Stability and bifurcation of an axially moving beam tuned to three-to-one internal resonances

Huang, Jianliang; Su, R.K.L.; Li, W.H.; Chen, S.H.

doi:10.1016/j.jsv.2010.04.037

Cited by 111 publications

(41 citation statements)

References 24 publications

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“…Generally, a small parametric excitation can produce a large response, and the system loses its stability when the frequency of the parametric excitation is close to double of the system's natural frequency, which is so called principal parametric resonance. Following the interesting feature of this system, the stability analysis for coupled and parametric excited system like BCP model can be solved directly with application of the perturbation methods, for example, harmonic balance method [24], multiple scale method [25][26][27][28][29]. The representative work was demonstrated by Alfriend and Rand [30] who applied a general perturbation technique to study the stability of infinitesimal motions in the non-autonomous elliptic RTBP.…”

Section: Candiceqyj@163commentioning

confidence: 99%

Parametric stability analysis for planar bicircular restricted four-body problem

Qian

Yang

et al. 2018

Astrodyn

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Section: Candiceqyj@163commentioning

confidence: 99%

Parametric stability analysis for planar bicircular restricted four-body problem

Qian

Yang

et al. 2018

Astrodyn

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“…Huang et al [13] applied incremental harmonic balance (IHB) method to analyse three-to-one subharmonic internal resonance. Tang and all [14] investigated primary resonances as well as subharmonic and superharmonic resonances caused by weak and strong external excitations of axially moving Timoshenko beam.…”

Section: Introductionmentioning

confidence: 99%

Influence of the longitudinal displacement on the nonlinear principal parametric resonance of the woodworking bandsaw

2017

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Original scientific paper The transverse vibrations of axially moving Timoshenko beam, as suitable mathematical models for woodworking bandsaws, are investigated. Special attention is paid to the influence of longitudinal displacement effect, as opposed to most models which can be usually encountered in the literature. This influence is introduced through the integro-partial differential equations. The expressions for the mode shapes in the case of hybrid supports with different torsion spring stiffness on the support points are also derived. The influence of mean beam velocity and axial tension on its natural frequencies and mode shapes is also investigated. Based on the nonlinear model, the amplitudes of the steady-state response are calculated for the case of principal parametric resonance. Developed program solution was tested on a number of earlier known examples. Present theoretical considerations, with the help of the program solution, is also used to analyse an example from industrial practice. Keywords: hybrid boundary conditions; method of multiple scales; numerical examples; principal parametric resonance; travelling Timoshenko beam Utjecaj uzdužnog pomaka na nelinearne glavne parametarske rezonancije tračne pileIzvorni znanstveni članak U radu su istražene poprečne vibracije aksijalno pomične Timoshenkove grede, kao podesnog modela za matematičko modeliranje tračnih pila. Posebno je obrađen utjecaj aksijalnog pomaka koji je, za razliku od većine modela koji se susreću u literaturi, uveden preko integro-parcijalne diferencijalne jednadžbe. Također su izvedeni izrazi za forme vibriranja za slučaj hibridnih oslonaca s različitim krutostima torzijskih opruga u točkama oslonaca. Ispitivan je utjecaj srednje brzine gibanja grede kao i aksijalnog naprezanja na vlastite frekvencije i oblike vibriranja. Razvijen je i nelinearni model na temelju kojega su izračunati amplitudni odzivi nelinearnih ravnomjernih vibracija za slučaj parametarske rezonancije. Izrađeno programsko rješenje testirano je na određenom broju ranije poznatih primjera. Iznijeta teorijska razmatranja, uz pomoć programskog rješenja, poslužila su i za analizu jednog od dostupnih primjera iz industrijske prakse.

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“…For example, Sze et al [12] and Huang et al [13] investigated the subcritical resonant dynamic response of an axially moving beam by means of the incremental harmonic balance method. Wickert [14] examined the nonlinear dynamics of an axially moving tensioned beam in both sub-and supercritical axial speed regimes.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamical Behavior of Axially Accelerating Beams: Three-Dimensional Analysis

Ghayesh

Farokhi

2016

Journal of Computational and Nonlinear Dynamics

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The three-dimensional (3D) nonlinear dynamics of an axially accelerating beam is examined numerically taking into account all of the longitudinal, transverse, and lateral displacements and inertia. Hamilton's principle is employed in order to derive the nonlinear partial differential equations governing the longitudinal, transverse, and lateral motions. These equations are transformed into a set of nonlinear ordinary differential equations by means of the Galerkin discretization technique. The nonlinear global dynamics of the system is then examined by time-integrating the discretized equations of motion. The results are presented in the form of bifurcation diagrams of Poincare maps, time histories, phase-plane portraits, Poincare sections, and fast Fourier transforms (FFTs). The three-dimensional (3D) nonlinear dynamics of an axially accelerating beam is examined numerically taking into account all of the longitudinal, transverse, and lateral displacements and inertia. Hamilton's principle is employed in order to derive the nonlinear partial differential equations governing the longitudinal, transverse, and lateral motions. These equations are transformed into a set of nonlinear ordinary differential equations by means of the Galerkin discretization technique. The nonlinear global dynamics of the system is then examined by time-integrating the discretized equations of motion. The results are presented in the form of bifurcation diagrams of Poincar e maps, time histories, phase-plane portraits, Poincar e sections, and fast Fourier transforms (FFTs).

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Stability and bifurcation of an axially moving beam tuned to three-to-one internal resonances

Cited by 111 publications

References 24 publications

Parametric stability analysis for planar bicircular restricted four-body problem

Parametric stability analysis for planar bicircular restricted four-body problem

Influence of the longitudinal displacement on the nonlinear principal parametric resonance of the woodworking bandsaw

Nonlinear Dynamical Behavior of Axially Accelerating Beams: Three-Dimensional Analysis

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