Component Mode Synthesis Using Nonlinear Normal Modes

Apiwattanalunggarn, Polarit; Shaw, Steven W.; Pierre, Christophe

doi:10.1007/s11071-005-2791-2

Cited by 42 publications

(16 citation statements)

References 26 publications

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“…NNMs [14]. This opens the door to the application of the methodology to investigate nonlinear oscillations of large-scale structural problems and po-tentially to the efficient coupling of, for example, a substructure represented by NNMs with a second one given by a finite-element discretization.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear normal modes in an intrinsic theory of anisotropic beams

Palacios

2011

Journal of Sound and Vibration

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Nonlinear normal modes in nonlinear oscillations of beams are derived from intrinsic equations, that is, using velocities and strains as primary degrees of freedom. Displacements and rotations are thus not system states but are instead obtained using the propagation of the local beam material reference frames, as in rigid-body dynamics. It is shown that the intrinsic variables suffice to describe the free vibrations of the beam. The approach does not need assumptions in the material properties, i.e., it is valid for general anisotropic behavior, or the beam kinematics, i.e., it is based on Cosserat's exact geometrical description of the deformable curve. Furthermore, the nonlinear modal equations in intrinsic coordinates are obtained from integrals involving only products of the mode shapes and known coefficients. Using this description, the nonlinear normal modes are sought through an asymptotic approximation to the invariant manifolds that define them in the space of intrinsic modal coordinates. Particular cases of homogeneous isotropic and composite cantilever beams are finally used to exemplify the approach. *

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Section: Introductionmentioning

confidence: 99%

Nonlinear normal modes in an intrinsic theory of anisotropic beams

Palacios

2011

Journal of Sound and Vibration

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“…Apiwattanalunggarn et al [97] developed a nonlinear extension of the fixed interface method, using nonlinear normal modes for application to large-scale structural systems based on finite element methods. Variations of the CMS method also greatly vary because of the variations of boundary conditions imposed on the substructures during analysis and consequently how the assembled structure is put together.…”

Section: Component Mode Synthesismentioning

confidence: 99%

Model Reduction Methods for Rotor Dynamic Analysis: A Survey and Review

Wagner

Younan

Allaire

et al. 2010

International Journal of Rotating Machinery

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The focus of this literature survey and review is model reduction methods and their application to rotor dynamic systems. Rotor dynamic systems require careful consideration in their dynamic models as they include unsymmetric stiffness, localized nonproportional damping, and frequency-dependent gyroscopic effects. The literature reviewed originates from both controls and mechanical systems analysis and has been previously applied to rotor systems. This survey discusses the previous literature reviews on model reduction, reduction methods applied to rotor systems, the current state of these reduction methods in rotor dynamics, and the ability of the literature to reduce the complexities of large order rotor dynamic systems but allow accurate solutions.

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“…However, it is possible to use classical Component Mode Synthesis (CMS) such as the Craig & Bampton [3] method and consider each sector as a substructure. Paired with NNMs, this method has been used for the study of friction nonlinearity [10,8], and in the case of cubic nonlinearity [1]. This paper proposes an original coupling of several methods used for the study of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis and Reduction of a Cyclic Symmetric System Subjected to Geometric Nonlinearities

Martin

Thouverez

2018

Journal of Engineering for Gas Turbines and Power

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The search for ever lighter weight has become a major goal in the aeronautical industry as it has a direct impact on fuel consumption. It also implies the design of increasingly thin structures made of sophisticated and flexible materials. This may result in nonlinear behaviours due to large structural displacements. Stator vanes can be affected by such phenomena, and as they are a critical part of turbojets, it is crucial to predict these behaviours during the design process in order to eliminate them. This paper presents a reduced order modelling process suited for the study of geometric nonlinearities. The method is derived from a classical Component Mode Synthesis with fixed interfaces, in which the reduced nonlinear terms are obtained through a STEP procedure using an adapted basis composed of linear modes completed by modal derivatives. The whole system is solved using a harmonic balance procedure and a classic iterative nonlinear solver. The application is implemented on a schematic stator vane model composed of nonlinear Euler-Bernoulli beams under von Kàrmàn assumptions.

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Component Mode Synthesis Using Nonlinear Normal Modes

Cited by 42 publications

References 26 publications

Nonlinear normal modes in an intrinsic theory of anisotropic beams

Nonlinear normal modes in an intrinsic theory of anisotropic beams

Model Reduction Methods for Rotor Dynamic Analysis: A Survey and Review

Dynamic Analysis and Reduction of a Cyclic Symmetric System Subjected to Geometric Nonlinearities

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