Abstract
The parametric instability behavior of a Timoshenko beam resting on an elastic foundation of the Winkler type is studied by the finite element technique. The effect of the elastic foundation on the natural frequencies, the static buckling loads and the regions of dynamic instability of the Timoshenko beams with different end conditions is investigated. The natural frequency and buckling load parameters for a Bernoulli-Euler beam, which is a special case of the present model, indicate excellent agreement with the available results. The dynamic instability diagrams for both beams are presented for different values of the elastic foundation constant. As the elastic foundation constant increases, the regions of dynamic instability are shifted away from the static buckling axis and the sizes of these regions are slightly decreased. Due to the effects of rotatory inertia and transverse shear deformation, the regions of dynamic instability are shifted closer to each other and the sizes of these regions are increased.
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