Abstract
An extension of the harmonic balance method is presented for calculation of the steady state (periodic) solutions in autonomous non-linear systems. The non-linear differential equation is expanded into a system of linear differential equations which are solved consecutively. An approximate solution which includes a few harmonics (the main oscillation) is found from the first equation of this system by the ordinary harmonic balance method. Other harmonics and the corrections of the main oscillation are found as the forced solutions of the second, third and the following equations of the system. To improve the efficiency of correction calculations a systematic method for derivation of the forcing term in these equations is given. As an example, a non-linear conservative system with a non-symmetric non-linearity of the polynomial type is considered.
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