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Accurate periodic solution for nonlinear vibration of thick circular sector slab
Iman Pakar,Mahmoud Bayat,Mahdi Bayat 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.16 No.5
In this paper we consider a periodic solution for nonlinear free vibration of conservative systems for thick circular sector slabs. In Energy Balance Method (EBM) contrary to the conventional methods, only one iteration leads to high accuracy of the solutions. The excellent agreement of the approximate frequencies and periodic solutions with the exact ones could be established. Some patterns are given to illustrate the effectiveness and convenience of the methodology. Comparing with numerical solutions shows that the energy balance method can converge to the numerical solutions very rapidly which are valid for a wide range of vibration amplitudes as indicated in this paper.
Nonlinear vibration of thin circular sector cylinder: An analytical approach
Iman Pakar,Mahmoud Bayat,Mahdi Bayat 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.17 No.1
In this paper, we try to prepare an accurate analytical solution for solving nonlinear vibration of thin circular sector cylinder. A new approximate solution called variational approach is presented and correctly applied to the governing equation of thin circular sector cylinder. The effect of important parameters on the response of the problem is considered. Some comparisons have been presented between the numerical solution and the present approach. The results show an excellent agreement between these methods. It has been illustrated that the variational approach can be a useful method to solve nonlinear problems by considering the effects of important parameters.
On the large amplitude free vibrations of axially loaded Euler-Bernoulli beams
Mahmoud Bayat,Iman Pakar,Mahdi Bayat 국제구조공학회 2013 Steel and Composite Structures, An International J Vol.14 No.1
In this paper Hamiltonian Approach (HA) have been used to analysis the nonlinear free vibration of Simply-Supported (S-S) and for the Clamped-Clamped (C-C) Euler-Bernoulli beams fixed at one end subjected to the axial loads. First we used Galerkin’s method to obtain an ordinary differential equation from the governing nonlinear partial differential equation. The effect of different parameter such as variation of amplitude to the obtained on the non-linear frequency is considered. Comparison of HA with Runge-Kutta 4th leads to highly accurate solutions. It is predicted that Hamiltonian Approach can be applied easily for nonlinear problems in engineering.
Nonlinear vibration of multi-body systems with linear and nonlinear springs
Mahmoud Bayat,Iman Pakar,Mahdi Bayat 국제구조공학회 2017 Steel and Composite Structures, An International J Vol.25 No.4
In this paper, nonlinear vibration of multi-degree of freedom systems are studied. It has been tried to develop the mathematical model of systems by second-order nonlinear partial differential equations. The masses are connected with linear and nonlinear springs in series. A great effort has been done to solve the nonlinear governing equations analytically. A new analytical method called Variational Iteration Method (VIM) is proposed and successfully applied to the problem. The linear and nonlinear frequencies are obtained and the results are compared with numerical solutions. The first order of Variational Iteration Method (VIM) leads us to high accurate solution.
An accurate novel method for solving nonlinear mechanical systems
Mahdi Bayat,Iman Pakar,Mahmoud Bayat 국제구조공학회 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.51 No.3
This paper attempts to investigate the nonlinear dynamic analysis of strong nonlinear problems by proposing a new analytical method called Hamiltonian Approach (HA). Two different cases are studied to show the accuracy and efficiency of the method. This approach prepares us to obtain the nonlinear frequency of the nonlinear systems with the first order of the solution with a high accuracy. Finally, to verify the results we present some comparisons between the results of Hamiltonian approach and numerical solutions using Runge-Kutta’s [RK] algorithm. This approach has a powerful concept and the high accuracy, so it can be apply to any conservative nonlinear problems without any limitations.
Analytical solution for nonlinear vibration of an eccentrically reinforced cylindrical shell
Mahmoud Bayat,Iman Pakar,Mahdi Bayat 국제구조공학회 2013 Steel and Composite Structures, An International J Vol.14 No.5
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.
Nonlinear vibration of conservative oscillator’s using analytical approaches
Mahmoud Bayat,Iman Pakar,Mahdi Bayat 국제구조공학회 2016 Structural Engineering and Mechanics, An Int'l Jou Vol.59 No.4
In this paper, a new analytical approach has been presented for solving nonlinear conservative oscillators. Variational approach leads us to high accurate solution with only one iteration. Two different high nonlinear examples are also presented to show the application and accuracy of the presented approach. The results are compared with numerical solution using runge-kutta algorithm in different figures and tables. It has been shown that the variatioanl approach doesn’t need any small perturbation and is accurate for nonlinear conservative equations.
Accurate semi-analytical solution for nonlinear vibration of conservative mechanical problems
Mahmoud Bayat,Iman Pakar 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.61 No.5
In this paper, it has been tried to propose a new semi analytical approach for solving nonlinear vibration of conservative systems. Hamiltonian approach is presented and applied to high nonlinear vibration systems. Hamiltonian approach leads us to high accurate solution using only one iteration. The method doesn’t need any small perturbation and sufficiently accurate to both linear and nonlinear problems in engineering. The results are compared with numerical solution using Runge- Kutta-algorithm. The procedure of numerical solution are presented in detail. Hamiltonian approach could be simply apply to other powerfully non-natural oscillations and it could be found widely feasible in engineering and science.
Study of complex nonlinear vibrations by means of accurate analytical approach
Mahmoud Bayat,Iman Pakar,Mahdi Bayat 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.17 No.5
In the current study, we consider a new class of analytical periodic solution for free nonlinear vibration of mechanical systems. Hamiltonian approach is applied to analyze nonlinear problems which occur in dynamics. The proposed method doesn't have the limitations of the classical methods and leads us to a high accurate solution by only one iteration. Two well known examples are studied to show the convenience and effectiveness of this approach. Runge-Kutta's algorithm is also applied and the results of it are compared with the Hamiltonian approach. High accuracy of the proposed approach reveals that the Hamiltonian approach can be very useful for other nonlinear practical problems in engineering.
An accurate novel method for solving nonlinear mechanical systems
Bayat, Mahdi,Pakar, Iman,Bayat, Mahmoud Techno-Press 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.51 No.3
This paper attempts to investigate the nonlinear dynamic analysis of strong nonlinear problems by proposing a new analytical method called Hamiltonian Approach (HA). Two different cases are studied to show the accuracy and efficiency of the method. This approach prepares us to obtain the nonlinear frequency of the nonlinear systems with the first order of the solution with a high accuracy. Finally, to verify the results we present some comparisons between the results of Hamiltonian approach and numerical solutions using Runge-Kutta's [RK] algorithm. This approach has a powerful concept and the high accuracy, so it can be apply to any conservative nonlinear problems without any limitations.