Modal Substructuring of Geometrically Nonlinear Finite-Element Models

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

doi:10.2514/1.j054036

Cited by 42 publications

(18 citation statements)

References 36 publications

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“…For example, NNMs have been used to understand the dynamic behaviour of full-scale aircraft and satellites [17,18], as a tool in substructuring [19] and the construction of reduced-order models [20], and for damage detection in engineering structures [21]. Along with such large-scale mechanical structures, NNMs have also seen successful application to MEMS devices [22], nanostructures [23] and to acoustic–structure interactions [24].…”

Section: Introductionmentioning

confidence: 99%

Identifying the significance of nonlinear normal modes

et al. 2017

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Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system—highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared with simulated forced responses to verify these findings.

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Section: Introductionmentioning

confidence: 99%

Identifying the significance of nonlinear normal modes

et al. 2017

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“…An example of linear problem in harmonic aeroacoustics with nonaffine dependence in the frequency is available in the work of Casenave et al Some nonlinearities can be treated without approximation, for example, the advection term is fluid dynamics (with a ROM based on a Galerkin method in our context) only requires the precomputation of an order‐3 tensor in the form

\int_{normalΩ} ψ_{i} \cdot false(ψ_{j} \cdot \nabla false) ψ_{k}

, 1 ≤ i , j , k ≤ n , see the work of Akkari et al for the reduction of the nonlinear Navier‐Stokes equations, with an exact operator compression step. Other examples can be found in structural dynamics with geometric nonlinearities, where order‐2 and order‐3 tensors can be precomputed, see section 3.2 in the work of Kuether and the work of Mignolet et al…”

Section: Reduced Order Modelingmentioning

confidence: 99%

A nonintrusive distributed reduced‐order modeling framework for nonlinear structural mechanics—Application to elastoviscoplastic computations

Casenave

Akkari

Bordeu

et al. 2019

Numerical Meth Engineering

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Summary In this work, we propose a framework that constructs reduced‐order models for nonlinear structural mechanics in a nonintrusive fashion and can handle large‐scale simulations. Three steps are carried out: (i) the production of high‐fidelity solutions by commercial software, (ii) the offline stage of the model reduction, and (iii) the online stage where the reduced‐order model is exploited. The nonintrusivity assumes that only the displacement field solution is known, and the proposed framework carries out operations on these simulation data during the offline phase. The compatibility with a new commercial code only needs the implementation of a routine converting the discretized solution into our in‐house data format. The nonintrusive capabilities of the framework are demonstrated on numerical experiments using commercial versions of Z‐set and Ansys Mechanical. The nonlinear constitutive equations are evaluated by using an external plugin. The large‐scale simulations are handled using domain decomposition and parallel computing with distributed memory. The features and performances of the framework are evaluated on two numerical applications involving elastoviscoplastic materials: the second one involves a model of high‐pressure blade, where the framework is used to extrapolate cyclic loadings in 6.5 hours, whereas the reference high‐fidelity computation would take 9.5 days.

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“…The parameter values used to obtain these plots for different values of k and ε were m 1 = m 2 = 1, with c = 0 and f 1 = 0. Here, the black solid lines describe the solutions obtained from Equations (34) and (35), while the colored, dashed lines represent the backbone curves computed from Equation (33). Equations (33) to (35).…”

Section: Of 22mentioning

confidence: 99%

“…Furthermore, nonlinear normal modes have been used to identify localized modes in micro-electromechanical devices [28] for the development of a new kind of low frequency acoustic absorber [29] and for the analysis of nonlinear vibrations for double-walled carbon nanotubes [30]. Also, the nonlinear normal modes have helped in the understanding of the dynamic response behavior of full-scale aircrafts and satellites [31,32] as a tool for sub-structuring [33], for the construction of reduced-order models [34], and for damage detection in engineering structures [35], among others uses.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems

et al. 2018

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Featured Application: The qualitative and quantitative dynamic behavior of two degree-offreedom nonlinear systems can be studied by using their corresponding decoupled one degree of freedom Duffing type equivalent representation forms in the sense of Lyapunov, with the advantage of capturing amplitude-dependent nonlinear mode shapes.Abstract: The aim of this paper focuses on finding equivalent representation forms of forced, damped, two degree-of-freedom, nonlinear systems in the sense of Lyapunov by using a nonlinear transformation approach that provides decoupled, forced, damped, nonlinear equations of the Duffing type, under the assumption that the driving frequency and the external forces are equal in both systems. The values of Lyapunov characteristic exponents (LCEs), Lyapunov largest exponents (LLE), and time-amplitude and frequency-amplitude curves computed from numerical integration solutions, indicate that the decoupled Duffing-type equations are equivalent, in the sense of Lyapunov, to the original dynamic system, since both set of motion equations tend to have the same qualitative and quantitative behaviors.

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Modal Substructuring of Geometrically Nonlinear Finite-Element Models

Cited by 42 publications

References 36 publications

Identifying the significance of nonlinear normal modes

Identifying the significance of nonlinear normal modes

A nonintrusive distributed reduced‐order modeling framework for nonlinear structural mechanics—Application to elastoviscoplastic computations

Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems

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