Perturbation analysis of natural oscillations of elastic structures with damage

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration Pub Date : 2025-09-01 DOI:10.1016/j.jsv.2025.119429

Yury Vetyukov

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Abstract

A mathematical justification is given for the energy based approach to estimating the changes in the natural frequencies of an elastic structure when a small flexibility or mass is added. In particular, we consider the situation where the vibration modes of the perturbed structure are not kinematically admissible for the original one. Local damage (cracks), imperfect boundary conditions (elastic supports instead of ideal ones), shear compliance of a beam or of a plate are examples of such structural changes. The rigorous asymptotic procedure establishes a relationship between the frequency shift and the complementary energy of the added compliance calculated for the vibration mode of the original structure, whatever its type, be it a rod, a plate or a shell. Special treatment is required in case of repeated (multiple) natural frequencies. Examples ranging from simple toy models to a practically relevant model of a plate with a crack are demonstrated. The approach is particularly efficient when the effort for the vibration analysis of the original structure is essentially lower than that of the perturbed one. Parametric studies with varying damage severity and configuration result as a post-processing of a single solution for the unperturbed structure.

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有损伤弹性结构固有振动的摄动分析

给出了基于能量的方法估算弹性结构在加入小柔度或小质量时固有频率变化的数学依据。特别地，我们考虑了摄动结构的振动模态在运动上与原结构不允许的情况。局部损伤（裂缝）、不完美的边界条件（弹性支撑代替理想支撑）、梁或板的剪切顺应性都是这种结构变化的例子。严格的渐近过程建立了对原始结构的振动模式计算的频率移和附加柔度的互补能量之间的关系，无论其类型是杆，板还是壳。在重复（多个）固有频率的情况下需要特殊处理。从简单的玩具模型到具有裂纹的板的实际相关模型都进行了演示。当对原结构进行振动分析的努力基本上低于对受扰动结构进行振动分析的努力时，这种方法特别有效。具有不同损伤严重程度和结构的参数化研究结果是对无扰动结构的单一解的后处理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Sound and Vibration 工程技术-工程：机械

CiteScore

9.10

自引率

10.60%

发文量

551

审稿时长

69 days

期刊介绍： The Journal of Sound and Vibration (JSV) is an independent journal devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. There is an emphasis on fundamental work that has potential for practical application. JSV was founded and operates on the premise that the subject of sound and vibration requires a journal that publishes papers of a high technical standard across the various subdisciplines, thus facilitating awareness of techniques and discoveries in one area that may be applicable in others.