International Journal of Mechanical Sciences ( IF 7.1 ) Pub Date : 2021-11-03 , DOI: 10.1016/j.ijmecsci.2021.106915 Carlos E.N. Mazzilli 1 , Paulo B. Gonçalves 2 , Guilherme R. Franzini 1
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This paper addresses a detailed literature review on non-linear modes of vibration and its role in obtaining more efficient reduced-order models, as compared to those obtained by Galerkin's method using classical linear modes. Examples that emphasise the superior quality of the former models are supplied. Regarding the review on non-linear modes, a chronological development is presented, stressing the main stages of definitions, properties, methods for evaluation and application of non-linear modes to engineering problems, from Poincaré to Liapunov, from Rosenberg and Vakakis to Shaw and Pierre, from past to present.
中文翻译：
基于非线性模式的降阶建模
本文详细介绍了非线性振动模式及其在获得更有效降阶模型方面的作用，与使用经典线性模式的 Galerkin 方法获得的模型相比。提供的示例强调了以前型号的卓越品质。关于非线性模式的回顾，介绍了一个时间顺序的发展，强调了非线性模式在工程问题中的定义、性质、评估方法和应用的主要阶段，从 Poincaré 到 Liapunov，从 Rosenberg 和 Vakakis 到 Shaw 和皮埃尔，从过去到现在。
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