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

DOI:https://doi.org/10.1016/j.ymssp.2016.07.010· OSTI ID:1339292

Schoneman, Joseph D. ^[1]; Allen, Matthew S. ^[1]; Kuether, Robert J. ^[2]

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1. Univ. of Wisconsin-Madison, Madison, WI (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1339292
• Report Number(s): SAND--2016-1674J; PII: S0888327016302369
• Journal Information: Mechanical Systems and Signal Processing, Journal Name: Mechanical Systems and Signal Processing Journal Issue: PA Vol. 84; ISSN 0888-3270
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
geometric nonlinearity
nonlinear normal modes
random response