耗散机械系统的保结构模型降阶
Structure-Preserving Model Reduction for Dissipative Mechanical Systems
AI总结：
本文综述了针对二阶耗散机械系统的保结构模型降阶方法，涵盖模态截断、平衡截断及有理插值等不同途径，并通过数值算例验证了这些方法在振动抑制问题中的有效性。
摘要：
机械系统中的振动抑制通常由二阶动力学模型描述，即使在今天，从计算资源角度看，这在机械工程中仍是一项具有挑战性的任务。一种解决办法是采用保结构模型降阶方法，为具有相同结构的原始动力学系统构造易于求解的代理模型。在我们的工作中，我们概述了最近发展的针对二阶系统的保结构模型降阶方法。这些方法基于不同形式的模态截断和平衡截断，以及有理插值。数值算例用于说明所有所述方法的有效性。
英文摘要：
Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model order reduction to construct easy-to-evaluate surrogates for the original dynamical system having the same structure. In our work, we present an overview of recently developed structure-preserving model reduction methods for second-order systems. These methods are based on modal and balanced truncation in different variants, as well as on rational interpolation. Numerical examples are used to illustrate the effectiveness of all described methods.
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