轴向激励屈曲简支梁动力特性的数值研究-南京林业大学学报.pdf

第 26 卷第 2 期 南京林业大学学报(自然科学版 V0 1. 26 , No. 2 2002 年 3 月 Journal of N anjing Forestry U niversity( N atural Sciences Edition) Mar. , 2002 轴向激励屈曲简支梁动力特性的数值研究 陈宁 (南京林业大学机械电子工程学院，江苏 南京 210037) 摘要:利用有限差分原理，考虑转动惯量的影响，在轴向激励作用下，对屈曲梁的动力特性进 行数值研究。用数值方法进行计算的结果与利用 Galerkiin 法将偏微分方程转化成常微分方 程进行分析的结果基本吻合，证实系统中存在周期倍化、拟周期运动和混沌运动等复杂动力学 行为，表明该方法具有良好的精确性和收敛性。 关键词:参激屈曲梁;非线性动力学;混沌运动;周期倍化 中图分类号 0322 文献标识码:A 文章编号: 1000- 2006(2002)02- 0044- 05 Numerical Investigation on Dynamical Behaviours of A Buckled Beam Under Axial Harmonic Excitation CHEN Ning ( College of Electronic and Mechanical Engineering Nanjing Forestry University , Nanjin g 210037 , China) Abstract: The dynamical behaviours of a simplγsupport buckled beam under axial harmonic excitation are investigated using the direct numerical method , and the effect of rotary inertia is considered too. The gov- erned equation of buckled beam is transformed to the nonlinear partial differential equations of physical vari- ables such as moment , velocity and displacement. By using a stable, explicit finite difference scheme to solve the equations and the solutions is equivalent to the Galerkiin solutions. Various complex dynamical b矿 haviours such as period doubling , quas卜periodic and chaotic motion in this system are show n , and the result also demonstrated that the finite difference method is more convenient than other tradition methods for the study of buckled beams. Key words: Parametric exciting buckled beam; N onlinear dynamics; Chaotic motion; Period doubling Tseng 和 Dugundli 首次发现屈曲梁的混沌运动后[汀，屈曲梁的非线性动力特性及混沌运动引起许 多学者的注意。 Holmes 给出了屈曲梁基本动力学模型 Duffing 方程[2] 。近年来，国