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Structural Engineering and Mechanics Volume 73, Number 1, January10 2020 , pages 83-95 DOI: https://doi.org/10.12989/sem.2020.73.1.083 |
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Formulae for the frequency equations of beam-column system carrying a fluid storage tank |
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Tamer. A. El-Sayed and Said. H. Farghaly
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| Abstract | ||
| In this work, a mathematical model of beam-column system carrying a double eccentric end mass system is investigated, and solved analytically based on the exact solution analysis. The model considers the case in which the double eccentric end mass is a rigid storage tank containing fluid. Both Timoshenko and Bernoulli-Euler beam bending theories are considered. Equation of motion, general solution and boundary conditions for the present system model are developed and presented in dimensional and non-dimensional format. Several important non-dimensional design parameters are introduced. Symbolic and/or explicit formulae of the frequency and mode shape equations are formulated. To the authors knowledge, the present reduced closed form symbolic and explicit frequency equations have not appeared in literature. For different applications, the results are validated using commercial finite element package, namely ANSYS. The beam-column system investigated in this paper is significant for many engineering applications, especially, in mechanical and structural systems. | ||
| Key Words | ||
| thick beam-column, free vibration, exact solution, tank with fluid, eccentric mass | ||
| Address | ||
| Department of Mechanical Design, Faculty of Engineering, Mataria, Helwan University,P.O. Box 11718, Helmeiat-Elzaton, Cairo, Egypt | ||