Vibration of axially moving beam supported by viscoelastic foundation

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• 作者：Haijuan Zhang ; Jian Ma ; Hu Ding ; Liqun Chen
• 关键词：axially moving beam ; viscoelastic foundation ; complex modal analysis ; natural frequency ; forced vibration
• 刊名：Applied Mathematics and Mechanics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：38
• 期：2
• 页码：161-172
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics; Classical Mechanics; Mathematical Modeling and Industrial Mathematics;
• 出版者：Shanghai University
• ISSN：1573-2754
• 卷排序：38

文摘

In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton’s principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.