Instability of vibrations of a mass that moves uniformly along a beam on a periodically inhomogeneous foundation

Verichev, Stanislav; Metrikine, Andrei V.

doi:10.1016/s0022-460x(02)00936-7

Cited by 49 publications

(18 citation statements)

References 16 publications

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“…| | 1 and |γ| 1 respectively. The same assumption is also emphasized in [8] where the small parameter µ 1, for the same reason stated above. Also, most of these models only considered variation in stiffness whereas the damping in treated as constant.…”

Section: Introductionmentioning

confidence: 63%

“…The accuracy of this method, however, depends on the speed of the vehicle as well as the degree of variation in the random track stiffness, with fairly poor results obtained for speeds and stiffness variations over 30%. Verichev and Metrikine [8] studied the instability of a mass moving along a beam that is supported on an inhomogeneous elastic foundation with periodically varying stiffness. Perturbation analysis was used to obtain analytic expressions for the vibration conditions of the beam to become unstable.…”

Section: Introductionmentioning

confidence: 99%

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Vibration of a beam on continuous elastic foundation with nonhomogeneous stiffness and damping under a harmonically excited mass

Koroma

Hussein

Owen

2014

Journal of Sound and Vibration

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A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. AbstractIn this paper, a proposed method of analysis of a beam that is continuously supported on a linear nonhomogeneous elastic foundation and subjected to a harmonically excited mass is presented. The solution is obtained by decomposing the nonhomogeneous foundation properties and the beam displacement response into double Fourier summations which are solved in the frequency-wavenumber domain, from which the space-time domain response can be obtained.The method is applied to railway tracks with step variation in foundation properties. The validity of this method is checked, through examples, against existing methods for both homogeneous and nonhomogeneous foundation parameters. The effect of inhomogeneity and the magnitude of the mass are also investigated. It is found that a step variation in foundation properties leads to a reduction in the beam displacement and an increase in the resonance frequency, for increasing step change, with the reverse occurring for decreasing s. Furthermore, a beam on nonhomogeneous foundation may exhibit multiple resonances corresponding to the foundation stiffness of individual sections, as the mass moves through the respective sections along the beam.

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Section: Introductionmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Vibration of a beam on continuous elastic foundation with nonhomogeneous stiffness and damping under a harmonically excited mass

Koroma

Hussein

Owen

2014

Journal of Sound and Vibration

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“…Because of the one-dimensional modeling, these studies cannot be used for quantitative prediction of the train-track stability but they convey an important message that the stability is not guaranteed at high speeds. Moreover, as shown by Metrikine and Vesnitsky (1996) and Verichev and Metrikine (2003), because of the track inhomogeneity the train can loose its stability at low speeds because of parametric resonance. Such instability could arise, for example, in the models, which have been recently studied by Andersen et al (2002) and Andersen and Nielsen (2003b).…”

Section: Introductionmentioning

confidence: 93%

Stability of a two-mass oscillator moving on a beam supported by a visco-elastic half-space

Metrikine

Verichev

Blaauwendraad

2005

International Journal of Solids and Structures

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“…Using the impulsive parametric excitation theory, Aldraihem and Baz [29] investigated dynamic stability of a stepped beam subjected to periodic parametric excitations caused by moving mass crossing. Verichev and Metrikine [30] studied a similar stability problem for a beam lying on a periodically inhomogeneous continuous foundation using perturbation analysis. In a recent study, Ghomeshi and Keshmiri [31] used the homotopy perturbation method to identify resonance parameters in the moving mass problem.…”

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confidence: 99%

On the parametric excitation of a Timoshenko beam due to intermittent passage of moving masses: instability and resonance analysis

2014

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A Timoshenko beam excited by a sequence of identical moving masses is studied as a time-varying problem. The effects of centripetal and Coriolis accelerations besides the vertical component of acceleration of the moving mass are considered. Using Galerkin procedure, the partial differential equations of motion which are derived by Hamilton's principle are transformed to ordinary differential equations. The incremental harmonic balance method is implemented to determine the boundary curve of instability and other companion curves of resonance in the parameter plane. A new approach for identifying the conditions of resonance is investigated by presenting an intuitive definition of resonance for time-varying systems. The influence of employing different deformation theories on the critical parameter values of stability and resonance curves is studied. The validity of the instability and resonance curves is examined by numerical simulations and also ascertained through comparing with those reported in the literature.

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Instability of vibrations of a mass that moves uniformly along a beam on a periodically inhomogeneous foundation

Cited by 49 publications

References 16 publications

Vibration of a beam on continuous elastic foundation with nonhomogeneous stiffness and damping under a harmonically excited mass

Vibration of a beam on continuous elastic foundation with nonhomogeneous stiffness and damping under a harmonically excited mass

Stability of a two-mass oscillator moving on a beam supported by a visco-elastic half-space

On the parametric excitation of a Timoshenko beam due to intermittent passage of moving masses: instability and resonance analysis

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