Model order reduction of geometrically nonlinear dynamic structures is often achieved via a static condensation procedure, whereby high-frequency modes are assumed to be quasi-statically coupled to a small set of lower frequency modes, which form the reduction basis. This approach is mathematically justifiable for structures characterized by slow/fast dynamics, such as thin plates and slender beams, and has been shown to provide highly accurate results. Nevertheless, selecting the reduction basis without a priori knowledge of the full-order dynamics is a challenging task; retaining redundant modes will lead to computationally suboptimal reduced-order models (ROMs), while omitting dynamically significant modes will lead to inaccurate results, and important features such as internal resonances may not be captured. In this study, we demonstrate how the error associated with static condensation can be efficiently approximated during model reduction. This approximate error can then be used as the basis of a method for predicting when dynamic modal interactions will occur, which will guide the reduction basis selection process. Equivalently, this may serve as a tool for verifying the accuracy of ROMs without the need for full-order simulations. The proposed method is demonstrated using a simple oscillator and a finite element model of a clamped–clamped beam.

几何非线性动态结构的模型降阶通常是通过静态压缩程序实现的，其中假设高频模式准静态耦合到一小组低频模式，这些模式构成了降阶基础。这种方法对于具有慢/快动力学特征的结构（例如薄板和细长梁）在数学上是合理的，并且已被证明可以提供高度准确的结果。然而，选择没有先验的减少基础全阶动力学知识是一项具有挑战性的任务；保留冗余模式将导致计算上次优的降阶模型 (ROM)，而忽略动态重要模式将导致结果不准确，并且可能无法捕获内部共振等重要特征。在这项研究中，我们展示了如何在模型简化过程中有效地近似与静态冷凝相关的误差。然后，该近似误差可用作预测动态模态相互作用何时发生的方法的基础，这将指导约简基础选择过程。同样，这可以用作验证 ROM 准确性的工具，而无需全阶模拟。所提出的方法是使用一个简单的振荡器和一个夹紧-夹紧梁的有限元模型来演示的。