Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundations

Exact analysis of beams on two-parameter elastic foundations

The response of an elastic beam on a two-dimensional tensionless Pasternak foundation that is subjected to a central concentrated harmonic load is investigated. The tensionless character of the foundation results in the creation of lift-off regions between the beam and the foundation. Since the contact regions are not known in advance, the problem appears as a nonlinear one, and the calculation of the roots of a nonlinear equation is needed to obtain contact lengths of the beam. The governing equations obtained for the contact and lift-off regions are solved by using the trigonometric-hyperbolic functions. Several numerical examples are provided to show the effects of the foundation stiffness parameters and the frequency parameter on the lift-off regions and the vertical displacements of the beam. It is concluded that more than one contact length may arise in the solution for a fixed frequency parameter, and this parameter may cause to interchange the contact and lift-off regions.

The response of a finite beam on a tensionless Pasternak foundation subjected to a harmonic load

A finite element procedure is developed for analysing the flexural vibrations of a uniform Timoshenko beam-column on a two-parameter elastic foundation. The beam-column is discretized into a number of simple elements with four degrees of freedom each. The governing matrix equation for small-amplitude, free vibrations of the beam-column on the elastic foundation is derived from Hamilton's principle. Several numerical examples are provided to show the effects of axial force, foundation stiffness parameters, partial elastic foundation, shear deformation and rotatory inertia on the natural frequencies of the beam-column.

Vibrations of timoshenko beam‐columns on two‐parameter elastic foundations

Vibration of Timoshenko beams on three-parameter elastic foundation

Calcul des frequences naturelles pour diverses rigidites relatives, pour etudier l'effet sur l'element poutre-poteau du contact continu avec le sol et de la force axiale, utilisation de modeles a deux parameres pour le sol (Filonenko-Borodich et Gasternau et Vlasov), avec comparaison au modele de Winkler

A. J. Valsangkar

Papers

Vibrations of beam‐columns on two‐parameter elastic foundations