Abstract
In the determination of response of nonlinear structures, computational burden is always a major problem even if frequency domain methods are used. One of the methods used to decrease the computational effort is the modal superposition method for nonlinear systems where the modes of the linear system are used in the calculation. However, depending on the type of the nonlinearity, in order to obtain an accurate response, the number of modes retained in the response calculations needs to be increased, which increases the number of nonlinear equations to be solved. In this study, a method is proposed to decrease the number of modes used for systems having nonlinearities where the equivalent stiffness varies between two limiting values. For such systems, one can define different linear systems for each value of the limiting equivalent stiffness. In this study, it is proposed to use a combination of these linear mode shapes in the modal superposition method. It is shown that proper combination of mode shapes of different linear systems provides satisfactory results by keeping the number of modes used at a minimum. The method is demonstrated on case studies where describing function method is used in the analysis of the nonlinear system.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Menq, C.H., Griffin, J.H., Bielak, J.: The influence of microslip on vibratory response, Part II: a “comparison with experimental results”. J. Sound Vib. 107(2), 295–307 (1986)
Chen, J.J., Menq, C.H.: Prediction of the resonant response of frictionally constrained blade systems using constrained mode shapes. In: Proceedings of the International Gas Turbine & Aero Engine Congrees & Exhibition, Stockholm, Sweden, 1998
Petrov, E.P.: A high-accuracy model reduction for analysis of nonlinear vibrations in structures with contact interfaces. J. Eng. Gas Turb. Power 133(10), 102503/1–102503/10 (2011)
Kuran, B., Özgüven, H.N.: A modal superposition method for nonlinear structures. J. Sound Vib. 189(3), 315–339 (1996)
Cigeroglu, E., An, N., Menq, C.H.: A microslip friction model with normal load variation induced by normal motion. Nonlinear Dyn. 50(3), 609–626 (2007)
Cigeroglu, E., An, N., Menq, C.H.: Forced response prediction of constrained and unconstrained structures coupled through frictional contacts. J. Eng. Gas Turb. Power 131(2), 11 (2009)
Cigeroglu, E., Özgüven, H.N.: Non-linear vibration analysis of bladed disks with dry friction dampers. J. Sound Vib. 295, 1028–1043 (2006)
Tanrıkulu, O., Kuran, B., Özgüven, H.N., Imregun, M.: Forced harmonic response analysis of non-linear structures using describing functions. AIAA J. 31(7), 1313–1320 (1993)
Gelb, A., Vander Velde, W.E.: Multiple-input describing functions and nonlinear system design. McGraw-Hill, New York (1968)
Atherton, D.P.: Nonlinear control engineering: Describing Function Analysis and Design. Van Nostrand Reinhold, London, 627 (1975)
Cigeroglu, E., Samandari, H.: Nonlinear free vibration of double walled carbon nanotubes by using describing function method with multiple trial functions. Phys. E 46, 160–173 (2012)
Groll, G.V., Ewins, D.J.: The harmonic balance method with arc-length continuation in rotor/stator contact problems. J. Sound Vib. 241(2), 223–233 (2001)
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
Ferhatoğlu, E., Ciğeroğlu, E., Özgüven, H.N. (2016). A Modal Superposition Method for the Analysis of Nonlinear Systems. 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_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-29910-5_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29909-9
Online ISBN: 978-3-319-29910-5
eBook Packages: EngineeringEngineering (R0)