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Simulation and experimental validation of modal analysis for non-linear symmetric systems

机译：非线性对称系统模态分析的仿真与实验验证

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A dual approach, direct and inverse, is proposed for the study of a subset of discrete mechanical nonlinear systems. Applying the definition of a "mode" for a non-linear system, the response calculation is refined for a class of mechanical systems possessing elastic restoring forces proportional to the cube of the displacement. The relationship between the modal natural frequencies and modal amplitudes of oscillation is analytically computed using the Harmonic Balance Method. An identification method, which operates on the free response of the system, is presented and it is shown to be capable of recovering these functional relationships. Comparisons of the analytical approximation and identification solutions are made in order to evaluate the method's effectiveness and its range of application. This comparison is achieved through numerical simulation. An experiment performed on a physical mechanical system exhibiting non-linear behaviour is then presented. For such a system, the analytical relationships between modal natural frequencies and modal amplitudes of oscillation are calculated using its mechanical parameters. These relationships are compared with those identified experimentally and finally the results and possible extensions to the work are discussed.
机译：为研究离散机械非线性系统的子集，提出了直接和反向对偶方法。根据非线性系统的“模式”定义，对一类机械系统进行了响应计算，该系统具有与位移立方成比例的弹性恢复力。模态固有频率与振荡模态振幅之间的关系是使用谐波平衡法进行解析计算的。提出了一种识别方法，该方法可对系统的自由响应进行操作，并且可以恢复这些功能关系。为了评估该方法的有效性及其应用范围，对分析的近似方法和识别方法进行了比较。这种比较是通过数值模拟实现的。然后提出了对表现出非线性行为的物理机械系统进行的实验。对于这样的系统，模态固有频率和模态振动振幅之间的解析关系是使用其机械参数计算得出的。将这些关系与通过实验确定的关系进行比较，最后讨论了结果和可能的扩展。

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