NDLI: Post-critical behavior of damped beam columns with variable cross section subjected to distributed follower forces

Content Provider	Springer Nature Link
Author	Tsiatas, G. C. Katsikadelis, J. T.
Copyright Year	2008
Abstract	In this paper the post-critical behavior of beam columns with variable mass and stiffness properties subjected to follower forces arbitrarily distributed along their length in the presence of damping (both internal and external) is investigated using a complete nonlinear dynamic analysis. Although the static nonlinear analysis is more economical in computational cost, it is associated only with the loss of local stability via flutter or divergence. Thus, the nonlinear dynamic analysis is adopted in order to examine the global stability of the system. The governing equations of hyperbolic type are derived in terms of the displacements by considering (a) nonlinear response including the axial deformation, (b) nonlinear response excluding the axial deformation and (c) linear response. Moreover, as the cross-sectional properties of the beam vary along its axis, the resulting coupled nonlinear differential equations have variable coefficients. Their solution is achieved using the analog equation method (AEM) of Katsikadelis. Besides its accuracy and effectiveness, this method overcomes the shortcoming of a possible FEM solution which may experience a lack of convergence. The problems treated in this investigation include beam columns with various load distributions, such as constant, linear and parabolic. Some of the conclusions detected in studying the nonlinear dynamic stability of Beck’s column with variable cross section (Katsikadelis and Tsiatas, Nonlinear dynamic stability of damped Beck’s column with variable cross section. Int. J. Non-linear Mech. 42, 164–171, 2007), are also valid for the case of distributed loads. The important, however, finding is that the post-critical response under distributed loads depends on the law of distribution of mass and stiffness properties, which may lead also to explosive flutter (unbounded amplitude), in contrast to Beck’s column (end-tip load) where the motion is always bounded.
Starting Page	429
Ending Page	441
Page Count	13
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	56
Issue Number	4
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2008-08-22
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Post-critical Nonlinear dynamic stability Nonlinear dynamic analysis Nonconservative Distributed follower forces Analog equation method Variable cross section Automotive Engineering Mechanical Engineering Mechanics Vibration, Dynamical Systems, Control
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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