Parametric instability of a circular ring subjected to moving springs

Canchi, Sripathi Vangipuram; Parker, Robert G.

doi:10.1016/j.jsv.2005.10.007

Cited by 29 publications

(19 citation statements)

References 18 publications

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“…The fixed points (α = γ = 0) of (29) give the steady state leading order response and the frequency response relation…”

Section: Perturbation Analysismentioning

confidence: 99%

“…The stability of the steady state solutions in (31) is determined by the real parts of the eigenvalues of the Jacobian matrix linearized from the solvability conditions (29). The nonlinear characteristics emerge qualitatively and quantitatively from (31).…”

Section: Perturbation Analysismentioning

confidence: 99%

“…The significance of the phase of mesh stiffnesses on dynamic responses has been discussed recently in [24,[27][28][29]. This work discusses the interplay of the phases with contact ratios, and their significant impact on nonlinear response for fundamental, secondary, and subharmonic resonances.…”

Section: Introductionmentioning

confidence: 98%

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Nonlinear dynamics of idler gear systems

Liu

Parker

2007

Nonlinear Dyn

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This work examines the nonlinear, parametrically excited dynamics of idler gearsets. The two gear tooth meshes provide two interacting parametric excitation sources and two possible tooth separations. The periodic steady state solutions are obtained using analytical and numerical approaches. Asymptotic perturbation analysis gives the solution branches and their stabilities near primary, secondary, and subharmonic resonances. The ratio of mesh stiffness variation to its mean value is the small parameter. The time of tooth separation is assumed to be a small fraction of the mesh period. With these stipulations, the nonsmooth separation function that determines contact loss and the variable mesh stiffness are reformulated into a form suitable for perturbation. Perturbation yields closed-form expressions that expose the impact of key parameters on the nonlinear response. The asymptotic analysis for this strongly nonlinear system compares well to separate harmonic balance/arclength continuation and numerical integration solutions. The expressions in terms of fundamental design quantities have natural practical application.

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“…The fixed points (α = γ = 0) of (29) give the steady state leading order response and the frequency response relation…”

Section: Perturbation Analysismentioning

confidence: 99%

Section: Perturbation Analysismentioning

confidence: 99%

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Nonlinear dynamics of idler gear systems

Liu

Parker

2007

Nonlinear Dyn

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“…1(f). This rather complicated behavior is difficult to predict and even to interpret as it was reported in the studies of numerous mechanical systems, see, e.g, [20,21,24,25,27,29,35,36,39,43,48]. The present work reveals that the untwisting of the Campbell diagrams is determined by a limited number of singular eigenvalue surfaces.…”

Section: Introductionmentioning

confidence: 47%

“…1(a) the mesh of the eigenvalue branches (5) is shown for the 6 d.o.f.-system (2) with the frequencies ω 1 = 1, ω 2 = 3, and ω 3 = 6 that imitate the distribution of the doublets in the spectrum of a circular ring [35]. To illustrate typical untwisting of the Campbell diagram, we plot in Fig.…”

Section: A Model Of a Weakly Anisotropic Rotor Systemmentioning

confidence: 99%