Elastic Lateral Torsional Buckling of Beams Under External Moments: A New Type of Nonconservative Problem
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Published:2023-11-23
Issue:
Volume:
Page:
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ISSN:0219-4554
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Container-title:International Journal of Structural Stability and Dynamics
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language:en
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Short-container-title:Int. J. Str. Stab. Dyn.
Author:
Wen Y.12ORCID,
Liu Y. X.1ORCID,
Song H. X.1ORCID
Affiliation:
1. School of Civil Engineering, Central South University, Changsha 410075, P. R. China
2. MOE Key Laboratory of Engineering, Structures of Heavy-haul Railway, Central South University, Changsha 410075, P. R. China
Abstract
The important character of the applied moment with a fixed line of direction as implied in deriving the governing differential equations of LTB for elastic beams, however, is not represented in stating the boundary conditions based on conventional energy approaches. This paper sets out to consider the boundary conditions derived by conventional potentials in order to identify the ignored second-order moments that need to be added for maintaining the initial direction of the applied moment during LTB. By taking into account the non-zero work done by these ignored moments for modifying original potentials, the nonconservative nature of the elastic LTB of beam under external moments is clarified in two aspects — by discovering the path-dependent property of the non-zero work and by demonstrating that only trivial solution of LTB mode is expected from the analytical solution of the governing differential equations. Using the concept of dynamic instability, an analysis procedure combining the numerical solution of an eigen-value problem and the bisection method is proposed to identify the first appearance of imaginary or conjugate complex frequencies and to determine the value of the critical moment. Demonstrative examples are considered for illuminating the elastic LTB behavior using conventional energy methods and revised virtual work equation. It has been found that the critical moments given by conventional potentials are generally not consistent with each other unless the work done by the ignored second-order moments vanishes. However, consistent critical moment, under which the free vibrating amplitude of elastic beam is increased unboundedly with time, can be obtained by the kinetic approach based on any revised virtual work equation, indicating the necessity of considering the nonconservative nature of non-follower applied moment.
Funder
Natural Science Foundation of China
Natural Science Foundation of Hunan Province
Postdoctoral Research Foundation of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Building and Construction,Civil and Structural Engineering
Cited by
1 articles.
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