Nonlinearities in rotating systems have been seen to cause a wide variety of rich phenomena; however, the understanding of these phenomena has been limited because numerical approaches typically rely on “brute force” time simulation, which is slow due to issues of step size and settling time, cannot locate unstable solution families, and may miss key responses if the correct initial conditions are not used. This work uses numerical continuation to explore the responses of such systems in a more systematic way. A simple isotropic rotor system with a smooth nonlinearity is studied, and the rotating frame is used to obtain periodic solutions. Asynchronous responses with oscillating amplitude are seen to initiate at certain drive speeds due to internal resonance, in a manner similar to that observed for nonsmooth rotor–stator contact systems in the previous literature. These responses are isolated, in the sense that they will only meet the more trivial synchronous responses in the limit of zero damping and out of balance forcing. In addition to increasing our understanding of the responses of these systems, the work establishes the potential of numerical continuation as a tool to systematically explore the responses of nonlinear rotor systems.

已经看到旋转系统中的非线性会导致各种各样的丰富现象；然而，对这些现象的理解是有限的，因为数值方法通常依赖于“蛮力”时间模拟，由于步长和稳定时间的问题，这种模拟很慢，无法定位不稳定的解决方案系列，如果正确，可能会错过关键响应不使用初始条件。这项工作使用数值延拓以更系统的方式探索此类系统的响应。研究了具有平滑非线性的简单各向同性转子系统，并利用旋转坐标系获得周期解。由于内部共振，在某些驱动速度下可以看到具有振荡幅度的异步响应，以类似于在先前文献中观察到的非光滑转子 - 定子接触系统的方式。这些响应是孤立的，从某种意义上说，它们只会在零阻尼和失衡强迫的限制下满足更微不足道的同步响应。除了增加我们对这些系统响应的理解之外，这项工作还确立了数值延拓作为系统探索非线性转子系统响应的工具的潜力。