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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 5432516, 22 pages
Research Article

Nonlinear Dynamic Behavior Analysis of Pressure Thin-Wall Pipe Segment with Supported Clearance at Both Ends

School of Mechanical Engineering & Automation, Northeastern University, Shenyang, Liaoning 110819, China

Received 24 March 2016; Revised 30 May 2016; Accepted 31 May 2016

Academic Editor: Francesco Tornabene

Copyright © 2016 Chaofeng Li 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.


An analysis of nonlinear behaviors of pressure thin-wall pipe segment with supported clearance at both ends was presented in this paper. The model of pressure thin-wall pipe segment with supported clearance was established by assuming the restraint condition as the work of springs in the deformation directions. Based on Sanders shell theory, Galerkin method was utilized to discretize the energy equations, external excitation, and nonlinear restraint forces. And the nonlinear governing equations of motion were derived by using Lagrange equation. The displacements in three directions were represented by the characteristic orthogonal polynomial series and trigonometric functions. The effects of supporting stiffness and supported clearance on dynamic behavior of pipe wall were discussed. The results show that the existence of supported clearance may lead to the changing of stiffness of the pipe vibration system and the dynamic behaviors of the pipe system show nonlinearity and become more complex; for example, the amplitude-frequency curve of the foundation frequency showed hard nonlinear phenomenon. The chaos and bifurcation may emerge at some region of the values of stiffness and clearance, which means that the responses of the pressure thin-wall pipe segment would be more complex, including periodic motion, times periodic motion, and quasiperiodic or chaotic motions.