Nonlinear forced vibrations of rotating anisotropic beams

Bekhoucha, Ferhat; Rechak, Saïd; Duigou, Laëtitia; Cadou, Jean-Marc

doi:10.1007/s11071-013-1040-3

Cited by 27 publications

(19 citation statements)

References 32 publications

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“…It is worth noticing that the VK model is naturally quadratic, whereas the Inxt model is cubic so that numerous additional variables (R p k , Q p k ) must be added, as in [42] for piezoelectric laminated beams. Other works [13,56] use elegant formulations of the equations of motion , first proposed in [31], using both the displacement and the velocity as variables. By expansion onto a suitable basis, a naturally quadratic formulation is obtained, which is exact without any restriction on the displacement/rotation magnitude.…”

Section: Numerical Solvingmentioning

confidence: 99%

“…The same subject is also addressed in [39] with a refined model based on a Cosserat theory of rods, that is used to compute nonlinear modes through the multiple scale perturbation method. Nonlinear resonance curves are also computed in [13], with a fully numerical approach based on a Galerkin discretization with Legendre polynomials and a continuation method (harmonic balance coupled to an asymptotic numerical technique).…”

Section: Introductionmentioning

confidence: 99%

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Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

2016

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This work addresses the large amplitude nonlinear vibratory behavior of a rotating cantilever beam, with applications to turbomachinery and turbopropeller blades. The aim of this work is twofold. Firstly, we investigate the effect of rotation speed on the beam nonlinear vibrations and especially on the hardening/softening behavior of its resonances and the appearance of jump phenomena at large amplitude. Secondly, we compare three models to simulate the vibrations. The first two are based on analytical models of the beam, one of them being original. Those two models are discretized on appropriate mode basis and solve by a numerical following path method. The last one is based on a finite-element discretization and integrated in time. The accuracy and the validity range of each model are exhibited and analyzed.

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Section: Numerical Solvingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

2016

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“…The latter could be done by directly computing the truncated spectrum of Hill's matrix for a given periodic state. But a confusion subsists as for the sorting method one should use for the spurious computed spectrum, between eigenvalue [9,27,45] or eigenvector sorting [2,22,26,41]. Furthermore, only Floquet exponents are usually considered and modal informations from FFs are usually neglected.…”

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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“…The determination of their dynamic characteristics (natural frequencies and mode shapes) are of great importance in design and control. A significant number of studies have been published on the bending vibrations of rotating beams, with the main objective of predicting the natural frequencies and associated mode shapes, as well as investigating their variations with angular velocity and other effects such as hub radius, taper and shear deformation [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. A review of several studies on rotating beams has been presented by Bazoun [19].…”

Section: Introductionmentioning

confidence: 99%

“…[27] used a dynamic model based on a geometrically exact approach and applied the MMS to construct the NNM. The nonlinearity depends on the angular velocity [17], and the rotating beam may exhibit hardening or softening behaviour depending on the geometric and kinematic conditions [13]. In [28], an algorithm is developed equivalent to the Lyapunov-Schmidt reduction for the computation of nonlinear free vibration curves from a Hopf bifurcation point.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear free vibrations of centrifugally stiffened uniform beams at high angular velocity

Bekhoucha

Rechak

Duigou

et al. 2016

Journal of Sound and Vibration

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Nonlinear forced vibrations of rotating anisotropic beams

Cited by 27 publications

References 32 publications

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

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

Nonlinear free vibrations of centrifugally stiffened uniform beams at high angular velocity

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