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Title: 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 spring-mass system and a clamped-clamped 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 frequency-energy 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, single-degree-of-freedom nonlinear models are found to predict majormore » 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 frequency-energy dependence of the nonlinear modes that are excited.« less

Authors:
 [1];  [1];  [2]
  1. Univ. of Wisconsin-Madison, Madison, WI (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1339292
Report Number(s):
SAND-2016-1674J
Journal ID: ISSN 0888-3270; PII: S0888327016302369
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
Mechanical Systems and Signal Processing
Additional Journal Information:
Journal Volume: 84; Journal Issue: PA; Journal ID: ISSN 0888-3270
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 spring-mass system and a clamped-clamped 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 frequency-energy 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, single-degree-of-freedom 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 frequency-energy 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}
}

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