• Journal of KSNVE
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• v.10 no.6
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• pp.1075-1082
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• 2000

The paper describes the vibration and stability of tapered beams on two-parameter elastic foundations. The two-parameter elastic foundations are constructed by distributed Winkler springs and a shearing layer as of ten used in soil models. The shear deformation and the rotatory inertia of a beam are taken into account. Governing equations are derived from energy expressions using Hamilton\`s principle. The associated eigenvalue problems are solved to obtain the free vibration frequencies or the buckling loads. Numerical results for the vibration of a beam with an axial force are presented and compared when other solutions are available. Vibration frequencies, mode shapes, and critical forces of a tapered Timoshenko beam on elastic foundations under an axial force are investigated for various thickness ratios, shear foundation parameters, Winkler foundation parameters and boundary conditions.