被介质包围的非线性弹性杆波动方程的精确解  

Exact Solutions for Wave Equation of Nonlinear Elastic Rod Embedded in a Medium

作　　者：郭鹏 武祥[2,3,4] 王良璧[2,3] GUO Peng;WU Xiang;WANG Liangbi(School of Materials Science and Engineering,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China;School of Mechatronic Engineering,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China;Key Laboratory of Railway Vehicle Thermal Engineering,Ministry of Education,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China;School of Mechanical Engineering,Tianjin University,Tianjin 300350,China)

机构地区：[1]兰州交通大学材料科学与工程学院,甘肃兰州730070 [2]兰州交通大学机电工程学院,甘肃兰州730070 [3]兰州交通大学铁道车辆热工教育部重点实验室,甘肃兰州730070 [4]天津大学机械工程学院,天津300350

出　　处：《力学季刊》2023年第3期731-738,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(51776093,52066009);甘肃省高等学校产业支撑引导项目(2019C-06);甘肃省重大科技专项资助项目(21ZD4GA027)。

摘　　要：应用推广的tanh函数方法对被介质包围的非线性弹性杆波动方程进行了求解.得到了该方程的精确孤波解,对部分结果通过数值模拟得到了解的图像.本文获得的结果完善了相关文献已有的研究成果.从求解过程可以看出,推广的tanh函数方法是一种简便有效的方法,可用于求解其它非线性方程或方程组.The wave equation of nonlinear elastic rod embedded in a medium is solved by the extended tanh-function method.The exact solitary wave solution of the equation is obtained.The graphs of some solutions are given through numerical simulation.The results show that the present findings enrich the existing research results in the related literature.The extended tanh-function method is shown to be simple,effective and can be applied for many other nonlinear equations.

关 键 词：推广的tanh函数方法 非线性弹性杆 波动方程 精确解 

分 类 号：O343.5[理学—固体力学]