Testing nonlinear structures to characterise their internal nonlinear forces is challenging. Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and responses cannot be ignored. Even if the intended excitation is a single frequency sinusoidal force, the interaction of the shaker and the nonlinear structure can lead to harmonics in the applied force. The effects of these higher harmonics of the input force on nonlinear model identification in structural dynamics are often neglected. The objective of this study is to introduce an identification method, motivated by the alternating frequency/time approach using harmonic balance (AFTHB), which is able to consider both multi-harmonic forces and multi-harmonic responses of the system. The proposed AFTHB method can include all significant harmonics by selecting an appropriate time step and sampling frequency to guarantee the accuracy of the results. An analytical harmonic-balance-based (AHB) approach is also considered for comparison. However, the inclusion of all significant harmonics of the response in the analytical expansion of the nonlinear functions is often cumbersome. Furthermore, the AFTHB method can easily cope with complex nonlinearities such as Coulomb friction and with multi-degree of freedom nonlinear systems. Including the effect of higher harmonics in the identification process reduces the approximation error due to truncation and very accurate approximation of the balanced equations of each harmonic is obtained. The proposed identification method requires prior knowledge or an appropriate estimation of the type of system nonlinearities. However, the method of model selection may be used for a set of candidate models, and avoiding a dictionary of arbitrary candidate basis functions significantly reduces the computational costs. This paper highlights the important features of the AFTHB method to ensure accurate estimation using four simulated and two experimental examples. The effects of the number of harmonics considered, the modelling error, measurement noise and the frequency range on the quality of the estimated model are demonstrated.

测试非线性结构以表征其内部非线性力具有挑战性。通常非线性结构被谐波力激发并产生多谐波响应。在许多系统中，尤其是具有强非线性的系统中，力和响应中的高次谐波的影响不容忽视。即使预期的激励是单频正弦力，振动台和非线性结构的相互作用也会导致施加力的谐波。输入力的这些高次谐波对结构动力学中的非线性模型识别的影响经常被忽略。本研究的目的是介绍一种识别方法，由使用谐波平衡（AFTHB）的交替频率/时间方法驱动，它能够同时考虑系统的多谐波力和多谐波响应。所提出的 AFTHB 方法可以通过选择适当的时间步长和采样频率来包括所有重要的谐波，以保证结果的准确性。还考虑使用基于分析谐波平衡（AHB）的方法进行比较。然而，在非线性函数的解析展开中包含响应的所有重要谐波通常很麻烦。此外，AFTHB 方法可以轻松处理复杂的非线性问题，例如库仑摩擦和多自由度非线性系统。在识别过程中包括高次谐波的影响减少了由于截断而导致的近似误差，并且获得了每个谐波平衡方程的非常准确的近似值。所提出的识别方法需要先验知识或对系统非线性类型的适当估计。然而，模型选择的方法可以用于一组候选模型，并且避免任意候选基函数的字典显着降低了计算成本。本文重点介绍了 AFTHB 方法的重要特征，以确保使用四个模拟示例和两个实验示例进行准确估计。演示了考虑的谐波数量、建模误差、测量噪声和频率范围对估计模型质量的影响。避免使用任意候选基函数的字典显着降低了计算成本。本文重点介绍了 AFTHB 方法的重要特征，以确保使用四个模拟示例和两个实验示例进行准确估计。演示了考虑的谐波数量、建模误差、测量噪声和频率范围对估计模型质量的影响。避免使用任意候选基函数的字典显着降低了计算成本。本文重点介绍了 AFTHB 方法的重要特征，以确保使用四个模拟示例和两个实验示例进行准确估计。演示了考虑的谐波数量、建模误差、测量噪声和频率范围对估计模型质量的影响。