A Combined Modal/Finite Element Analysis Technique for the Dynamic Response of a Non-Linear Beam to Harmonic Excitation

McEwan, M I; Wright, J.F.; Cooper, Jonathan E.; Leung, A.Y.T.

doi:10.1006/jsvi.2000.3434

Cited by 143 publications

(87 citation statements)

References 22 publications

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“…stress levels; however, this method requires careful investigation when conducting a fatigue life calculation based on the EL-derived PSD response [23]. Finally, for a non-linear response prediction, McEwan et al [24] extended an FE-based modal approach to the case of multi-modal, non-linear beam vibrations. The method was used to model isotropic beams with simply supported and fully clamped boundary conditions, with free vibration and steady state harmonic excitation considered.…”

Section: Prediction and Measurement Of The Non-linear Response Due Tomentioning

confidence: 99%

A review of analytical methods for aircraft structures subjected to high-intensity random acoustic loads

Cunningham

White

2004

Proceedings of the Institution of Mechanical Engineers, Part G:

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A review of the acoustic fatigue design process for aircraft structures is presented in this paper, together with the current design guides, which are used to predict the stresses that an acousticallly loaded aircraft structure may experience in service. These methods are based on linear theory and use the single-degree-of-freedom approximation method. A recent programme of research which uses this method together with the finite element method to predict the root mean square strains experienced by acoustically excited, doubly curved sandwich panels is briefly discussed. Recent developments in prediction methods based on the non-linear dynamic response of thermoacoustic loaded structures are reviewed, and suggestions are made as to possible future directions in the area of acoustic fatigue research.

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Section: Prediction and Measurement Of The Non-linear Response Due Tomentioning

confidence: 99%

A review of analytical methods for aircraft structures subjected to high-intensity random acoustic loads

Cunningham

White

2004

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…In practice, those modes allow to reveal intrinsic vibrational properties [28] or the local stability behavior of structures in equilibria [21,31]. They can also be used as a projection basis to reduce the dimensionality of linear or nonlinear vibrational structural models [23,25].…”

Section: Introductionmentioning

confidence: 99%

Modal and stability analysis of structures in periodic elastic states: application to the Ziegler column

Bentvelsen

Lazarus

2017

Nonlinear Dyn

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We present a spectral method to compute the transverse vibrational modes, or Floquet Forms (FFs), of a 2D bi-articulated bar in periodic elastic state due to an end harmonic compressive force. By changing the directional nature of the applied load, the trivial straight Ziegler column exhibits the classic instabilities of stationary states of dynamical system. We use this simple structure as a numerical benchmark to compare the various spectral methods that consist in computing the FFs from the spectrum of a truncated Hill matrix. We show the necessity of sorting this spectrum and the benefit of computing the fundamental FFs that converge faster. Those FFs are almost-periodic entities that generalize the concept of harmonic modal analysis of structures in equilibria to structures in periodic states. Like their particular harmonic relatives, FFs allow to get physical insights in the bifurcations of periodic stationary states. Notably, the local loss of stability is due to the frequency lock-in of the FFs for certain modulation parameters. The presented results could apply to many structural problems in mechanics, from the vibrations of rotating machineries with shape imperfections to the stability of periodic limit cycles or of any slender structures with tensile or compressive periodic elastic stresses.

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“…Notwithstanding the above difficulties, the ROM capabilities have progressed from applications to flat structures (see [2][3][4][5][6][7][8][9]), to moderately large motions of curved structures (see [10][11][12][13][14]). Further, the coupling of these nonlinear structural reduced order models with aerodynamics, either full or reduced order model has also been successfully demonstrated in [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling

Perez

Wang

Mignolet

2014

Journal of Sound and Vibration

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The focus of this investigation is on a first assessment of the predictive capabilities of nonlinear geometric reduced order models for the prediction of the large displacement and stress fields of panels with localized geometric defects, the case of a notch serving to exemplify the analysis. It is first demonstrated that the reduced order model of the notched panel does indeed provide a close match of the displacement and stress fields obtained from full finite element analyses for moderately large static and dynamic responses (peak displacement of 2 and 4 thicknesses). As might be expected, the reduced order model of the virgin panel would also yield a close approximation of the displacement field but not of the stress one. These observations then lead to two "enrichment" techniques seeking to superpose the notch effects on the virgin panel stress field so that a reduced order model of the latter can be used. A very good prediction of the full finite element stresses, for both static and dynamic analyses, is achieved with both enrichments.

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A Combined Modal/Finite Element Analysis Technique for the Dynamic Response of a Non-Linear Beam to Harmonic Excitation

Cited by 143 publications

References 22 publications

A review of analytical methods for aircraft structures subjected to high-intensity random acoustic loads

A review of analytical methods for aircraft structures subjected to high-intensity random acoustic loads

Modal and stability analysis of structures in periodic elastic states: application to the Ziegler column

Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling

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