DYNAMIC ANALYSIS OF TIMOSHENKO BEAM ON PASTERNAK FOUNDATION
Lucas Silva Soares1; Wallison Kennedy da Silva Bezerra1; Simone dos Santos Hoefel1
1 Universidade Federal do Piauí (UFPI)
doi:10.20906/CPS/CILAMCE2017-1336
Resumo
Free vibration analysis of beams on the elastic foundation is necessary for an optimal design in engineering applications. This paper analyzes the effect of Winkler and Pasternak parameters in the natural frequencies of a Timoshenko beam. For this purpose, the natural frequencies are obtained by solving the partial differential equation governing the problem. A finite element is developed using cubic and quadratic polynomials for transverse displacement and slope, respectively, for a two-node beam element with two degrees of freedom per node. The finite element and the analytic solutions are compared and discussed with some numerical examples. The results presented a high accuracy and reliability for the beam-foundation iteration problem. The presence of the Pasternak foundation increases the natural frequencies of the beam. The growth of the frequencies on Pasternak foundation is due to the shear layer stiffness, and it reduces the influence of the elastic stiffness. The use of the Euler-Bernoulli beam on Winkler foundation over Timoshenko beam on Pasternak foundation presents a significant inaccuracy, except for specific values of rotational inertia.
Palavras-chave: Free Vibration Analysis; Timoshenko Beam Theory; Winkler Foundation; Pasternak Foundation; Finite Element Analysis