The periodic solutions of a strongly cubic nonlinear oscillator whose motion is described with the generalized Rayleigh equation are studied. Approximate analytic solving methods are introduced. A new method based on homotopy and averaging is developed to determine the limit cycle motion. The obtained analytical solutions are compared with those calculated by the elliptic harmonic balance method with generalized Fourier ... Read more

ABSTRACT: In this paper, He’s energy balance method is applied to nonlinear oscillators. The obtained results are valid for the whole solution domain with high accuracy. Comparison is made with the solutions obtained by using He’s frequency-amplitude formulation and Runge-Kutta method to show the efficiency of the energy balance method. Read more

In this paper, the periodic solutions of a strongly quadratic nonlinear oscillator whose motion is described with the generalized Van der Pol equation are studied. A new method based on homotopy and averaging is employed to determine the limit cycle motion. Three types of quadratic nonlinearity are considered: the coefficients of the linear and quadratic terms are positive, the coefficient ... Read more

This paper applies modified He's iteration perturbation method to study periodic solutions of strongly nonlinear oscillators. Some examples are given to illustrate the effectiveness and convenience of the method. The results are compared with the numerical solution and the comparison showed a proper accuracy of this method. Read more