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

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• 作者：Sami Karkar¹ ; ^{sami.karkar@epfl.ch" class="auth_mail} ; Bruno Cochelin ^{bruno.cochelin@centrale-marseille.fr" class="auth_mail} ; Christophe Vergez ^{vergez@lma.cnrs-mrs.fr" class="auth_mail}
• 刊名：Journal of Sound and Vibration
• 出版年：9 June, 2014
• 年：2014
• 卷：333
• 期：12
• 页码：2554-2567
• 全文大小：801 K

文摘

The high-order purely frequency-based harmonic balance method (HBM) presented by Cochelin and Vergez (2009) and extended by Karkar et al. (2013) 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.