A comparative study of the harmonic balance method and the orthogonal collocation method on stiff nonlinear systems

作者：Karkar Sami^*; Cochelin Bruno; Vergez Christophe

来源：Journal of Sound and Vibration, 2014, 333(12): 2554-2567.

DOI：10.1016/j.jsv.2014.01.019

The high-order purely frequency-based harmonic balance method (HBM) presented by Cochelin and Vergez (2009) [1] and extended by Karkar et al. (2013) [2] now allows to follow the periodic solutions of regularized non-smooth systems (stiff systems). This paper compares its convergence property to a reference method in applied mathematics: orthogonal collocation with piecewise polynomials. A first test is conducted on a nonlinear smooth 2 degree-of-freedom spring mass system, showing better convergence of the HBM. The second test is conducted on a one degree-of-freedom vibro-impact system with a very stiff regularization of the impact law. The HBM continuation of the nonlinear mode was found to be very robust, even with a very large number of harmonics. Surprisingly, the HBM was found to have a better convergence than the collocation method for this vibro-impact system.

• 出版日期2014-6-9