［非线性偏微分方程的数值分析（几何分析）及应用非小振幅振动下弦振动方程及近似解］木文在非攀枝花学院本科毕业设计（论文）［非线性偏微分方程的数值分析（几何分析）及应用——非小振幅振动下弦振动方程的及近似解］学生姓名：姚徐学生学号：bxxjs02016院（系）：计算机学院年级专业：信息与计算科学指导教师：蒲利春教授助理指导教师::刘立新讲师副教授二OO六年五月根据我们对弦振动的研究，木文在非小振幅振动下，推导出弦振动的非线性偏微分方程：d2uk*La=—=-----------------—udrm•.UloriginUXX1+《1+M291+“dx__*在特定条件：血昇）一0心0»、叭TO和半TO下，将上述暫方程简at丄饥3化知二基*仝并运用了行波法和和数学Maple软件求出行了Utt的行波解:叽”1+叭(qx-ct)(c2+2/?^)4-2ln(\2c2e畑丿=--------------c+2pq2“GM丿2c29AvW+2pq丿C%S+2M匕+2ln—2c2ec2+2pqC2q,c为待定系数，p=」S_为胡克系数丄（）为固定拉直时弦的长度，叫弦2*叫询的质量），并应用Maple程序图象讨论了2心J）其解的物理性质当。本文在非小振幅振动下，推导出弦振动的非线性偏微分方程组，在特定条件下，将方程组转简化为方程，运用了数学Maple软件分析和求解。并讨论出方程无双曲函数解关键词非小弦振幅弦振动，偏微分方程，非线性，近似解originABSTRACTTheoscillationamplitudevibrationinnon-small,thestudyofnonlinearpartialdifferentialequationofstringvibration:_cl2u_k*L.側"dt2叫宓“Tnspecificterms,withtheq2£=1,§=_2必(+£〃|),—Oand^T0,willc2dt13aiisimplifytheequationforequation:ut{=——*—.Andtheuseofthelawandmon8in1+"；mathematicswaveofthewaveofMaplesoftwarederiveXieof%”:叫tdiscussedbyMapleproceduresofthephysicalnature.Keywords:Non-smalloscillationamplitudestringvibration,beingdifferentialequation,nonlinear,similarXie目录摘要..............................................................................................................................IABSTRACT....................................................................................................................II1绪论..........................................................................................................................21.1课题背景..............................................................................................................2LL1题冃及研究冃的..............................................................................................21.1.2研究意义......................................................................................................31.2课题所涉及的问题在国内外研究............................................................................22方程推导....................................................................................................................52.1方程推导..............................................................................................................52^2方程简化讨论及分析...........................................................................................................................93方程求解..................................................................................................................113.1行波法求解........................................................................................................10(qx-ct)(c，+2In"22c2Mm)=------7-^―c+2pq2<c2+2pq>22c2c2</L0+2/?^2L()+21n2cSc1+2pq•Xieof3・2双曲函数法求解................................................................................................12321双曲函数法介绍...............................................................................................