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A theoretical approach to the interaction between buckling and resonance instabilities

Carpinteri, Alberto and Paggi, Marco A theoretical approach to the interaction between buckling and resonance instabilities. Journal of Engineering Mathematics, 78 (1). pp. 19-35. ISSN 0022-0833 (2013)

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Abstract

This article deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem is reduced to a generalized eigenproblem where both the loading multiplier and the natural frequency of the system are unknown. According to this approach, all of the forms of instabilities intermediate between those of pure buckling and pure forced resonance can be investigated. Numerous examples are analyzed, including discrete mechanical systems with one to n degrees of freedom, continuous mechanical systems, such as oscillating deflected beams subjected to a compressive axial load, as well as oscillating beams subjected to lateral–torsional buckling. A general finite element procedure is also outlined, with the possibility to apply the proposed approach to any general bi- or tri-dimensional framed structure. The proposed results provide a new insight in the interpretation of coupled phenomena such as flutter instability of long-span or high-rise structures.

Item Type: Article
Identification Number: 10.1007/s10665-011-9478-0
Uncontrolled Keywords: Buckling; Continuous mechanical systems; Discrete mechanical systems; Finite elements; Flutter; Resonance
Subjects: T Technology > TJ Mechanical engineering and machinery
Research Area: Computer Science and Applications
Depositing User: Prof Marco Paggi
Date Deposited: 03 Dec 2013 13:54
Last Modified: 09 Oct 2014 09:20
URI: http://eprints.imtlucca.it/id/eprint/2007

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