Citation: | ZHANG Xiaoming, LI Zhi, YU Jiangong. Dispersion Characteristics of Circumferential Evanescent Guided Waves in Orthotropic Cylindrical Curved Plates[J]. Journal of Beijing University of Technology, 2018, 44(5): 770-776. DOI: 10.11936/bjutxb2017050060 |
It is very difficult to solve the problem of the evanescent guided wave described by the complex root. To deal with this problem, an improved orthogonal polynomial method was proposed, which could obtain all the real, imaginary and complex solutions. For validation and illustration purposes, the proposed approach was applied to solving the problem of the dispersion curves of the evanescent guided waves in a cylindrical curved plate with a big radius-thickness ratio. The results agree well with the results of the plate from the existing literature. Dispersion curves of the circumferential evanescent guided waves in various cylindrical curved plates were obtained by using the present approach, and the three dimensional full dispersion curves were also obtained. The effects of different radius-thickness ratios and elastic parameters on the dispersion characteristics of circumferential evanescent guided waves in cylindrical curved plates were illustrated.
[1] |
BENMEDDOUR F, TREYSSÈDE F, LAGUERRE L. Numerical modeling of guided wave interaction with non-axisymmetric cracks in elastic cylinders[J]. International Journal of Solids and Structures, 2011, 48(5):764-774. doi: 10.1016/j.ijsolstr.2010.11.013
|
[2] |
HUANG K H, DONG S B. Propagating waves and edge vibrations in anisotropic composite cylinders[J]. Journal of Sound and Vibration, 1984, 96(3):363-379. doi: 10.1016/0022-460X(84)90363-8
|
[3] |
RATASSEPP M, KLAUSON A, CHATI F, et al. Edge resonance in semi-infinite thick pipe:numerical predictions and measurements[J]. Journal of the Acoustical Society of America, 2008, 124(2):875-885. doi: 10.1121/1.2945163
|
[4] |
DILIGENT O, LOWE M J S, LE CLEZIO E, et al. Prediction and measurement of nonpropagating Lamb modes at the free end of a plate when the fundamental antisymmetric mode A0 is incident[J]. Journal of the Acoustical Society of America, 2003, 113(6):3032-3042. doi: 10.1121/1.1568758
|
[5] |
PAGNEUX V, MAUREL A. Determination of Lamb mode eigenvalues[J]. Journal of the Acoustical Society of America, 2001, 110(3):1307-1314. doi: 10.1121/1.1391248
|
[6] |
DAMLJANOVI AĆ V, WEAVER R L. Propagating and evanescent elastic waves in cylindrical waveguides of arbitrary cross section[J]. Journal of the Acoustical Society of America, 2004, 115(4):1572-1581. doi: 10.1121/1.1687424
|
[7] |
AN Y K. Measurement of crack-induced non-propagating Lamb wave modes under varying crack widths[J]. International Journal of Solids and Structures, 2015, 62:134-143. doi: 10.1016/j.ijsolstr.2015.02.021
|
[8] |
KRUSHYNSKA A A, MELESHKO V V. Normal waves in elastic bars of rectangular cross section[J]. Journal of the Acoustical Society of America, 2011, 129(3):1324-1335. doi: 10.1121/1.3531800
|
[9] |
吴斌, 禹建功, 何存富.正交各向异性空心圆柱体中的周向超声导波[J].工程力学, 2007, 24(8):37-42. http://www.cqvip.com/QK/95324X/200708/25220027.html
WU B, YU J G, HE C F. Guided circumferential waves in orthotropic hollow cylinders[J]. Engineering Mechanics, 2007, 24(8):37-42. (in Chinese) http://www.cqvip.com/QK/95324X/200708/25220027.html
|
[10] |
ELMAIMOUNI L, LEFEBVRE J E, ZHANG V, et al. A polynomial approach to the analysis of guided waves in anisotropic cylinders of infinite length[J]. Wave Motion, 2005, 42(2):177-189. doi: 10.1016/j.wavemoti.2005.01.005
|
[11] |
YU J G, ZHANG C Z. Effects of initial stress on guided waves in orthotropic functionally graded plates[J]. Applied Mathematical Modelling, 2014, 38(2):464-478. doi: 10.1016/j.apm.2013.06.029
|
[12] |
张小明, 禹建功, 王裕清.初应力对单向复合材料圆柱板周向波的影响[J].固体力学学报, 2013, 34(6):607-613. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=gtlxxb201306010
ZHANG X M, YU J G, WANG Y Q. Effects of initial stresses on circumferential waves in unidirectional cylindrical curved plates[J]. Chinese Journal of Solid Mechanics, 2013, 34(6):607-613. (in Chinese) http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=gtlxxb201306010
|
[13] |
郭永强. 回传射线矩阵法的理论及其应用[D]. 杭州: 浙江大学, 2008: 261-262.
