ABSTRACT
The incremental harmonic balance method (IHB) has been developed to study the control and dynamic stability of the strongly nonlinear oscillators. The method of analysis for obtaining the primary and higher-order subharmonic frequency response curves for multi-degree of freedom systems with time-delayed state feedback is discussed. A reformulation of the IHB method is then presented for the efficient tracing of frequency response curves using path following and parametric continuation technique amenable to IHB form. The stability of uncontrolled responses is obtained by Floquet’s theory using Hsu's scheme, whereas the stability of controlled responses is obtained using the semi-discretization method for delay differential equations (DDEs). According to Floquet’s theory of stability analysis, if the absolute values of all eigenvalues of the transition matrix are less than unity, then the periodic solution is stable. If at least one of the eigenvalues has a magnitude greater than one, then the periodic solution is unstable. The way the eigenvalues leave the unit circle determines the nature of bifurcations.
