SECOND SPECTRUM OF TIMOSHENKO BEAM ON PASTERNAK FOUNDATION
Wallison Kennedy da Silva Bezerra1; Lucas Silva Soares1; Simone dos Santos Hoefel1
1 Universidade Federal do Piauí
doi:10.20906/CPS/CILAMCE2017-0215
Resumo
In many soil-structure interaction problems, the soil medium model used is the Winkler foundation for mathematical simplicity. However, this foundation model cannot represent the behavior of foundation materials for all engineering applications. The Pasternak model can accomplish a more realistic and generalized description of the soil behavior. For structures with a large aspect ratio of height and length, Timoshenko beam theory is used, instead of Euler-Bernoulli theory, since it takes both shear and rotary inertia into account. This paper investigates the effects of the Pasternak foundation on the dynamic response of the Timoshenko beam. A finite element is developed using cubic and quadratic polynomials, which are made interdependent by requiring them to satisfy the static homogeneous differential equations associated with Timoshenko beam theory. The influence of the foundation on the second spectrum is concerned. The results showed that the presence of the foundation anticipates the second spectrum and does not have a significant influence in its frequencies. Also, the presence of the foundation permits a distinction between the two spectra for boundary conditions that do not factorize.
Palavras-chave: Finite Element Method; Timoshenko Beam Theory; Pasternak Foundation; Second Spectrum; Free Vibration Analysis