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TECHNICAL BRIEF

# Modeling of Nonlinear Oscillations for Viscoelastic Moving Belt Using Generalized Hamilton’s Principle

[+] Author and Article Information
L. H. Chen

College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, P. R. Chinachenlihua@.bjut.edu.cn

W. Zhang1

College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, P. R. Chinasandyzhang0@yahoo.com

Y. Q. Liu

College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, P. R. ChinaJdyqliu@emails.bjut.edu.cn

1

Corresponding author.

J. Vib. Acoust 129(1), 128-132 (Jun 08, 2006) (5 pages) doi:10.1115/1.2346691 History: Received November 23, 2005; Revised June 08, 2006

## Abstract

In this paper, the nonlinear governing equations of motion for viscoelastic moving belt are established by using the generalized Hamilton’s principle for the first time. Two kinds of viscoelastic constitutive laws are adopted to describe the relation between the stress and strain for viscoelastic materials. Moreover, the correct forms of elastic strain energy, kinetic energy, and the virtual work performed by both external and viscous dissipative forces are given for the viscoelastic moving belt. Using the generalized Hamilton’s principle, the nonlinear governing equations of three-dimensional motion are established for the viscoelastic moving belt. Neglecting the axial deformation, the governing equations of in-plane motion and transverse nonlinear oscillations are also derived for the viscoelastic moving belt. Comparing the nonlinear governing equations of motion obtained here with those obtained by using the Newton’s second law, it is observed that the former completely agree with the latter.

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## Figures

Figure 1

The model of a viscoelastic moving belt

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