Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; Allen, Matthew S.

doi:10.2514/1.J053838

Title: Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

Journal Article · Tue Sep 15 00:00:00 EDT 2015 · AIAA Journal

DOI:https://doi.org/10.2514/1.J053838· OSTI ID:1237462

Kuether, Robert J. ^[1]; Deaner, Brandon J. ^[2]; Hollkamp, Joseph J. ^[3]; Allen, Matthew S. ^[1]

Univ. of Wisconsin, Madison, WI (United States)
Mercury Marine, Fond du Lac, WI (United States)
U.S. Air Force Research Lab., Wright-Patterson Air Force Base, OH (United States)

Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: Air Force Office of Scientific Research, OH (United States)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1237462

Report Number(s):: SAND-2015-2368J; 579511

Journal Information:: AIAA Journal, Vol. 53, Issue 11; ISSN 0001-1452

Publisher:: AIAACopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 55 works

Citation information provided by
Web of Science

References (26)

Reduced-Order Models for Acoustic Response Prediction of a Curved Panel Gordon, Robert; Hollkamp, Joseph 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference https://doi.org/10.2514/6.2011-2081	conference	June 2012
Verification Studies on Hypersonic Structure Thermal/Acoustic Response and Life Prediction Methods Tzong, George T.; Liguore, Salvatore L. 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference https://doi.org/10.2514/6.2013-1664	conference	April 2013
Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques Peeters, M.; Viguié, R.; Sérandour, G. Mechanical Systems and Signal Processing, Vol. 23, Issue 1 https://doi.org/10.1016/j.ymssp.2008.04.003	journal	January 2009
A numerical approach to directly compute nonlinear normal modes of geometrically nonlinear finite element models Kuether, Robert J.; Allen, Matthew S. Mechanical Systems and Signal Processing, Vol. 46, Issue 1 https://doi.org/10.1016/j.ymssp.2013.12.010	journal	May 2014
Normal Modes of Nonlinear Dual-Mode Systems Rosenberg, R. M. Journal of Applied Mechanics, Vol. 27, Issue 2 https://doi.org/10.1115/1.3643948	journal	June 1960
NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW Vakakis, A. F. Mechanical Systems and Signal Processing, Vol. 11, Issue 1 https://doi.org/10.1006/mssp.1996.9999	journal	January 1997
Nonlinear normal modes, Part I: A useful framework for the structural dynamicist Kerschen, G.; Peeters, M.; Golinval, J. C. Mechanical Systems and Signal Processing, Vol. 23, Issue 1 https://doi.org/10.1016/j.ymssp.2008.04.002	journal	January 2009
Dynamic testing of nonlinear vibrating structures using nonlinear normal modes Peeters, M.; Kerschen, G.; Golinval, J. C. Journal of Sound and Vibration, Vol. 330, Issue 3 https://doi.org/10.1016/j.jsv.2010.08.028	journal	January 2011
Nonlinear modal models for sonic fatigue response prediction: a comparison of methods Hollkamp, Joseph J.; Gordon, Robert W.; Spottswood, S. Michael Journal of Sound and Vibration, Vol. 284, Issue 3-5 https://doi.org/10.1016/j.jsv.2004.08.036	journal	June 2005
A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures Mignolet, Marc P.; Przekop, Adam; Rizzi, Stephen A. Journal of Sound and Vibration, Vol. 332, Issue 10 https://doi.org/10.1016/j.jsv.2012.10.017	journal	May 2013
A Finite Element time Domain Modal Formulation for Large Amplitude free Vibrations of Beams and Plates Shi, Y.; Mei, C. Journal of Sound and Vibration, Vol. 193, Issue 2 https://doi.org/10.1006/jsvi.1996.0295	journal	June 1996
Reduction Method for Finite Element Nonlinear Dynamic Analysis of Shells Tiso, Paolo; Jansen, Eelco; Abdalla, Mostafa AIAA Journal, Vol. 49, Issue 10 https://doi.org/10.2514/1.J051003	journal	October 2011
A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 1: Derivation Segalman, D. J.; Dohrmann, C. R. Journal of Vibration and Acoustics, Vol. 118, Issue 3 https://doi.org/10.1115/1.2888183	journal	July 1996
A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 2: Example Calculations Segalman, D. J.; Dohrmann, C. R.; Slavin, A. M. Journal of Vibration and Acoustics, Vol. 118, Issue 3 https://doi.org/10.1115/1.2888184	journal	July 1996
Determination of nonlinear stiffness with application to random vibration of geometrically nonlinear structures Muravyov, Alexander A.; Rizzi, Stephen A. Computers & Structures, Vol. 81, Issue 15 https://doi.org/10.1016/S0045-7949(03)00145-7	journal	July 2003
Nonlinear Sonic Fatigue Response Prediction from Finite Element Modal Models: A Comparison with Experiments Hollkamp, Joseph; Gordon, Robert; Spottswood, Stephen 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference https://doi.org/10.2514/6.2003-1709	conference	June 2012
A Combined Modal/Finite Element Analysis Technique for the Dynamic Response of a Non-Linear beam to Harmonic Excitation Mcewan, M. I.; Wright, J. R.; Cooper, J. E. Journal of Sound and Vibration, Vol. 243, Issue 4 https://doi.org/10.1006/jsvi.2000.3434	journal	June 2001
Reduced-order models for nonlinear response prediction: Implicit condensation and expansion Hollkamp, Joseph J.; Gordon, Robert W. Journal of Sound and Vibration, Vol. 318, Issue 4-5 https://doi.org/10.1016/j.jsv.2008.04.035	journal	December 2008
Alternative modal basis selection procedures for reduced-order nonlinear random response simulation Przekop, Adam; Guo, Xinyun; Rizzi, Stephen A. Journal of Sound and Vibration, Vol. 331, Issue 17 https://doi.org/10.1016/j.jsv.2012.03.034	journal	August 2012
System identification-guided basis selection for reduced-order nonlinear response analysis Rizzi, Stephen A.; Przekop, Adam Journal of Sound and Vibration, Vol. 315, Issue 3 https://doi.org/10.1016/j.jsv.2007.12.031	journal	August 2008
Relationships between Nonlinear Normal Modes and Response to Random Inputs Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J. 55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference https://doi.org/10.2514/6.2014-1514	conference	January 2014
Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment Lee, Young Sup; Kerschen, Gaetan; Vakakis, Alexander F. Physica D: Nonlinear Phenomena, Vol. 204, Issue 1-2 https://doi.org/10.1016/j.physd.2005.03.014	journal	May 2005
The Effect of Basis Selection on Thermal-Acoustic Random Response Prediction Using Nonlinear Modal Simulation Rizzi, Stephen; Przekop, Adam 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference https://doi.org/10.2514/6.2004-1554	conference	June 2012
Reduced-Order Modeling of Random Response of Curved Beams Using Implicit Condensation Gordon, Robert; Hollkamp, Joseph 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 14th AIAA/ASME/AHS Adaptive Structures Conference 7th, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR> 14th AIAA/ASME/AHS Adaptive Structures Conference<BR> 7th https://doi.org/10.2514/6.2006-1926	conference	June 2012
On the Use of Reduced-Order Models for a Shallow Curved Beam Under Combined Loading Spottswood, Stephen; Hollkamp, Joseph; Eason, Thomas 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 16th AIAA/ASME/AHS Adaptive Structures Conference 10t, 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference <br> 16th AIAA/ASME/AHS Adaptive Structures Conference<br> 10t https://doi.org/10.2514/6.2008-2235	conference	June 2012
Relationships between nonlinear normal modes and response to random inputs Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J. Mechanical Systems and Signal Processing, Vol. 84 https://doi.org/10.1016/j.ymssp.2016.07.010	journal	February 2017

