两种不同的情况，包括增加（或减少）质量，刚度和阻尼，以及增加弹簧质量子结构，这使该方法更加实用。该方法是基于与原始系统修改坐标相关的FRF，采用Sherman-Morrison and Woodbury（SMW）公式开发的。这种方法的优点是不需要物理模型和模态模型。相反，它仅需要FRF，可以通过实验模态测试直接对其进行测量。此提议策略的另一个显着特征是，仅需一步即可计算出修改后结构的FRF。使用各种数值示例证明了该方法的有效性。结果表明，该方法非常有效，可以在实际应用中考虑。使用各种数值示例证明了该方法的有效性。结果表明，该方法非常有效，可以在实际应用中考虑。使用各种数值示例证明了该方法的有效性。结果表明，该方法非常有效，可以在实际应用中考虑。