Instability of an oscillator moving along a Timoshenko beam on viscoelastic foundation

Mazilu, Traian; Dumitriu, Mădălina; Tudorache, Cristina

doi:10.1007/s11071-011-0068-5

Cited by 21 publications

(18 citation statements)

References 25 publications

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“…The problem of a moving oscillator on a flexible beam has been extensively studied in the literature [8,9], which is one cause of instability in railway vehicles [10]. In a roller coaster, however, the varying dynamical loads and speed caused by travelling along a spatial trajectory may not be neglected.…”

Section: Flexible Vehicle-track Interactionmentioning

confidence: 99%

Self‐excitability of roller coaster trains along spatial trajectories

Agustí,

Kecskeméthy

2023

Proc Appl Math and Mech

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It is well known that vibrations usually appear during a roller coaster ride, which in some cases leads to passenger discomfort and poses additional material and structural strain. However, the causes of such vibrations are still not fully understood or have not been rigorously tackled in the literature, mainly due to the lack of experiments and real data. While there have been technological advances that help to mitigate them to some degree, for instance by placing shock absorbers between the wheels and the bogie frame, an analysis of this phenomenon is required to make better decisions at the design stage. Here, two possible self‐excitation scenarios are analysed: a bogie instability in curved track sections and a train–track interaction from the point of view of a set of moving oscillators on a flexible spatial trajectory. In the first model, Hopf bifurcations are observed for a combination of reasonable parameters. In the second model, the numerical results also show increased vibrations for some train configurations, which potentially indicates that the track flexibility may not be overlooked. While this research proposes new causes of vibrations in roller coasters, experiments need to be carried out in order to corroborate the results.

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Section: Flexible Vehicle-track Interactionmentioning

confidence: 99%

Self‐excitability of roller coaster trains along spatial trajectories

Agustí,

Kecskeméthy

2023

Proc Appl Math and Mech

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“…The differential governing equations were converted into algebraic equations byassuming the deflection and rotation of the beam in harmonic forms with respect to time and space.Some researchers analyzed beams resting on viscoelastic foundations subjected to moving loads. Thevibration instability analysis of an oscillator moving along a Timoshenko beam was performed byMetrikine and Verichev (2001) and Mazilu et al (2012). The inHluence of a nonlinear foundation on thedynamic response of a periodically supported beam was investigated by Hoang et al (2016), based on the Euler-Bernoulli beam theory.…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic Substrates Effects on the Elimination or Reduction of the Sandwich Structures Oscillations Based on the Kelvin-Voigt Model

Molla-Alipur

Rajabi

2017

Lat. Am. j. solids struct.

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Effects of viscoelastic substrates on the sandwich structures oscillations are examined in this paper. In this regard, dynamic response of sandwich annular panels with FG polar orthotropic face sheets resting on viscoelastic substrate is presented. Young's modulus in the radial and circumferential direction, shear modulus and density of each face sheet may be varied continuously in the radial direction. The viscoelastic substrate is modeled as Kelvin-Voigt foundation. To describe more accurately response of sandwich structures, the governing dynamical equations are derived based on the layerwise theory and five systems of second order coupled partial differential equations are obtained. The effects of the stiffness and damping coefficients of the foundation on the dynamic behavior of sandwich plate are investigated for various transient loads and boundary condition. Since no available results may be found in literature to demonstrate the efficiency and accuracy of the obtained results, the obtained results are verified by comparison with finite element results based on the three dimensional theory of elasticity for some special cases.

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“…Analyses are performed to illustrate the accuracy of the developed method to investigate the effects of various parameters such as the load velocity, load frequency, shear deformation, foundation nonlinearity, damping, and axial compression on the beam's displacements and stresses. In [18], the issue of instability phenomenon of a three-mass oscillator uniformly moving along a continuously viscoelastic supported Timoshenko beam due to the excited Doppler waves is investigated. The proposed model corresponds to a two-level suspension vehicle running on a track and it includes the wheel/rail contact nonlinearities which contain the Hertzian contact characteristic and the possibility of contact loss.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Analysis of a Timoshenko Beam Resting on a Viscoelastic Foundation and Traveled by a Moving Mass

Mamandi

Kargarnovin

2014

Shock and Vibration

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The dynamic response of a Timoshenko beam with immovable ends resting on a nonlinear viscoelastic foundation and subjected to motion of a traveling mass moving with a constant velocity is studied. Primarily, the beam’s nonlinear governing coupled PDEs of motion for the lateral and longitudinal displacements as well as the beam’s cross-sectional rotation are derived using Hamilton’s principle. On deriving these nonlinear coupled PDEs the stretching effect of the beam’s neutral axis due to the beam’s fixed end conditions in conjunction with the von-Karman strain-displacement relations is considered. To obtain the dynamic responses of the beam under the act of a moving mass, derived nonlinear coupled PDEs of motion are solved by applying Galerkin’s method. Then the beam’s dynamic responses are obtained using mode summation technique. Furthermore, after verification of our results with other sources in the literature a parametric study on the dynamic response of the beam is conducted by changing the velocity of the moving mass, damping coefficient, and stiffnesses of the foundation including linear and cubic nonlinear parts, respectively. It is observed that the inclusion of geometrical and foundation stiffness nonlinearities into the system in presence of the foundation damping will produce significant effect in the beam’s dynamic response.

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Instability of an oscillator moving along a Timoshenko beam on viscoelastic foundation

Cited by 21 publications

References 25 publications

Self‐excitability of roller coaster trains along spatial trajectories

Self‐excitability of roller coaster trains along spatial trajectories

Viscoelastic Substrates Effects on the Elimination or Reduction of the Sandwich Structures Oscillations Based on the Kelvin-Voigt Model

Nonlinear Dynamic Analysis of a Timoshenko Beam Resting on a Viscoelastic Foundation and Traveled by a Moving Mass

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