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Math. Comput. Appl. 2017, 22(4), 44; doi:10.3390/mca22040044

The Analysis of Nonlinear Vibrations of Top-Tensioned Cantilever Pipes Conveying Pressurized Steady Two-Phase Flow under Thermal Loading

Department of Mechanical Engineering, University of Lagos, Akoka Yaba 101017, Nigeria
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Received: 5 October 2017 / Revised: 28 October 2017 / Accepted: 29 October 2017 / Published: 3 November 2017

Abstract

This paper studied the nonlinear vibrations of top-tensioned cantilevered pipes conveying pressurized steady two-phase flow under thermal loading. The coupled axial and transverse governing partial differential equations of motion of the system were derived based on Hamilton’s mechanics, with the centerline assumed to be extensible. Using the multiple-scale perturbation technique, natural frequencies, mode shapes, and first order approximate solutions of the steady-state response of the pipes were obtained. The multiple-scale assessment reveals that at some frequencies the system is uncoupled, while at some frequencies a 1:2 coupling exists between the axial and the transverse frequencies of the pipe. Nonlinear frequencies versus the amplitude displacement of the cantilever pipe, conveying two-phase flow at super-critical mixture velocity for the uncoupled scenario, exhibit a nonlinear hardening behavior; an increment in the void fractions of the two-phase flow results in a reduction in the pipe’s transverse vibration frequencies and the coupled amplitude of the system. However, increases in the temperature difference, pressure, and the presence of top tension were observed to increase the pipe’s transverse vibration frequencies without a significant change in the coupled amplitude of the system. View Full-Text
Keywords: Hamilton’s principle; nonlinear vibration; two-phase flow; critical mixture velocity; cantilever pipes; perturbation method Hamilton’s principle; nonlinear vibration; two-phase flow; critical mixture velocity; cantilever pipes; perturbation method
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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. (CC BY 4.0).

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MDPI and ACS Style

Adegoke, A.S.; Oyediran, A.A. The Analysis of Nonlinear Vibrations of Top-Tensioned Cantilever Pipes Conveying Pressurized Steady Two-Phase Flow under Thermal Loading. Math. Comput. Appl. 2017, 22, 44.

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