Abstract
Harmonic balance method (HBM) is one of the most popular and powerful methods, which is used to obtain response of nonlinear vibratory systems in frequency domain. The main idea of the method is to express the response of the system in Fourier series and converting the nonlinear differential equations of motion into a set of nonlinear algebraic equations. System response can be obtained by solving this nonlinear equation set in terms of the unknown Fourier coefficients. The accuracy of the solution is greatly affected by the number of harmonics included in the solution; hence, increasing the number of harmonics increases the accuracy of the solution at the expense of computational effort. Therefore, it is desirable to use an adaptive algorithm where the number of harmonics can be optimized in terms of both accuracy and computational effort. Until now, various adaptive harmonic balance methods have been formulated to perform this task. This paper presents an overview and a comparison of these adaptive harmonic balance methods in terms of their effectiveness.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
LaBryer, A., Attar, P.J.: A harmonic balance approach for large-scale problems in nonlinear structural dynamics. Comput. Struct. 88(17–18), 1002–1014 (2010)
Sarrouy, E., Sinou, J.: Non-linear periodic and quasi-periodic vibrations in mechanical systems-on the use of the harmonic balance methods. In: Ebrahimi, D.F. (ed.) Advances in Vibration Analysis Research InTech, Rijeka, Croatia, pp. 419–434. (2011)
Kim, Y., Choi, S.: A multiple harmonic balance method for the internal resonant vibration of a non-linear Jeffcott rotor. J. Sound Vib. 208, 745–761 (1997)
von Groll, G., Ewins, D.J.: The harmonic balance method with arc-length continuation in rotor/stator contact problems. J. Sound Vib. 241(2), 223–233 (2001)
Lau, S.L., Cheung, Y.K.: Amplitude incremental variational principle for nonlinear vibration of elastic systems. J. Appl. Mech. 48(4), 959 (1981)
Yuste, B.S.: Comments on the method of harmonic balance in which Jacobi elliptic functions are used. J. Sound Vib. 145(3), 381–390 (1991)
Kim, Y., Noah, S.: Quasi-periodic response and stability analysis for a non-linear Jeffcott rotor. J. Sound Vib. 190, 239–253 (1996)
Kim, T.C., Rook, T.E., Singh, R.: Super- and sub-harmonic response calculations for a torsional system with clearance nonlinearity using the harmonic balance method. J. Sound Vib. 281(3–5), 965–993 (2005)
Jaumouillé, V., Sinou, J.-J., Petitjean, B.: An adaptive harmonic balance method for predicting the nonlinear dynamic responses of mechanical systems—application to bolted structures. J. Sound Vib. 329(19), 4048–4067 (2010)
Grolet, A., Thouverez, F.: On a new harmonic selection technique for harmonic balance method. Mech. Syst. Sig. Process. 30, 43–60 (2012)
Yümer, M.E.: On the Non-Linear Vibration and Mistuning Identification of Bladed Disks. Middle East Technical University, Ankara, Turkey (2010)
Zhu, L., Christoffersen, C.E.: Adaptive harmonic balance analysis of oscillators using multiple time scales. In IEEE-NEWCAS Conference, 2005. The 3rd International, Quebec City, 187–190 (2005), doi: 10.1109/NEWCAS.2005.1496738
Gourary, M.M., Rusakov, S.G., Ulyanov, S.L., Zharov, M.M., Gullapalli, K.K., Mulvaney, B.J.: A New Computational Approach to Simulate Highly Nonlinear Systems by Harmonic Balance Method. In 16th IMACS WORLD CONGRESS 2000 on Scientific Computation, Applied Mathematics and Simulation. Lausanne, 366 (2000)
Maple, R.C., King, P.I., Orkwis, P.D., Mitch Wolff, J.: Adaptive harmonic balance method for nonlinear time-periodic flows. J. Comput. Phys. 193(2), 620–641 (2004)
Cameron, T.M., Griffin, J.H.: An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems. J. Appl. Mech. 56(1), 149 (1989)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Sert, O., Ciğeroğlu, E. (2016). Adaptive Harmonic Balance Methods, A Comparison. In: Di Miao, D., Tarazaga, P., Castellini, P. (eds) Special Topics in Structural Dynamics, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-29910-5_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-29910-5_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29909-9
Online ISBN: 978-3-319-29910-5
eBook Packages: EngineeringEngineering (R0)