GUO Y Q. The method of reverberation-ray matrix and its applications[D]. Hangzhou: Zhejiang University, 2008: 261-262. (in Chinese)
|
[14] |
QUINTANILLA F H, LOWE M J S, CRASTER R V. Full 3D dispersion curve solutions for guided waves in generally anisotropic media[J]. Journal of Sound and Vibration, 2015, 363:545-559. https://spiral.imperial.ac.uk/bitstream/10044/1/28100/2/Hernando%20Quintilla%202015%20Guided%20waves%203D%20dispersion%20curves%20JSV.pdf
|
[1] | HE Cunfu, DING Dongdong, LIU Xiucheng, MA Kun, WU Bin. Magnetic Incremental Permeability Detection Method for Measuring the Thickness of Nickel Layer of 65Mn Steel Plate[J]. Journal of Beijing University of Technology, 2020, 46(7): 727-733. DOI: 10.11936/bjutxb2018120005 |
[2] | ZHANG Zhiqing, LI Shiyun, LI Chen, SHEN Bozhao. Lateral Acceleration Characteristics of Curves With Small Radius on Two-lane Highway[J]. Journal of Beijing University of Technology, 2019, 45(5): 452-458. DOI: 10.11936/bjutxb2017110046 |
[3] | XU Pengfei, ZHANG Gong, LI Xiaolu, ZHANG Huige, MA Jianhui. Experiment Study of Axial Compression Performance of Concrete Filled Steel Tube Short Column With Different Wall Thickness[J]. Journal of Beijing University of Technology, 2017, 43(10): 1514-1520. DOI: 10.11936/bjutxb2016100053 |
[4] | YAN Jianzhuo, JIANG Miaowen, CHEN Jimin, LIANG Chenxiao. Automobile Body Integration Manufacturing and Thickness Optimization for Stereo Lithography 3D Printing[J]. Journal of Beijing University of Technology, 2017, 43(4): 551-556. DOI: 10.11936/bjutxb2016020033 |
[5] | LIU Zeng-hua, ZHAO Ji-chen, WU Bin, HE Cun-fu. Experimental Research on Hole-like Defect Detection in Plate Based on Ultrasonic Guided Waves Technique[J]. Journal of Beijing University of Technology, 2011, 37(1): 27-32. |
[6] | CAO Wan-lin, LI Gang, ZHANG Jian-wei, ZHANG Wen-jiang, GENG Hai-xia. Seismic Behavior of Steel-plate Shear Walls With Concrete Filled Steel Tube Columns and Different Ratio of Height to Sectional Thickness of the Walls[J]. Journal of Beijing University of Technology, 2010, 36(8): 1059-1068. |
[7] | YU Jian-gong, WU Bin, HE Cun-fu. The Finite Element Simulation of a Longitudinal Defect Detection in an Anisotropic Cylindrical Curved Plate by Guided Circumferential Waves[J]. Journal of Beijing University of Technology, 2007, 33(6): 567-571. |
[8] | QIAO Jian-gang, RONG Jian, REN Fu-tian, LIU Xiao-ming. Research on Horizontal Curves Radius Based on Driver Humanity on Two-lane Highway in Chinese Mountain Areas[J]. Journal of Beijing University of Technology, 2006, 32(1): 33-37. |
[9] | Huang Hezhi. The Optimization Method of Heaping up Equal Radius Spheres[J]. Journal of Beijing University of Technology, 1993, 19(2): 45-54. |
[10] | E Cuoguang. An Approximate Analytical Method for Thick Hologram Gratings[J]. Journal of Beijing University of Technology, 1990, 16(2): 45-51. |