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.

翻译：通常由二阶动态模型描述的机械系统中的抑制振动是机械工程在计算资源方面的艰巨任务,即使现在也是如此,一种补救措施是结构保护模式,减少结构维持模式,为结构相同的原动力系统建造易于评估的代孕器。我们在工作中概述了最近为二阶系统开发的结构保护模式的减少模式。这些方法基于不同变体的模式和平衡脱节以及合理的内插。用数字例子来说明所有所述方法的有效性。