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Steel and Composite Structures Volume 24, Number 6, August30 2017 , pages 671-677 DOI: https://doi.org/10.12989/scs.2017.24.6.671 |
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Analytical study on non-natural vibration equations |
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Mahmoud Bayat and Iman Pakar
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| Abstract | ||
| In this paper, two powerful analytical methods called Variational Approach (VA) and Hamiltonian Approach (HA) are used to solve high nonlinear non-Natural vibration problems. The presented approaches are works well for the whole range of amplitude of the oscillator. The first iteration of the approaches leads us to high accurate solution. Numerical results are also presented by using Runge-Kutta's [RK] algorithm. The full comparison between the presented approaches and the numerical ones are shown in figures. The effects of important parameters on the response of nonlinear behavior of the systems are studied completely. Finally, the results show that the Variational Approach and Hamiltonian approach are strong enough to prepare easy analytical solutions. | ||
| Key Words | ||
| Hamiltonian Approach (HA); Variational Approach (VA); nonlinear vibration; analytical method | ||
| Address | ||
| (1) Mahmoud Bayat: Young Researchers and Elite Club, Roudehen Branch, Islamic Azad University, Roudehen, Iran; (2) Iman Pakar: Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran. | ||