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Frequency Response Calculations of a Nonlinear Structure a Comparison of Numerical Methods
Linnaeus University, Faculty of Technology, Department of Mechanical Engineering. (Maskinteknik)
Linnaeus University, Faculty of Technology, Department of Mechanical Engineering. (Maskinteknik)ORCID iD: 0000-0002-4404-5708
Chalmers tekniska högskola. (Strukturdynamik)
2014 (English)In: Nonlinear Dynamics, Volume 2: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014 / [ed] Gaetan Kerschen, Springer, 2014, p. 35-44Conference paper, Published paper (Refereed)
Abstract [en]

Mechanical systems having presence of nonlinearities are often represented by nonlinear ordinary differential 5 equations. For most of such equations, exact analytic solutions are not found; thus numerical techniques have to be used. 6 In many applications, among which model calibration can be one, steady-state frequency response functions are the desired 7 quantities to calculate. 8 The objective of this paper is to compare the performance of computations of nonlinear frequency response functions 9 (FRFs) calculated directly within the frequency domain, using the Multi-Harmonic Balance method, with the time-domain 10 methods Runge–Kutta, Newmark and Pseudo Force in State Space (PFSS). The PFSS method is a recently developed state- 11 space based force feedback method that is shown to give efficient solutions. 12 The accuracy and efficiency of the methods are studied and compared using a model of a cantilever beam connected to a 13 non-linear spring at its free end.

Place, publisher, year, edition, pages
Springer, 2014. p. 35-44
Keywords [en]
Numerical methods, simulation, Nonlinear, Structural Dynamics, Harmonic Balancing, State Space
National Category
Engineering and Technology Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
URN: urn:nbn:se:lnu:diva-33610DOI: 10.1007/978-3-319-04522-1_4ISI: 000342929100004Scopus ID: 2-s2.0-84907377218ISBN: 978-3-319-04522-1 (print)ISBN: 978-3-319-04522-1 (print)OAI: oai:DiVA.org:lnu-33610DiVA, id: diva2:710104
Conference
International Modal Analysis Conference (IMAC XXXII) A Conference and Exposition on Structural Dynamics, February 3–6, 2014, Orlando, Florida
Funder
VinnovaAvailable from: 2014-04-04 Created: 2014-04-04 Last updated: 2015-05-24Bibliographically approved
In thesis
1. Model Calibration of Nonlinear Mechanical Systems Using Multi-Harmonic Frequency Response Functions
Open this publication in new window or tab >>Model Calibration of Nonlinear Mechanical Systems Using Multi-Harmonic Frequency Response Functions
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In industry, linear finite element models are commonly employed to represent global structural behavior. It is crucial that the computational models are able to accurately represent the structures’ behavior. This cannot always be achieved by the use of linear models.

When vibrational test data show significant nonlinear characteristics, an initial linear finite element model may be judged insufficient in representing the structural behavior. Although an initial model can give a good foundation for the understanding of the dynamic behavior of the structure, the parameters that capture the nonlinear effects are most likely not included. Therefore, a set of candidate parameters controlling the nonlinear effect have to be added. The selection of such candidates is a delicate task which solution is preferably supported by engineering insight into the characteristics of the structure.

One part of this work is on the selection of parameters, among all possibly uncertain properties, together with the forming of the objective function to be used for calibration. To obtain precise estimates of the parameters, the objective function data have to be informative with respect to the selected parameters. Further the parameters have to be identifiable. To improve these qualities, a multi-harmonic sinusoidal excitation was designed since the corresponding steady-state responses at the sub- and super- harmonics were shown to contain valuable information for the calibration process. Model calibration of nonlinear systems made by minimizing the differences between predicted and measured multi-harmonic frequency response functions.

Further, in the calibration, multi-harmonic frequency response functions need to be calculated recurrently in order to reach convergence; therefore a fast simulation scheme was required. The performance of computations of multi-harmonic frequency response functions calculated using time domain as well as frequency domain simulation techniques were studied and compared.

Finally, the proposed calibration method was validated by use of experimental testing on a replica of the Ecole de Lyon nonlinear benchmark structure. It was shown in the validation results that the predictions stemming from the calibrated model matched the experimental data well.

Place, publisher, year, edition, pages
Växjö: Linnaeus University, 2014. p. 75
Keywords
finite element model calibration, multi-harmonic frequency response function, Fisher information matrix, nonlinear structural dynamics, identifiability, data informativeness
National Category
Mechanical Engineering
Research subject
Technology (byts ev till Engineering), Mechanical Engineering
Identifiers
urn:nbn:se:lnu:diva-34736 (URN)
Presentation
2014-06-12, 13:32 (English)
Opponent
Supervisors
Funder
Vinnova
Available from: 2014-06-09 Created: 2014-06-06 Last updated: 2015-05-24Bibliographically approved

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Chen, YoushengLinderholt, Andreas

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