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Steel and Composite Structures Volume 14, Number 5, May 2013 , pages 511-521 DOI: https://doi.org/10.12989/scs.2013.14.5.511 |
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Analytical solution for nonlinear vibration of an eccentrically reinforced cylindrical shell |
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Mahmoud Bayat, Iman Pakar and Mahdi Bayat
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| Abstract | ||
| In this study we have considered the governing nonlinear equation of an eccentrically reinforced cylindrical shell. A new analytical method called He\'s Variational Approach (VA) is used to obtain the natural frequency of the nonlinear equation. This analytical representation gives excellent approximations to the numerical solution for the whole range of the oscillation amplitude, reducing the respective error of angular frequency in comparison with the variation approach method. It has been proved that the variational approach is very effective, convenient and does not require any linearization or small perturbation. Additionally it has been demonstrated that the variational approach is adequately accurate to nonlinear problems in physics and engineering. | ||
| Key Words | ||
| eccentrically reinforced cylindrical shell; stringer shell; nonlinear vibration; variational approach; Runge-Kutta | ||
| Address | ||
| 1 Mahmoud Bayat: Young Researchers and Elites club, Science and Research Branch, Islamic Azad University, Tehran, Iran; 2 Iman Pakar, Mahdi Bayat: Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran | ||