Instability of Vibrations of Mass(es) Moving Uniformly on a Two-Layer Track Model: Parameters Leading to Irregular Cases and Associated Implications for Railway Design

Dimitrovová, Zuzana

doi:10.3390/app132212356

Cited by 1 publication

(6 citation statements)

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“…It is demonstrated that there are several situations with rather unpredictable behavior, especially at low damping levels, as already shown for simpler, one-layer [34] and two-layer models [35,51]. In the semi-analytical approach, the so-called instability lines are traced, indicating the moving mass as a function of velocity in a limiting situation where one of the induced frequencies is real-valued.…”

Section: Introductionmentioning

confidence: 64%

“…As already mentioned in the Introduction, the three-viscoelastic-layer railway track model is widely used for its simplicity, numerical efficiency, and ability to effectively estimate the real behavior, as demonstrated in [71,72]. Its description was already given in previous works on layered models [51,52], but it is repeated here for completeness. In this model, the rail is modeled by a beam that is supported by linear spring-damper elements standing for rail pads, which are connected to point masses representing sleepers' masses, which are, in turn, supported by linear spring-damper elements modeling the ballast, including its shear resistance.…”

Section: Mechanical Model and Governing Equationsmentioning

confidence: 99%

“…A more complex vehicle model can also be used to study the stability issue [48,49]. The track is modeled using an Euler-Bernoulli infinite beam on a continuous foundation with one elastic layer [28,29,31,32,34] or two [35,50,51] or three elastic layers [52]. Instead of the Euler-Bernoulli beam, the Timoshenko beam can also be used [42,43,53].…”

Section: Introductionmentioning

confidence: 99%

“…When investigating the quality of a system to be stable according to the velocity of a moving object, in certain cases, depending on the nature of the moving object and the elastic structure, zones of stability alternating with zones of instability have been identified [42,51,52], but the first zone on the velocity axis is always a zone of stability, and therefore, the critical velocity of a moving object refers to the transition from this zone to the first zone of instability that follows it.…”

Section: Introductionmentioning

confidence: 99%

“…Relatively recently, a new semi-analytical method for analyzing the response of an elastic structure to a moving object has been proposed [10,11,34,35,38,51,52,59]. The main objective of this method is to determine the full dynamic response of the structure directly as a sum of residues.…”

Section: Introductionmentioning

confidence: 99%

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Semi-Analytical Approach and Green’s Function Method: A Comparison in the Analysis of the Interaction of a Moving Mass on an Infinite Beam on a Three-Layer Viscoelastic Foundation at the Stability Limit—The Effect of Damping of Foundation Materials

Dimitrovová,

Mazilu

2024

Materials

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In this paper, the interaction of a mass moving uniformly on an infinite beam on a three-layer viscoelastic foundation is analyzed with the objective of determining the lowest velocity at the stability limit, called, in this context, the critical velocity. This issue is important for rail transport and, in particular, for the high-speed train, because the moving mass is the basic model of a vehicle, and the infinite beam on a three-layer viscoelastic foundation is the usual mechanical representation of the railway track. In addition to this, the advantages and disadvantages of the two implemented methods, namely, the semi-analytical approach and the Green’s function method, are summarized in terms of computational time, the precision of the obtained results, limitations, and the feasibility of implementation. All results are presented in a dimensionless form to cover a wide range of possible scenarios. Some results may be considered academic, however, results related to a particular railway track are also included. Particular attention is paid to the influence of the damping of materials in the foundation upon the critical velocity of the moving mass. Regarding the semi-analytical approach, it is demonstrated that the critical velocities can be obtained in an exact manner by tracing the branches of the so-called instability lines in the velocity–moving-mass plane. This analysis can be maintained within the real domain. As for the time series, they can be determined by a numerical inverse Laplace transform. Moreover, thanks to the analytical form of the final result in the Fourier domain, each value corresponding to a specific time instant can be obtained directly, that is, without the previous time history. Regarding the Green’s function method, this is used to verify a few points delimiting the stable and unstable regions of the moving mass with the help of the D-decomposition approach. Additionally, a numerical algorithm based on the Green’s function and convolution integral written for dimensionless quantities is used to calculate the time series of the moving mass. In addition to identifying the critical velocity of the moving mass, its connection with the critical velocity of the moving force is emphasized, and the possibility of validating the results on long finite beams using modal expansion is presented and described.

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Section: Introductionmentioning

confidence: 64%