engleski

Oscillator with a sum o non-integral order non-linearities

In this paper free and self-excited vibrations of conservative oscillators with quasi-polynomial non-linearity are considered. Mathematical model of the system is a second order differential equation with a non-linearity of quasi-polynomial type which terms are of integer and/or special rational order. For the case when only one non-linear term exists the exact analytical solution of the differential equation is determined as a cosine-Ateb function. Based on this solution the asymptotic averaging procedure for solving the perturbed strong non-linear differential equation is developed. The method does not require the existence of the small parameter in the system. Special attention is given to the case when the dominant term is a linear one, and to the case when it is of any non-linear order. Exact solutions of the averaged differential equations of motion are obtained. The obtained results are compared with 'exact' numerical solutions and previously obtained analytical approximate ones. Advantages and disadvantages of the suggested procedure are discussed.

Second order linear nonhomogeneous ODE; Incomplete Beta function; Ateb(h)-functions; Periodic solutions; Perturbation method; Averaging procedure

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