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Structural Engineering and Mechanics Volume 37, Number 5, March10 2011 , pages 489-507 DOI: https://doi.org/10.12989/sem.2011.37.5.489 |
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Dynamic response of a Timoshenko beam on a tensionless Pasternak foundation |
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Irfan Coskun, Hasan Engin and Ayfer Tekin
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| Abstract | ||
| The dynamic response of a Timoshenko beam on a tensionless Pasternak foundation is investigated by assuming that the beam is subjected to a concentrated harmonic load at its middle. This action results in the creation of lift-off regions between the beam and the foundation that effect the character of the response. Although small displacements for the beam and the foundation are assumed, the problem becomes nonlinear since the contact/lift-off regions are not known at the outset. The governing equations of the beam, which are coupled in deflection and rotation, are obtained in both the contact and lift-off regions. After removing the coupling, the essentials of the problem (the contact regions) are determined by using an analytical-numerical method. The results are presented in figures to demonstrate the effects of some parameters on the extent of the contact lengths and displacements. The results are also compared with those of Bernoulli-Euler, shear, and Rayleigh beams. It is observed that the solution is not unique; for a fixed value of the frequency parameter, more than one solution (contact length) exists. The contact length of the beam increases with the increase of the frequency and rotary-inertia parameters, whereas it decreases with increasing shear foundation parameter. | ||
| Key Words | ||
| Timoshenko beam; Pasternak foundation; lift-off. | ||
| Address | ||
| Irfan Coskun: Faculty of Civil Engineering, Yildiz Technical University, Davutpasa Campus, 34210 Esenler, Istanbul, Turkey Hasan Engin: Faculty of Civil Engineering,I stanbul Technical University, 34469 Maslak, Istanbul, Turkey Ayfer Tekin: Faculty of Civil Engineering, Yildiz Technical University, Davutpasa Campus, 34210 Esenler, Istanbul, Turkey | ||