Alemdar, Bulent N.Gulkan, Polat H.Dinckal, Cigdem2020-04-172025-09-182020-04-172025-09-182016Dinckal, 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).0315-14681208-6029https://doi.org/10.1139/cjce-2015-0130https://hdl.handle.net/20.500.12416/10747Gulkan, Polat/0000-0001-7542-7082An 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.eninfo:eu-repo/semantics/closedAccessElastic Winkler FoundationDynamic Shape FunctionsFrequency-Dependent Dynamic Stiffness MatrixDistributed MassDynamic StabilityArticle10.1139/cjce-2015-01302-s2.0-84981165798