In this paper, we introduce a nonlinear dynamic substructuring technique to efficiently evaluate nonlinear systems with localized nonlinearities in the frequency domain. A closed-form equation is derived from coupling the dynamics of substructures and nonlinear connections. The method requires the linear frequency response functions of the substructures, which can be calculated independently using reduced-order methods. Increasing the number of linear bases in the reduction method for substructures does not affect the number of nonlinear equations, unlike in component mode synthesis techniques. The performance of the method is evaluated through three case studies: a lumped parameter system with cubic nonlinearity, bars with a small gap (normal contact), and a plate with a couple of nonlinear energy sinks. The results demonstrate promising accuracy with significantly reduced computational cost.

中文翻译：

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频域中的非线性动态子结构


在本文中，我们介绍了一种非线性动态子结构技术，以有效地评估在频域中具有局部非线性的非线性系统。闭式方程是通过对子结构和非线性连接的动力学进行耦合而得出的。该方法需要子结构的线性频率响应函数，可以使用降阶方法独立计算。与组件模式合成技术不同，在子结构的简化方法中增加线性碱基的数量不会影响非线性方程的数量。该方法的性能通过三个案例研究进行评估：具有三次非线性的集总参数系统、具有小间隙的杆（法向接触）和具有一对非线性能量汇的板。结果表明，计算成本显著降低，准确性有希望。