摘要
研究了运动薄膜的速度对非线性强迫振动的影响。基于Von Karman薄板理论推导出轴向运动薄膜大挠度振动方程,应用Galerkin方法对振动偏微分方程组进行离散,得到系统的状态方程,采用4阶Runge-Kutta法对系统状态方程进行数值求解,利用分岔图分析了薄膜非线性振动特性与速度的关系,得到了薄膜产生混沌的区间和稳定工作区间。通过时程图、相图、Poincare截面图和功率谱分析系统的周期运动和混沌运动。
The effect of the velocity of moving membrane on the nonlinear forced vibration is investigated in this paper.Large deflection vibration equation of an axially moving membrane is deduced by using the Von Karman thin plate theory.Galerkin method is applied to discretize vibration differential equations of the membrane,and then the state equation of the system is obtained.The state equation of the system is numerically solved by the fourth order Runge-Kutta method,and the relationship between the nonlinear vibration characteristics and the velocity of the membrane is analyzed by using the bifurcation diagram.The chaotic region and stable working region of the moving membrane are obtained.The periodic motion and chaos motion of the system are analyzed by time histories,phase-plane portraits,Poincare maps and power spectrum.
作者
邵明月
武吉梅
王砚
应戍狄
赵凡
Shao Mingyue;Wu Jimei;Wang Yan;Ying Shudi;Zhao Fan(School of Mechanical and Precision Instrument Engineering,Xi′an University of Technology,Xi′an 710048,China;Faculty of Printing.Packing and Digital Media Engineering,Xi′an University of Technology,Xi′an 710048,China;School of Civil Engineering and Architecture,Xi′an University of Technology,Xi′an 710048,China)
出处
《机械科学与技术》
CSCD
北大核心
2018年第12期1817-1822,共6页
Mechanical Science and Technology for Aerospace Engineering
基金
国家自然科学基金项目(11272253
61671376)
西安理工大学博士学位论文创新基金项目(310-252071702)
陕西省自然科学基金项目(2018JM5023
2018JM1028
2018JM5119)资助
