Abstract We show how spectral submanifold (SSM) theory can be used to extract forced-response curves without any numerical simulation in high-degree-of-freedom, periodically forced mechanical systems. We use multivariate recurrence relations to construct the SSMs, achieving a major speed-up relative to earlier autonomous SSM algorithms. The increase in computational efficiency promises to close the current gap between studying lower-dimensional academic examples and analyzing larger systems obtained from finite-element modeling, as we illustrate on two different discretized damped-forced beam models. Using the exact reduction procedure via SSMs for obtaining forced response curves, we further demonstrate speed gains of several orders in magnitude relative to the available state-of-the-art continuation packages, while retaining accuracy.

中文翻译：

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高维机械系统中谱子流形的模型简化和强迫响应计算。

摘要 我们展示了如何使用谱子流形 (SSM) 理论在高自由度、周期性受迫机械系统中无需任何数值模拟即可提取受迫响应曲线。我们使用多元递推关系来构建 SSM，相对于早期的自主 SSM 算法实现了重大的加速。正如我们在两个不同的离散阻尼受力梁模型中所说明的那样，计算效率的提高有望缩小研究低维学术示例与分析从有限元建模获得的更大系统之间的当前差距。使用通过 SSM 的精确缩减程序来获得强制响应曲线，我们进一步证明了相对于可用的最先进延续包的几个数量级的速度增益，同时保持准确性。