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Structural Engineering and Mechanics Volume 66, Number 6, June25 2018 , pages 703-711 DOI: https://doi.org/10.12989/sem.2018.66.6.703 |
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Timoshenko theory effect on the vibration of axially functionally graded cantilever beams carrying concentrated masses |
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Carlos A. Rossit, Diana V. Bambill and Gonzalo J. Gilardi
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| Abstract | ||
| In this paper is studied the effect of considering the theory of Timoshenko in the vibration of AFG beams that support ground masses. As it is known, Timoshenko theory takes into account the shear deformation and the rotational inertia, provides more accurate results in the general study of beams and is mandatory in the case of high frequencies or non-slender beams. The Rayleigh-Ritz Method is employed to obtain approximated solutions of the problem. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study. The incidence of the Timoshenko theory is analyzed for different cases of beam slenderness, variation of its cross section and compositions of its constituent material, as well as different amounts and positions of the attached masses. | ||
| Key Words | ||
| vibration of beams; AFG beam; tapered beam; Timoshenko beam; attached masses; Rayleigh-Ritz method | ||
| Address | ||
| Carlos A. Rossit, Diana V. Bambill and Gonzalo J. Gilardi: Department of Engineering, Universidad Nacional del Sur(UNS) Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Avenida Alem 1253, (8000) Bahía Blanca, República Argentina | ||