Cited By (6)

Performance‐based seismic design of tuned inerter dampers Radu, Alin; Lazar, Irina F.; Neild, Simon A. Structural Control and Health Monitoring, Vol. 26, Issue 5 https://doi.org/10.1002/stc.2346	journal	February 2019
Stochastic reduced-order models for stable nonlinear ordinary differential equations Radu, Alin Nonlinear Dynamics, Vol. 97, Issue 1 https://doi.org/10.1007/s11071-019-04967-x	journal	May 2019
On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models Givois, Arthur; Grolet, Aurélien; Thomas, Olivier Nonlinear Dynamics, Vol. 97, Issue 2 https://doi.org/10.1007/s11071-019-05021-6	journal	June 2019
Identifying the significance of nonlinear normal modes Hill, T. L.; Cammarano, A.; Neild, S. A. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2199 https://doi.org/10.1098/rspa.2016.0789	journal	March 2017
Aircraft Active Flutter Suppression: State of the Art and Technology Maturation Needs Livne, Eli Journal of Aircraft, Vol. 55, Issue 1 https://doi.org/10.2514/1.c034442	journal	January 2018
Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J. AIAA Journal, Vol. 55, Issue 5 https://doi.org/10.2514/1.j055215	journal	May 2017

Similar Records

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

Journal Article · Wed Mar 29 00:00:00 EDT 2017 · AIAA Journal · OSTI ID:1237462

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

Relationships between nonlinear normal modes and response to random inputs

Journal Article · Mon Jul 25 00:00:00 EDT 2016 · Mechanical Systems and Signal Processing · OSTI ID:1237462

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

Multi-mode quasi-static excitation for systems with nonlinear joints

Journal Article · Wed Feb 15 00:00:00 EST 2023 · Mechanical Systems and Signal Processing · OSTI ID:1237462

Singh, Aabhas; Allen, Matthew S.; Kuether, Robert J.

Related Subjects

97 MATHEMATICS AND COMPUTING

Title: Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

Citation Formats

References (26)

Cited By (6)

Similar Records

Related Subjects