The in-plane free vibration of an elastically supported thin ring rotating at high speeds revisited

Lü, Tao; Tsouvalas, Apostolos; Metrikine, Andrei V.

doi:10.1016/j.jsv.2017.05.013

Cited by 23 publications

(28 citation statements)

References 16 publications

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“…The static equilibrium is solved from the nonlinear governing equations the same way as Ref. [3]. To obtain to characteristic equation from the linearised governing equations, it is assumed that the dynamic displacements are w 0 (θ, t) = R W e inθ+iωt , u 0 (θ, t) = R U e inθ+iωt , φ 1 (θ, t) = Φ e inθ+iωt (14) in which ω is the natural frequency in space-fixed reference system, n is the circumferential mode number and i = √ −1.…”

Section: Derivation Of Governing Equationsmentioning

confidence: 99%

“…Resonant speeds of a rotating ring are defined as the speeds at which resonances of the ring subjected to a stationary load occur. They are the speeds which satisfy the conditionω = 0 [3,5], namely the natural frequency in the space-fixed coordinate becomes zero at these speeds. By substitutingω = 0 into the characteristic equation 16, one can solve for resonant speeds for each circumferential wavenumber.…”

Section: Critical Speeds Of Rotating Rings 31 Resonant Speedsmentioning

confidence: 99%

“…It has been shown in [3] that instability may occur for certain combination of parameters. Divergence instability of the n = 0 rotational mode always occurs at lower rotational speeds compared to flutter of higher modes.…”

Section: Critical Speeds Associated With Instabilitymentioning

confidence: 99%

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In-plane vibration of rotating rings using a high order theory

2018

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In-plane dynamics of rotating rings on elastic foundation is a topic of continuous research, especially in the field of tire dynamics. When the inner surface of a ring is connected to a stiff foundation, the through-thickness variation of radial and shear stress needs to be accounted for. This effect is often overlooked in the ring models proposed in the literature. In this paper, a new high order theory is developed for the in-plane vibration of rotating rings whose inner surface is connected to an immovable hub by distributed springs while the outer surface is stress-free. The high-order terms are chosen such that the boundary conditions at the inner and outer surfaces are satisfied at all times. Instability, which is usually overlooked in the literature, is predicted using the present model. Resonant speeds are investigated, at which modes appear as a stationary displacement pattern to a space-fixed observer. The exact satisfaction of boundary conditions at the inner and outer ring surfaces together with the through-thickness variation of the radial and shear stresses are shown to be of significant importance when the ring rotates at high speeds or is supported by relatively stiff foundation.

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Section: Derivation Of Governing Equationsmentioning

confidence: 99%

Section: Critical Speeds Of Rotating Rings 31 Resonant Speedsmentioning

confidence: 99%

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In-plane vibration of rotating rings using a high order theory

2018

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“…Rigid carcass ring 6 is the main feature of RT-tire model (Figure 3(a)) and a flexible unit representing the residual stiffness, the tread can be characterized with the rim of the dislocation formation, the effective road input is substituted by road height, and effective rolling radius, 8 achieve the simulation of rolling condition. FT-tire model (Figure 3(b)) simplified the tire as the flexible tread on elastic foundation, in which tread referred as flexible tread, sidewall and inflation pressure referred as elastic foundation, 7 and the FT-tire model can achieve the deformation of tread.…”

Section: Introductionmentioning

confidence: 99%

“…Structural tire model: (a) rigid ring tire model (RT-tire)6 and (b) flexible ring tire model (FT-tire) 7. …”

mentioning

confidence: 99%

Vibration transfer function of in-plane rigid–elastic-coupled tire model for heavy-loaded radial tire

Liu

Gao

Wang

et al. 2017

Advances in Mechanical Engineering

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The modeling and vibration transfer function of in-plane rigid-elastic-coupled tire model is put forward for researching the heavy-loaded radial tire with the feather of larger radial length and width ratio. The coupled characteristic of tread and sidewall is taken into consideration, and the coupled natural frequencies are analyzed with the normal pressure and fixed rim. The rigid-elastic coupling equation is modeled with the flexible beam on elastic foundation, which tread is modeled as the Euler beam and the sidewall is regarded as the sub-sectional spring with lumped mass. The dynamic equation is discrete with finite difference method, and three-parameter rigid-elastic-coupled tire model is derived based on the geometrical and structural parameters. The structural parameters of the tire are identified by the genetic algorithm based on the experimental modal parameter of heavy-loaded tire, and the higher order modal frequency is predicted with the analytic method. The analytical transfer function between tread and tread, tread and sidewall is derived. Experimental and theoretical results show that the in-plane rigid-elastic-coupled tire model can achieve the higher precision on predicting the transfer function and vibration feature of heavy-loaded tire within the frequency band of 300 Hz, compared with the method which only considers the coupling of tread and rim and is limited to 180 Hz.

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Bifurcation and chaos of the traveling membrane on oblique supports subjected to external excitation

Shao

Qing

2020

J Mech Sci Technol

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The in-plane free vibration of an elastically supported thin ring rotating at high speeds revisited

Cited by 23 publications

References 16 publications

In-plane vibration of rotating rings using a high order theory

In-plane vibration of rotating rings using a high order theory

Vibration transfer function of in-plane rigid–elastic-coupled tire model for heavy-loaded radial tire

Bifurcation and chaos of the traveling membrane on oblique supports subjected to external excitation

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