Abstract In numerous engineering structures with local nonlinearities, the nonlinear effects are usually localized and most parts of the structures behave linearly. Considering this, a reduced-order modelling technique for generally damped systems with localized nonlinearities is proposed. Firstly, the linear parts with non-proportional damping of the system is separated to form one component, which can be formulated in state space and transformed into the modal coordinates using its linear vibration complex modes. The residual flexibility matrix, which can be formulated by using a set of equivalent higher-order complex modes, has been developed to improve the accuracy by capturing the effects of the neglected higher-order complex modes. Secondly, the rest regions of the system form another component behaving nonlinearly, which is kept in its original form to adopt the entire set of nonlinear terms. Next, the second-order differential synthesis equation can be obtained by using compatibility conditions at the junctions. In order to calculate dynamic response of the system, the aforementioned synthesis equation needs to transform into the first-order differential equation because of the singularity of the equivalent mass matrix. Finally, two numerical examples are given to illustrate the effectiveness and the efficiency of the presented method.

中文翻译：

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具有局部非线性的一般阻尼系统使用混合坐标的复分量模态合成方法

摘要 在众多具有局部非线性的工程结构中，非线性效应通常是局部的，结构的大部分部分表现为线性。考虑到这一点，提出了一种用于具有局部非线性的一般阻尼系统的降阶建模技术。首先，将系统中具有非比例阻尼的线性部分分离成一个分量，在状态空间中将其公式化，并利用其线性振动复模态转化为模态坐标。剩余柔度矩阵可以通过使用一组等效的高阶复模来制定，通过捕捉被忽略的高阶复模的影响来提高精度。其次，系统的其余区域形成另一个表现非线性的组件，它保持其原始形式以采用整个非线性项集。接下来，利用节点处的兼容性条件可以得到二阶微分综合方程。为了计算系统的动态响应，由于等效质量矩阵的奇异性，上述综合方程需要转化为一阶微分方程。最后，给出了两个数值例子来说明所提出方法的有效性和效率。由于等效质量矩阵的奇异性，上述合成方程需要转化为一阶微分方程。最后，给出了两个数值例子来说明所提出方法的有效性和效率。由于等效质量矩阵的奇异性，上述合成方程需要转化为一阶微分方程。最后，给出了两个数值例子来说明所提出方法的有效性和效率。