轴压圆柱壳受径向扰动时非线性波的传播  

Propagation of Nonlinear Wave in an Axially Compressed Cylindrical Shell Subjected to Radial Disturbance

作　　者：周义清[1,2] 张涛[1] 张善元[1] 

机构地区：[1]太原理工大学应用力学与生物医学工程研究所,山西太原030024 [2]中北大学理学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2010年第5期533-537,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10772129)

摘　　要：以弹性圆柱壳受轴压作用下的静力平衡状态为参考构形,对其受径向扰动时非线性波的传播特征进行了研究.采用由环向对数应变描述的非线性应变-位移关系,建立了支配受轴压圆柱壳径向轴对称运动的非线性波动方程.借助约化摄动法(Reductive Perturbation Technique,RPT),由可解条件导出了非线性Sc¨hrodinger方程(Nonlinear Sch¨rodinger,NLS).采用行波法求解NLS方程,给出了周期波解及退化条件下的包络孤立子解.对亮孤子和暗孤子存在的条件分析表明:轴向压应力的取值对解的性质有重要影响.由Hirota提出的直接法得到了双孤子解的表达形式.The static equilibrium state in axial compressive force was taken as reference configuration, the propagation property of nonlinear wave in an axially compressed cylindrical shell subjected to radial disturbance was studied. Using the logarithmic hoop strain to describe nonlinear strain-displacement relation, the nonlinear flexural wave equation governing axisymmetric radial motion of the cylindrical shell was derived. By means of the reductive perturbation technique （RPT）, the nonlinear Schrodinger equation （NLSE） was obtained from solvability condition. The cnoidal wave and envelope soliton solutions were given by the traveling-wave method. The existence conditions of bright soliton and dark soliton indicate that the axial stress has important effect on the propagation property of the nonlinear wave. Two-soliton solution is obtained by the so-called Hirota＇s bilinearization method.

关 键 词：圆柱壳 对数环向应变 非线性弯曲波 约化摄动法 包络孤立子 

分 类 号：O347.4[理学—固体力学]