Free vibration analysis of planar rotating rings by wave propagation

Huang, Diangui; Tang, Liang; Cao, Rui

doi:10.1016/j.jsv.2013.04.019

Cited by 37 publications

(22 citation statements)

References 13 publications

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“…Furthermore, non-reciprocal devices can be used to realize one-way filters and isolation (Fleury et al 2015, Cummer et al 2016. In mechanical systems, weak non-reciprocal wave propagation occurs in rotating rings, in which the rotation introduces a mechanical bias that leads to different wavenumber and phase velocity values for waves propagating in opposite directions (Huang et al 2013). The mechanical bias is due to Coriolis forces (Beli et al 2015), which are responsible for breaking reciprocity (Onsager 1931a).…”

Section: Introductionmentioning

confidence: 99%

Non-reciprocal elastic wave propagation in spatiotemporal periodic structures

2016

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We study longitudinal and transverse wave propagation in beams with elastic properties that are periodically varying in space and time. Spatiotemporal modulation of the elastic properties breaks mechanical reciprocity and induces one-way propagation. We follow an analytic approach to characterize the non-reciprocal behavior of the structures by analyzing the symmetry breaking of the dispersion spectrum, which results in the formation of directional band gaps and produces shifts of the first Brillouin zone limits. This approach allows us to relate position and width of the directional band gaps to the modulation parameters. Moreover, we identify the critical values of the modulation speed to maximize the non-reciprocal effect. We numerically verify the theoretical predictions by using a finite element model of the modulated beams to compute the transient response of the structure. We compute the two-dimensional Fourier transform of the collected displacement fields to calculate numerical band diagrams, showing excellent agreement between theoretical and numerical dispersion diagrams.

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Section: Introductionmentioning

confidence: 99%

Non-reciprocal elastic wave propagation in spatiotemporal periodic structures

2016

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“…Simplified tire models with an analytical expression or purely empirically/semi-empirical formulae, such as the magic model [7], brush model [8], and LuGre model [9], etc., are used to investigate the longitudinal and lateral dynamics of the tire-road interactions with the computationally effective feature, while the structural elasticity and the flexible deformation of the tire belt and tire sidewall are ignored, leading to the existing deviation under certain manoeuvres. At the other extreme, taking the advantage the powerful computation and the composite characteristic [10], detailed tire models, such as the finite element tire model [6], absolute nodal coordinate formulation (ANCF) finite element tire model [11], and spectral element tire model [12], present the detail material feature and geometrical feature at the expense of much computation resource. Additionally, the detailed tire/road contacting feature can be investigated with the detailed tire and road model, while the large computation resource, the extensive finite element analysis (FEA)-oriented pre-processing, and the difficultly-obtained material parameters limit the extended application for vehicle dynamics.…”

Section: Introductionmentioning

confidence: 99%

Development of the Flexible Ring on an Elastic Continuous Foundation Tire Model for Planar Vibration of the Heavy Load Radial Tire

2018

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This paper investigates the planar vibration characteristic of heavy load radial tires with a large flat ratio. A proposed tire model with a flexible ring on an elastic continuous foundation is investigated utilizing kinematic modeling and experimental modal analysis. Planar coupling deformation of the radial and tangential direction is considered to enrich the kinematic characteristic of the flexible belt and the continuous sidewall; a flexible ring on an elastic continuous foundation tire model is proposed to investigate the coupling vibration characteristic between the flexible belt and the continuous sidewall. In-extensibility assumption is utilized to simplify the proposed tire model and the planar vibration modal features of the heavy load radial tire are discussed. The variation of the inflation pressure on the radial and tangential stiffness of the sidewall spring model is enriched into the flexible ring on an elastic continuous foundation tire model to extend the modal prediction of the tires with a different inflation pressure. Taking the relative error between the experimental and analytical modal resonance frequency of the tested tire with a different inflation pressure as the object value, structural parameters of the proposed tire model are identified by a backward genetic algorithm. Experimental and theoretical results show that: the planar coupling vibration characteristic of the heavy load radial tire can be predicted precisely with the flexible ring on an elastic continuous foundation tire model; meanwhile, considering the linear variations of the radial and tangential sidewall stiffness due to the inflation pressure, the proposed tire model can be extended to analyze the vibration characteristic of the heavy load radial tire with a different inflation pressure.

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“…They considered two sets of orthogonal sti eners in an arbitrary direction. The vibrational analysis of extensional and in-extensional rotating rings based on the wave propagation approach was performed by Huang et al [20]. Cooley and Parker [17] also carried out the vibrational analysis of the rotating rings.…”

Section: Introductionmentioning

confidence: 99%

Vibrational characteristics of size dependent vibrating ring gyroscope

Karimzadeh

Ahmadian

2018

Scientia Iranica

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Abstract. In this paper, vibrational analysis of a size-dependent micro-ring gyroscope under electrostatic DC voltage is performed. Governing equations of size-dependent micro rings and corresponding nite-element formulation of circular micro ring along with eight half circular sti eners embedded inside the ring are derived based on the modi ed couple stress theory, Hamilton's principle, and in-extensionality approximation. Frequency analysis indicates that the obtained mode shape of the ring gyroscope is slightly di erent from the one previously reported in the literature. Size-dependent behavior of the gyroscope is studied, and related ndings con rm the gap between classic and non-classic natural frequencies and pull-in voltage when the ring thickness is in order of material length scale parameter. Two di erent orientations for the actuation electrodes of the micro-ring gyroscope are implemented, and the e ect of these orientations on the static de ection, pull-in instability, and device frequencies in the sense (45 direction) and drive (0 direction) directions is investigated. Results reveal that the pull-in phenomena take place under lower voltages for 0 and 45 orientation of electrodes in comparison with 0 orientation; frequency split occurs in higher voltages for 0 and 45 orientation. A comparison between nite-element numerical natural frequencies of single ring and previously obtained analytical ones shows excellent agreement.

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Free vibration analysis of planar rotating rings by wave propagation

Cited by 37 publications

References 13 publications

Non-reciprocal elastic wave propagation in spatiotemporal periodic structures

Non-reciprocal elastic wave propagation in spatiotemporal periodic structures

Development of the Flexible Ring on an Elastic Continuous Foundation Tire Model for Planar Vibration of the Heavy Load Radial Tire

Vibrational characteristics of size dependent vibrating ring gyroscope

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