A method for nonlinear modal analysis and synthesis: Application to harmonically forced and self-excited mechanical systems

Krack, Malte; Scheidt, Lars Panning‐von; Wallaschek, Jörg

doi:10.1016/j.jsv.2013.08.009

Cited by 84 publications

(101 citation statements)

References 31 publications

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“…Nonlinear complex modes are an extension of nonlinear normal modes to dissipative systems, that aims at taking advantage of numerical and frequency-based formulation such as the harmonic balance method to compute the free vibrations of damped nonlinear structures. First introduced in [5], they have proved tremendously interesting to study all sorts of nonlinear systems [6,16,18], and are fundamentals to the reduced-order modeling technique presented here. Only a brief reminder is provided here to introduce some notations, but more details can be found in [5,6,16,18].…”

Section: Nonlinear Complex Modesmentioning

confidence: 99%

“…Figure 2 shows the variations of the first natural frequency and corresponding modal damping as a function of the displacement amplitude |x 1 |. These so-called backbones are thoroughly explained in previous papers [5,6,18] and will not be discussed here. However, it should be remembered in the following sections that nonlinear complex modes are functions of a parameter describing the intensity of the nonlinear effects, here the amplitude of vibration |x 1 |, and that the modes of friction-damped systems exhibit an optimum damping point, corresponding to a maximum dissipation arising from the nonlinearity.…”

Section: Nonlinear Complex Modesmentioning

confidence: 99%

“…As performed in [6] in a modal synthesis procedure, the term f nl |e k is replaced by the sum of the analogous vectors in the eigenproblem (4), which yields the set of equations (10), where the second line accounts now for f nl |e k . The matrixK differs from the matrix K owing to the fixed boundary conditions enforced during the computation of the modes.…”

Section: Nonlinear Superelementmentioning

confidence: 99%

“…For such systems, standard techniques may indeed fail to find a satisfying compromise between order-reduction and accuracy, due to the lack of representativity of the reduction basis. From this perspective, owing to their ability to capture the essence of the nonlinearities [5,6], nonlinear complex modes are interesting candidates in devising new effective and efficient approaches to reduce nonlinear models.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting algebraic system can thus be much smaller than that of a standard harmonic balance method (HBM), which requires to retain all nonlinear DOFs as master coordinates. The flexibility of nonlinear complex modes [5,6,16] makes this reduction technique suitable for the study of a broad range of nonlinearities, dissipative and non-smooth ones included.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A New Dynamic Substructuring Method for Nonlinear and Dissipative Systems

Joannin¹,

Chouvion²,

Thouverez³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. This work is devoted to the development of a new dynamic substructuring method inspired by classic fixed-interface component mode synthesis, in order to compute the steadystate vibrations of dissipative, nonlinear structures. For each substructure, the displacement field is sought as a multiharmonic oscillation made of standard static mode shapes, supplemented by the eigenvectors of the nonlinear complex modes of the substructure computed with fixed-boundary conditions. The method eventually leads to a strongly reduced nonlinear algebraic system, easily solved by iterative solvers. The procedure is tested on a lumped parameter model of bladed disk subjected to dry friction nonlinearities, with or without structural mistuning, and proves very efficient in terms of computational cost. These results emphasize the promising capabilities of this new reduced-order modeling technique to tackle such nonlinear systems exhibiting high modal density. 4611Colas Joannin, Benjamin Chouvion and Fabrice Thouverez

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Section: Nonlinear Complex Modesmentioning

confidence: 99%

Section: Nonlinear Complex Modesmentioning

confidence: 99%

Section: Nonlinear Superelementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A New Dynamic Substructuring Method for Nonlinear and Dissipative Systems

Joannin¹,

Chouvion²,

Thouverez³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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On the use of modal derivatives for nonlinear model order reduction

Weeger

Wever

Simeon

2016

Numerical Meth Engineering

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Modal derivative is an approach to compute a reduced basis for model order reduction of large-scale nonlinear systems that typically stem from the discretization of partial differential equations. In this way, a complex nonlinear simulation model can be integrated into an optimization problem or the design of a controller, based on the resulting small-scale state-space model. We investigate the approximation properties of modal derivatives analytically and thus lay a theoretical foundation of their use in model order reduction, which has been missing so far. Concentrating on the application field of structural mechanics and structural dynamics, we show that the concept of modal derivatives can also be applied as nonlinear extension of the Craig-Bampton family of methods for substructuring. We furthermore generalize the approach from a pure projection scheme to a novel reduced-order modeling method that replaces all nonlinear terms by quadratic expressions in the reduced state variables. This complexity reduction leads to a frequency-preserving nonlinear quadratic state-space model. Numerical examples with carefully chosen nonlinear model problems and three-dimensional nonlinear elasticity confirm the analytical properties of the modal derivative reduction and show the potential of the proposed novel complexity reduction methods, along with the current limitations.Thus, the eigenmodes are an orthonormal basis of R n w.r.t. the inner product weighted by M.The discretized linear static problemcan be transformed onto the eigenmodes using d Dˆq: Nonlinear problem and modal derivativesIn the previous section, we have seen that eigenmodes are an optimal basis for the reduction of linear problems where the right-hand side is composed from a subset of eigenmodes. Extending this idea to the nonlinear regime, we are now looking for the solution of the static problem

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