| NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD |
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| 引用本文： | Liu Zhifang Zhang Shanyuan. NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD[J]. Acta Mechanica Solida Sinica, 2006, 19(1): 1-8. DOI: 10.1007/s10338-006-0601-0 |
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| 作者姓名： | Liu Zhifang Zhang Shanyuan |
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| 作者单位： | Institute of Applied Mechanics，Taiyuan University of Technology，Taiyuan 030024，China |
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| 摘 要： | A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
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| 关 键 词： | 非线性波 有限形变 Poisson效应 Jacobi椭圆函数 |
| 收稿时间： | 2005-01-18 |
| 修稿时间： | 2005-12-05 |
NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD |
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| Liu Zhifang,Zhang Shanyuan. NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD[J]. Acta Mechanica Solida Sinica, 2006, 19(1): 1-8. DOI: 10.1007/s10338-006-0601-0 |
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| Authors: | Liu Zhifang Zhang Shanyuan |
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| Affiliation: | 1. College of Engineering, Peking Universiry, Beijing 100871, China;2. China Astronaut Research and Training Center, Department of Space Food and Nutrition, Beijing 100094, China;3. School of Public Health, Peking University, Beijing 100083, China;1. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762, USA;2. Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University, Riyadh 13318, Saudi Arabia;3. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;4. Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059 Bursa, Turkey;1. Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey;2. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran;3. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box-80203, Jeddah-21589, Saudi Arabia;4. Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50601 Kuala Lumpur, Malaysia;5. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, PR China;6. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;7. Science Program, Texas A & M University at Qatar, PO Box 23874, Doha, Qatar;1. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762, USA;2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;4. Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059 Bursa, Turkey;5. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, People''s Republic of China;6. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar;1. Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia;2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt;3. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia;1. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-7500, USA;2. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;4. Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100 Yozgat, Turkey;5. Institute of Physics Belgrade, Pregrevica 118, 11080 Zemun, Serbia |
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| Abstract: | A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed. |
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| Keywords: | nonlinear wave finite deformation Poisson effect Jacobi elliptic function |
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