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An explicit frequency response function formulation for multi-degree-of-freedom non-linear systems

机译：多自由度非线性系统的显式频率响应函数公式

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摘要

This paper presents a technique for the explicit formulation of frequency response functions (FRFs) for nonlinear MDOF systems, yielding closed-form analytical expressions. The technique produces FRFs at selected coordinates only, regardless of the system's size or the type of nonlinearity, The nonlinear formulation in this work is based on first-order describing functions, which represent the nonlinearities by amplitude-dependent coefficients. For the sake of clarity, the paper is focused on cubic stiffness and friction damping nonlinearities, although, given the generality of the formulation, the inclusion of other types should be straightforward. Conducted entirely in the physical domain, the approach is based on manipulating the coefficients stored in the explicitly formulated system matrices, thus the term "explicit". An enhanced version, which can tackle large systems, is also presented and validated against real measurements taken from a test rig. It was found that the nonlinear behaviour was predicted with reasonable accuracy in all cases studied.
机译：本文介绍了一种用于非线性MDOF系统的频率响应函数（FRF）的显式表示的技术，可得出闭合形式的解析表达式。该技术仅在选定坐标处生成FRF，而不管系统的大小或非线性的类型如何。这项工作中的非线性公式是基于一阶描述函数，该函数通过幅度相关系数来表示非线性。为了清楚起见，本文着重于立方刚度和摩擦阻尼非线性，尽管鉴于该公式的一般性，其他类型的包含也应很简单。该方法完全在物理域中进行，是基于操纵存储在明确制定的系统矩阵中的系数，因此称为“显式”。还介绍了可以处理大型系统的增强版本，并针对从测试台获得的实际测量结果进行了验证。结果发现，在所有研究情况下，非线性行为均以合理的精度进行了预测。

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