Nonlinear flexural wave equation and exact traveling solutions in beams
A nonlinear flexural wave equation of the beam taking account of large deflection and geometric dispersion was derived by means of the Hamilton principle. The results of qualitative analysis of the nonlinear evolution show that the equation has homoclinic or heteroclinic orbits on the phase plane, which corresponds to solitary wave or shock wave solution, respectively. Nonlinear flexural wave equation was solved by using the Jacobi elliptic function expansion method. Two kinds of exact periodic solutions of the nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition for the existence of these solutions was discussed, which is consistent with the qualitative analysis. The nonlinear Schrodinger equation was derived from the nonlinear flexural wave equation.
Zhi-fang Liu Tie-feng Wang Shan-yuan Zhang
Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, China College of Civil and Environmental Engineering, Taiyuan University of Technology,Taiyuan 030024, Chi
国际会议
The 5th International Conference on Nonlinear Mechanics(第五届国际非线性力学会议)
上海
英文
637-643
2007-06-11(万方平台首次上网日期,不代表论文的发表时间)