Relationships between nonlinear normal modes and response to random inputs
Abstract
The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). Here, this work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a springmass system and a clampedclamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequencyenergy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, singledegreeoffreedom nonlinear models are found to predict majormore »
 Authors:

 Univ. of WisconsinMadison, Madison, WI (United States)
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1339292
 Report Number(s):
 SAND20161674J
Journal ID: ISSN 08883270; PII: S0888327016302369
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Mechanical Systems and Signal Processing
 Additional Journal Information:
 Journal Volume: 84; Journal Issue: PA; Journal ID: ISSN 08883270
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING; nonlinear normal modes; geometric nonlinearity; random response
Citation Formats
Schoneman, Joseph D., Allen, Matthew S., and Kuether, Robert J. Relationships between nonlinear normal modes and response to random inputs. United States: N. p., 2016.
Web. doi:10.1016/j.ymssp.2016.07.010.
Schoneman, Joseph D., Allen, Matthew S., & Kuether, Robert J. Relationships between nonlinear normal modes and response to random inputs. United States. doi:10.1016/j.ymssp.2016.07.010.
Schoneman, Joseph D., Allen, Matthew S., and Kuether, Robert J. Mon .
"Relationships between nonlinear normal modes and response to random inputs". United States. doi:10.1016/j.ymssp.2016.07.010. https://www.osti.gov/servlets/purl/1339292.
@article{osti_1339292,
title = {Relationships between nonlinear normal modes and response to random inputs},
author = {Schoneman, Joseph D. and Allen, Matthew S. and Kuether, Robert J.},
abstractNote = {The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). Here, this work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a springmass system and a clampedclamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequencyenergy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, singledegreeoffreedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequencyenergy dependence of the nonlinear modes that are excited.},
doi = {10.1016/j.ymssp.2016.07.010},
journal = {Mechanical Systems and Signal Processing},
number = PA,
volume = 84,
place = {United States},
year = {2016},
month = {7}
}
Web of Science