EFFICIENT DETERMINATION OF HIGHER-ORDER PERIODIC-SOLUTIONS USING N-MODE HARMONIC-BALANCE

This paper presents a systematic procedure to explicitly determine the algebraic equations arising from the method of harmonic balance with an arbitrary number of modes in the assumed solutions. The technique c an be used for a wide variety of nonlinear oscillators (including syst ems of ordinary differential equations). The method is illustrated in the case of second-order differential equations with nonlinear restori ng force. Although numerical methods have been employed to solve the r esulting systems of algebraic equations, the general approach is analy tic. As such, this study confirms independently (i.e. nonsimulation) t he period-doubling cascade of an escape equation including the bifurca tion universal scaling laws.