随从力作用下运动薄膜的非线性强迫振动特性研究

Nonlinear forced vibration characteristics of membrane subjected to follower force

研究随从力作用下运动印刷薄膜的非线性强迫振动特性。基于Von Karman薄板理论推导出轴向运动薄膜的非线性振动方程,应用Galerkin方法对振动偏微分方程组进行离散,利用4阶龙格-库塔法对微分方程进行求解,得出薄膜非线性振动的时程图、相图、Poincare截面图和分岔图。分析了初始条件、随从力和长宽比对薄膜振动特性的影响。研究结果得出了薄膜稳定工作区间和发散失稳区间。

The nonlinear forced vibration characteristics of moving printing membrane subjected to follower force were studied. Based on the Von Karman plate theory, the nonlinear vibration equations of the axially moving membrane were derived. The partial differential equations of the vibration were discretized by the Galerkin method, and the differential equations were solved by the fourth-order Runge-Kutta method. The time history diagram, phase-plane portraits, Poincare maps and bifurcation diagrams were obtained. The effects of initial conditions, follower force and aspect ratio on the vibration characteristics of the membrane were analyzed. According to the research results, the stable working range and the divergent instability region of the membrane were obtained.