A new approximate analytical technique to address for non-linear problems, namely Optimal Homotopy Asymptotic Method (OHAM) is proposed and has been applied to thin film flow of a fourth grade fluid down a vertical cylinder. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a convenient way to control the convergence of approximation series and allows adjustment of convergence regions where necessary. The series solution has been developed and the recurrence relations are given explicitly. The results reveal that the proposed method is very accurate, effective and easy to use.

In this paper, a new analytical approach is proposed to investigate the electrical and mechanical behavior of a low-power permanent magnet synchronous generator (PMSG) in the presence of a wind gust. The proposed model for the wind gust and wind power system was analytically investigated using the optimal auxiliary functions method (OAFM), which has proven to be a reliable tool. The reaction of the system to a wind gust was explicitly obtained, which is useful for stability analysis, protection issues, and risk assessment concerning the PMSG. A substantial reduction of computations in analytically analysing a complicated dynamical system is ensured by this new approach, through some auxiliary functions and convergence-control parameters.

This paper deals with the analytical investigation of a multirotor system connected by a flexible coupling subjected to dynamic angular misalignment. A novel analytical approach is employed for this purpose, namely the optimal auxiliary functions method, which proved to be successfully used to obtain explicit analytical solutions to a system of strongly nonlinear differential equations with variable coefficients, useful in dynamic analysis of the considered multirotor system. The proposed procedure proved to be very efficient in practice for solving complicated nonlinear vibration problems.

In this paper we analyze the behavior of a permanent magnet generator used in a wind turbine system. Different from other works, the wind profile is considered

In the present work, the nonlinear oscillations of a pendulum wrapping on two cylinders is studied by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM). The equation of motion is derived from the Lagrange’s equation. Analytical solutions and natural frequency of the system are calculated. Our results obtained through this new procedure are compared with numerical ones and a very good agreement was found, which proves the accuracy of the method. The presented numerical examples show that the proposed approach is simple, easy to implement and very accurate.