This work investigates the time response of a Duffing oscillator with time-varying parameters (excitation frequency, linear stiffness, and mass) by approximate analytical and numerical methods. When the excitation frequency sweep covers the multisolution range, the characteristics of the response (maximum response, jump-up frequency, and jump-down frequency) mainly depend on the frequency sweep rate. If the frequency sweep is ended in the multisolution range, the sweep rate determines the energy orbit that the final response will capture. The results can be explained by comparing the state spaces of the oscillator with the change of basin of attraction of the high-energy orbit during the sweep. Furthermore, if the excitation is fixed at a specific frequency in the multisolution range, a method of natural frequency temporary modulation is proposed for the capture of the high-energy orbit. For practical realization, this method is completed by two ways, that is, the linear stiffness temporary modulation and mass temporary modulation. The modulation schedules of time-varying linear stiffness and mass are determined quantitatively, and it is proved that they could help capture the high-energy orbit similar to the excitation frequency sweep. The developed methods and results of this work can provide the guidelines to design nonlinear systems to work on preferred energy orbit.

中文翻译：

---

利用时变参数捕获Duffing振荡器的高能轨道。

这项工作通过近似分析和数值方法研究了具有时变参数（激励频率，线性刚度和质量）的Duffing振荡器的时间响应。当激励频率扫描覆盖多解范围时，响应的特性（最大响应，上跳频率和下跳频率）主要取决于扫频速率。如果频率扫描在多解范围内结束，则扫描速率将确定最终响应将捕获的能量轨道。通过比较振荡器的状态空间和扫描过程中高能轨道的吸引盆的变化，可以解释结果。此外，如果将激励固定在多解范围内的特定频率下，提出了一种自然频率临时调制的方法来捕获高能轨道。为了实际实现，该方法通过线性刚度临时调制和质量临时调制两种方式完成。定量确定了随时间变化的线性刚度和质量的调制时间表，并证明它们可以帮助捕获类似于激发频率扫描的高能轨道。这项工作的开发方法和结果可以为设计在首选能量轨道上工作的非线性系统提供指导。定量确定了随时间变化的线性刚度和质量的调制时间表，并证明它们可以帮助捕获类似于激发频率扫描的高能轨道。这项工作的开发方法和结果可以为设计在首选能量轨道上工作的非线性系统提供指导。定量确定了随时间变化的线性刚度和质量的调制时间表，并证明它们可以帮助捕获类似于激发频率扫描的高能轨道。这项工作的开发方法和结果可以为设计在首选能量轨道上工作的非线性系统提供指导。