Buckling dynamics of imperfect Elastica subject to various loading conditions |
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Authors: | Ümit Sönmez |
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Affiliation: | (1) Applied Mechanics Division, Department of Mechanical Engineering, Istanbul Technical University, Gümüşsuyu, Istanbul, 34407, Turkey |
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Abstract: | Buckling dynamics of a pinned-pinned flexible imperfect beam attached to a sliding mass is investigated using nonlinear Elastica
theory. Initially straight flexible buckling beam having pinned end boundary conditions loaded at one of its end with curved
imperfection is considered. Large deflection analysis of flexible beam is studied using nonlinear Elastica theory. Imperfection
analysis of the flexible beam is investigated considering the imperfection as an initial curvature. The governing differential
equations are expressed in terms of nonlinear functions that are typical of flexible beams, generally leading to highly implicit
relationships involving elliptic integrals and functions. Dynamic simulation of the flexible beam is studied using numerical
simulation procedures with various types of loading (step, ramp, and sinusoidal) assuming this member buckles in its first
mode. Dynamic response of the imperfect buckling Elastica has been obtained by using numerical Runge-Kutta methods. Load deflection
characteristics of flexible beams are presented in polynomial curve fits. The polynomial curve fits obtained from nonlinear
inextensible exact beam theory may then be used as the nonlinear lumped system stiffness. The buckling Elastica may find applications
in compliant mechanism design. The motivation behind this research is not only to present the dynamic behavior of the buckling
beam considering the magnitude of the imperfection but also to provide a tool to design new types of compliant mechanisms.
Original compliant mechanism designs are presented demonstrating where the buckling dynamics of imperfect Elastica or flexible
curved beams might be needed in mechanism design and synthesis. |
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Keywords: | Buckling dynamics Large deflection theory Geometric nonlinearities Imperfect columns Elastica theory Curved beams Compliant mechanism design Compliant mechanism dynamics Nonlinear dynamics of flexible beams |
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