运动薄膜的速度对非线性强迫振动的影响研究
The Effect of Moving Membrane Velocity on Nonlinear Forced Vibration

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