Structural Modification of Nonlinear FEA Subcomponents Using Nonlinear Normal Modes

Kuether, Robert J.; Allen, Mathew S.

doi:10.1007/978-1-4614-6540-9_4

Cited by 5 publications

(3 citation statements)

References 24 publications

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“…In the algorithm that follows, the QL mode shapes and frequencies will be adjusted based on the amount of strain energy experienced by the subcomponent. Note that each mode could instead be defined at a different energy level, as was done in [21], and this would perhaps be more in keeping with the spirit of the harmonic balance model in Eq. (4), but this was not explored in this work.…”

Section: A Quasi-linear Modal Modelmentioning

confidence: 95%

“…The quasi-linear NNM substructuring approach presented here is not capable of capturing this behavior because it is a purely nonlinear phenomenon which depends on the higher harmonics in the response and the quasi-linear analysis is based only on the fundamental frequency of each mode. As discussed in [21], the NNM backbone can be used to estimate candidate locations of internal resonances based on the points in the frequency-energy plane where the frequencies of the branches are integer related. On the other hand, when the internal resonances are not of interest, the quasi-linear algorithm provides a convenient means for estimating the backbone alone.…”

Section: B Nonlinear Substructuringmentioning

confidence: 99%

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Nonlinear Modal Substructuring of Systems with Geometric Nonlinearities

Kuether

Allen

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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The analysis of large, complicated structures can be simplified and made more computationally efficient if smaller, simpler subcomponents can be treated and assembled. Modal substructuring methods allow one to reduce the order of the model at the subcomponent level. Modes are also an intrinsic property of the subcomponent, so they lead to certain physical insights. While modal substructuring is relatively well developed for linear systems, it's counterpart has not yet been developed for nonlinear subcomponent models. This work presents two modal substructuring techniques that can be used to predict the nonlinear dynamic behavior of an assembly. The first method uses the nonlinear normal modes of each subcomponent in a quasi-linear model to estimate the nonlinear modes of the assembly. In the second approach, a small number of linear modes are used to create a nonlinear reduced order model of each substructure, and the reduced models are assembled to build the nonlinear equations of motion of the assembly. Each approach is compatible with the finite element method, allowing for analysis of realistic engineering structures with global nonlinearities. The two methods are validated by using them to predict the nonlinear modes of a simple assembly of geometrically nonlinear beams, and both are found to perform well.

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Section: A Quasi-linear Modal Modelmentioning

confidence: 95%

Section: B Nonlinear Substructuringmentioning

confidence: 99%

Nonlinear Modal Substructuring of Systems with Geometric Nonlinearities

Kuether

Allen

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…where K l is a constant matrix defining the linear part of the vector field and K nl1 and K nl2 are function matrices that define the quadratic and cubic parts of the vector field, respectively. This system was studied in more detail in [19]. For the purposes of this study, this reduced model will be considered the truth model and any approximation made in representing the structure with a 10 DOF model is irrelevant.…”

Section: Case Study Ii: a 10dof Systemmentioning

confidence: 99%

Multiharmonic Multiple-Point Collocation: A Method for Finding Periodic Orbits of Strongly Nonlinear Oscillators

Ardeh

Allen

2015

Journal of Computational and Nonlinear Dynamics

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An iterative method is proposed for finding periodic orbits of strongly nonlinear oscillators. The method combines the strength of analytical approaches, where the candidate solution is assumed in the form of a Fourier series, and the convenience of numerical methods that can be applied to larger systems with strong nonlinearity. The proposed method does not require integration of the vector field over any period of time and examples presented here illustrate that it is faster than traditional collocation algorithms, has a large radius of convergence, and is capable of finding several periodic orbits in each solution.

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