{"title":"Investigating the modal behaviors of a deep beam with a transverse open crack","authors":"Taejeong Lim , Hyun Woo Park","doi":"10.1016/j.jsv.2024.118613","DOIUrl":null,"url":null,"abstract":"<div><p>This paper investigates the modal behaviors of a deep beam with a transverse open crack. Unlike cracked shallow beams with aspect ratio (<em>L</em>/<em>h</em>) > 10, cracked deep beams with aspect ratio < 5 simultaneously exhibit near the crack both axial-bending coupling mode caused by mode I crack and shear (or sliding) mode caused by mode II crack, referred to as axial-bending-shear modal coupling. Therefore, for accurate modal behaviors prediction, appropriate compatibility equations accounting for both modes I and II crack should be employed for deriving a frequency equation. Because the derived frequency equation is nonlinear with respect to modal frequency, the modal frequencies are calculated through the Newton–Raphson method. The corresponding mode shapes are determined by substituting the calculated modal frequencies into the spectral solutions for either side of the crack. The validity of the proposed method was demonstrated through comparison to the finite element analysis and experimental results.</p></div>","PeriodicalId":17233,"journal":{"name":"Journal of Sound and Vibration","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Sound and Vibration","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022460X24003742","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper investigates the modal behaviors of a deep beam with a transverse open crack. Unlike cracked shallow beams with aspect ratio (L/h) > 10, cracked deep beams with aspect ratio < 5 simultaneously exhibit near the crack both axial-bending coupling mode caused by mode I crack and shear (or sliding) mode caused by mode II crack, referred to as axial-bending-shear modal coupling. Therefore, for accurate modal behaviors prediction, appropriate compatibility equations accounting for both modes I and II crack should be employed for deriving a frequency equation. Because the derived frequency equation is nonlinear with respect to modal frequency, the modal frequencies are calculated through the Newton–Raphson method. The corresponding mode shapes are determined by substituting the calculated modal frequencies into the spectral solutions for either side of the crack. The validity of the proposed method was demonstrated through comparison to the finite element analysis and experimental results.
本文研究了具有横向开放裂缝的深梁的模态行为。与长宽比 (L/h) > 10 的开裂浅梁不同，长宽比 < 5 的开裂深梁在裂缝附近同时表现出由模态 I 裂缝引起的轴向弯曲耦合模态和由模态 II 裂缝引起的剪切（或滑动）模态，即轴向弯曲-剪切模态耦合。因此，为了准确预测模态行为，在推导频率方程时应采用适当的兼容性方程，同时考虑模态 I 和模态 II 裂纹。由于推导出的频率方程与模态频率是非线性的，因此模态频率是通过牛顿-拉夫逊法计算得出的。将计算出的模态频率代入裂缝两侧的频谱解，即可确定相应的模态振型。通过与有限元分析和实验结果的比较，证明了所提方法的有效性。
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.
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