• Structural Engineering and Mechanics
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• 제65권4호
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• pp.409-413
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• 2018

In this paper, He's Variational Approach (VA) is used to solve high nonlinear vibration equations. The proposed approach leads us to high accurate solution compared with other numerical methods. It has been established that this method works very well for whole range of initial amplitudes. The method is sufficient for both linear and nonlinear engineering problems. The accuracy of this method is shown graphically and the results tabulated and results compared with numerical solutions.

• Smart Structures and Systems
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• 제15권5호
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• pp.1311-1327
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• 2015

In this paper, we have applied a new class of approximate analytical methods called Variational Approach (VA) for high nonlinear vibration equations. Three examples have been introduced and discussed. The effects of important parameters on the response of the problems have been considered. Runge-Kutta's algorithm has been used to prepare numerical solutions. The results of variational approach are compared with energy balance method and numerical and exact solutions. It has been established that the method is an easy mathematical tool for solving conservative nonlinear problems. The method doesn't need small perturbation and with only one iteration achieve us to a high accurate solution.

• Steel and Composite Structures
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• 제24권6호
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• pp.671-677
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• 2017

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.

• Steel and Composite Structures
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• 제14권5호
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• pp.511-521
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• 2013

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.

• Earthquakes and Structures
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• 제7권1호
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• pp.1-15
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• 2014

In this paper we consider three different cases and we apply Variational Approach (VA) to solve the non-natural vibrations and oscillations. The method variational approach does not demand small perturbation and with only one iteration can lead to high accurate solution of the problem. Some patterns are presented for these three different cease to show the accuracy and effectiveness of the method. The results are compared with numerical solution using Runge-kutta's algorithm and another approximate method using energy balance method. It has been established that the variational approach can be an effective mathematical tool for solving conservative nonlinear dynamical equations.

• Structural Engineering and Mechanics
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• 제57권6호
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• pp.1039-1049
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• 2016

In this research, an approximate analytical solution has been presented for nonlinear problems of vibratory systems in mechanical engineering. The new method is called Variational Approach (VA) which is applied in two different high nonlinear cases. It has been shown that the presented approach leads us to an accurate approximate analytical solution. The results of variational approach are compared with numerical solutions. The full procedure of the numerical solution is also presented. The results are shown that the variatioanl approach can be an efficient and practical mathematical tool in field of nonlinear vibration.