{"title":"矩形杆中波传播的半解析小波有限元方法","authors":"Wenxiang Ding, Liangtian Li, Hongmei Zhong, Ying Li, Danyang Bao, Sheng Wei, Wenbin Wang","doi":"10.1016/j.wavemoti.2024.103325","DOIUrl":null,"url":null,"abstract":"<div><p>Prior knowledge of the dispersion curves and mode shapes of guided waves provides valuable information for wave mode selection and excitation in the field of non-destructive evaluation (NDE) and structural health monitoring (SHM). They are typically computed by the matrix methods, the finite element (FE) and semi-analytical finite element (SAFE) methods. However, the former is prone to numerical instability, and the latter two are limited by the refinement level of the FE mesh. In this paper, a semi-analytical wavelet finite element (SAWFE) method is presented to characterize wave propagation in rectangular rods. The piecewise polynomial interpolation functions of the SAFE method are replaced by two-dimensional scaling functions of the B-spline wavelet on the interval (BSWI). To demonstrate the accuracy of the proposed SAWFE technique, the propagation of guided waves in an aluminium plate is studied first. Then, the propagation of guided waves in rectangular rods of arbitrary aspect ratio is investigated. The results of this work clearly show that the SAWFE method presented here has higher accuracy and efficiency than the SAFE method.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"128 ","pages":"Article 103325"},"PeriodicalIF":2.1000,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A semi-analytical wavelet finite element method for wave propagation in rectangular rods\",\"authors\":\"Wenxiang Ding, Liangtian Li, Hongmei Zhong, Ying Li, Danyang Bao, Sheng Wei, Wenbin Wang\",\"doi\":\"10.1016/j.wavemoti.2024.103325\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Prior knowledge of the dispersion curves and mode shapes of guided waves provides valuable information for wave mode selection and excitation in the field of non-destructive evaluation (NDE) and structural health monitoring (SHM). They are typically computed by the matrix methods, the finite element (FE) and semi-analytical finite element (SAFE) methods. However, the former is prone to numerical instability, and the latter two are limited by the refinement level of the FE mesh. In this paper, a semi-analytical wavelet finite element (SAWFE) method is presented to characterize wave propagation in rectangular rods. The piecewise polynomial interpolation functions of the SAFE method are replaced by two-dimensional scaling functions of the B-spline wavelet on the interval (BSWI). To demonstrate the accuracy of the proposed SAWFE technique, the propagation of guided waves in an aluminium plate is studied first. Then, the propagation of guided waves in rectangular rods of arbitrary aspect ratio is investigated. The results of this work clearly show that the SAWFE method presented here has higher accuracy and efficiency than the SAFE method.</p></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"128 \",\"pages\":\"Article 103325\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Wave Motion\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165212524000556\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165212524000556","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
A semi-analytical wavelet finite element method for wave propagation in rectangular rods
Prior knowledge of the dispersion curves and mode shapes of guided waves provides valuable information for wave mode selection and excitation in the field of non-destructive evaluation (NDE) and structural health monitoring (SHM). They are typically computed by the matrix methods, the finite element (FE) and semi-analytical finite element (SAFE) methods. However, the former is prone to numerical instability, and the latter two are limited by the refinement level of the FE mesh. In this paper, a semi-analytical wavelet finite element (SAWFE) method is presented to characterize wave propagation in rectangular rods. The piecewise polynomial interpolation functions of the SAFE method are replaced by two-dimensional scaling functions of the B-spline wavelet on the interval (BSWI). To demonstrate the accuracy of the proposed SAWFE technique, the propagation of guided waves in an aluminium plate is studied first. Then, the propagation of guided waves in rectangular rods of arbitrary aspect ratio is investigated. The results of this work clearly show that the SAWFE method presented here has higher accuracy and efficiency than the SAFE method.
期刊介绍:
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.