The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires explicit knowledge of nonlinear coefficients in the equations of motion, which limits their applicability to generic finite-element (FE) solvers. Here, we propose a non-intrusive algorithm for the computation of the SSMs and the associated ROMs up to arbitrary polynomial orders. This non-intrusive algorithm only requires system nonlinearity as a black box and hence, enables SSM-based model reduction via generic finite-element software. Our expressions and algorithms are valid for systems with up to cubic-order nonlinearities, including velocity-dependent nonlinear terms, asymmetric damping, and stiffness matrices, and hence work for a large class of mechanics problems. We demonstrate the effectiveness of the proposed non-intrusive approach over a variety of FE examples of increasing complexity, including a micro-resonator FE model containing more than a million degrees of freedom.

中文翻译：

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通过谱子流形对非线性有限元模型进行无数据非侵入式模型归约。


谱子流形 （SSM） 理论已成为构建高维非线性机械系统的严格、低维降阶模型 （ROM） 的强大工具。直接计算 SSM 需要明确了解运动方程中的非线性系数，这限制了它们对通用有限元 （FE） 求解器的适用性。在这里，我们提出了一种非侵入性算法，用于计算 SSM 和相关的 ROM，最高可达任意多项式阶数。这种非侵入式算法只需要系统非线性作为黑匣子，因此可以通过通用的有限元软件实现基于 SSM 的模型约简。我们的表达式和算法适用于具有最大三次级非线性的系统，包括与速度相关的非线性项、不对称阻尼和刚度矩阵，因此适用于一大类力学问题。我们通过各种复杂性不断增加的有限元示例证明了所提出的非侵入性方法的有效性，包括包含超过一百万个自由度的微谐振器 FE 模型。