Vibration of axially moving beam supported by viscoelastic foundation

作     者：Haijuan ZHANG Jian MA Hu DING Liqun CHEN Haijuan ZHANG Jian MA Hu DING Liqun CHEN

作者机构：Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China School of Mechanical Engineering Anhui University of Technology Maanshan 243032 Anhui Province China Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Shanghai 200072 China Department of Mechanics College of Sciences Shanghai University Shanghai 200444 China 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2017年第38卷第2期

页      面：161-172页

核心收录：

学科分类：08[工学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the State Key Program of the National Natural Science Foundation of China(No.11232009) the National Natural Science Foundation of China(Nos.11372171 and 11422214) 

主　　题：axially moving beam viscoelastic foundation complex modal analysis,natural frequency forced vibration 

摘      要：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.