| 随从力作用下运动薄膜的非线性强迫振动特性研究 |
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| 引用本文： | 邵明月,武吉梅,王砚,武秋敏,庆佳娟,卢瑶.随从力作用下运动薄膜的非线性强迫振动特性研究[J].振动与冲击,2020,39(10):215-219. |
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| 作者姓名： | 邵明月 武吉梅 王砚 武秋敏 庆佳娟 卢瑶 |
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| 作者单位： | 1.西安理工大学印刷包装与数字媒体学院，西安710048；
2.西安理工大学土木建筑工程学院，西安710048 |
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| 基金项目： | 陕西省自然科学基金(2018JM5023,2018JM1028,2018JM5119);西安理工大学博士学位论文创新基金(310-252071702)。 |
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| 摘 要： | 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。
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| 关 键 词： | 非线性振动 随从力 运动薄膜 4阶龙格-库塔法 |
Nonlinear forced vibration characteristics of membrane subjected to follower force |
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| SHAO Mingyue,WU Jimei,WANG Yan,WU Qiumin,QING Jiajuan,LU Yao.Nonlinear forced vibration characteristics of membrane subjected to follower force[J].Journal of Vibration and Shock,2020,39(10):215-219. |
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| Authors: | SHAO Mingyue WU Jimei WANG Yan WU Qiumin QING Jiajuan LU Yao |
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| Affiliation: | 1.School of Printing Packaging and Digital Media Engineering, Xi’an University of Technology, Xi’an 710048, China；
2.School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an 710048, China |
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| Abstract: | 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. |
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| Keywords: | nonlinear vibration follower force moving membrane fourth-order Runge-Kutta method |
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