Abstract
In this paper we demonstrate the utility of the High Dimensional Harmonic Balance (HDHB) method to compute periodic orbits of second-order delay-differential equations. In particular, the method has been successfully applied to capture the unstable limit cycles of a model of regenerative machine tool vibrations. Both the conventional harmonic balance and the HDHB methods are employed to investigate the dynamic behavior of the nonlinear delay equation. The results show an excellent agreement with those from time domain solutions. The advantages of HDHB over the classical Harmonic Balance method are highlighted and discussed.
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