Comparison of Linear and Nonlinear Modal Reduction Approaches

Ferhatoğlu, Erhan
Dreher, Tobias
Ciğeroğlu, Ender
Krack, Malte
Özgüven, Hasan Nevzat
Periodic vibration response of nonlinear mechanical systems can be efficiently computed using Harmonic Balance Method. However, computational burden may still be considerable and impede extensive parametric studies needed for, e.g., design optimization and prediction of vibration response especially when the degree of freedom is very large. In this work, the methods which had been previously developed by the authors for further model order reduction to one or a few coordinates are compared. The focus is placed mainly on modal approaches, namely Modal Superposition Method using Linear Modes (MSM-LM), Modal Superposition Method using Hybrid Modes (MSM-HM), and Modal Superposition Method using Nonlinear Modes (MSM-NM). Another method for vibration analysis of nonlinear structures is the Receptance Method (RM), in which the harmonic response of a nonlinear MDOF system is calculated from the receptances of the linear counterparts. This method exploits the sparsity of the nonlinear terms in frequency domain equations and therefore may be very efficient when the nonlinearity is local, which is the case in several applications. Performances and accuracies of these methods are compared with each other using the results of the direct analysis of the full order model as reference. The methods are applied to a benchmark system consisting of a finite element model of a beam with different nonlinear elements; but, only the results of dry friction elements are presented here. The focus is placed on periodic forced response regimes near resonances. Several conclusions and recommendations that may guide users are derived from the comparison studies. © 2020, Society for Experimental Mechanics, Inc.
Citation Formats
E. Ferhatoğlu, T. Dreher, E. Ciğeroğlu, M. Krack, and H. N. Özgüven, “Comparison of Linear and Nonlinear Modal Reduction Approaches,” presented at the Conference exposition on structural dynamics, Florida, Amerika Birleşik Devletleri, (28 - 31 Ocak 2019), Florida, Amerika, 2019, Accessed: 00, 2021. [Online]. Available: