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Mathematical Problems in Engineering
Volume 2018, Article ID 5756180, 14 pages
Research Article

Nonlinear Vibration of Ladle Crane due to a Moving Trolley

1School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China
2College of Economics and Management, Taiyuan University of Technology, Taiyuan 030024, China

Correspondence should be addressed to Gening Xu; nc.ude.tsuyt@gninegux

Received 19 September 2017; Revised 24 December 2017; Accepted 15 January 2018; Published 13 March 2018

Academic Editor: Xiao-Qiao He

Copyright © 2018 Yunsheng Xin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The structural vibration of the main beam of a crane causes fatigue damage and discomfort to the driver. The swing of the payload has an effect on positioning precision, especially for a ladle crane, and this directly affects production safety. To study the influence of system parameters on the vibration of a crane’s main beam and the angle of the payload, a system consisting of the main beam, trolley, payload, and cabin was constructed. A rigid-flexible coupling dynamic model of a moving trolley with a hanging payload that moves on the flexible main beam with a concentrated cabin mass is established, and the direct integration method is used to solve the nonlinear differential equations of system vibration, which are obtained through Lagrange’s equation. Then, the time domain responses of the flexible main beam, payload angle, and cabin vibration are obtained. The influences of the trolley running speed, quality of the payload, and quality and position of the cabin on the vibration of the main beam and payload angle are analyzed. The results indicate that the amplitude of the main beam is directly proportional to the quality of the trolley, payload, and cab; the position of the cabin is closer to the mid-span; the amplitude of the main beam is larger; the structural damping has some influence on the vibration of the main beam; and the swing angle of the payload is related to the maximum running speed of the trolley, acceleration time, and length of the wire rope. In order to reduce the vibration of the main beam and cabin, the connection stiffness of the cabin should be ensured during installation.