Dynamics of a beam-column element on an elastic foundation
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Date
2016
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Canadian Science Publishing
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Abstract
An exact analytical solution of a harmonically vibrating beam-column element resting on an elastic Winkler foundation is derived. The solution covers four cases comprised of constant compressive or tensile axial force with the restrictions k(s) - m omega(2) < 0 and k(s) - m omega(2) > 0. The proposed solution is not restricted to a particular range of magnitudes of the foundation parameter. Closed form solutions of dynamic shape functions are explicitly derived for each sub-case to obtain frequency-dependent dynamic stiffness terms that constitute the exact dynamic stiffness matrices. Four numerical examples are provided to demonstrate the merits of the present study.
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Keywords
Elastic Winkler Foundation, Dynamic Shape Functions, Frequency-Dependent Dynamic Stiffness Matrix, Distributed Mass, Dynamic Stability
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Citation
Dinckal, Cigdem; Alemdar, Bulent N.; Gulkan, Polat H., "Dynamics of a beam-column element on an elastic foundation", Canadian Journal of Civil Engineering, Vol. 43, No. 8, pp. 685-701, (2016).
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Source
Canadian Journal of Civil Engineering
Volume
43
Issue
8
Start Page
685
End Page
701