Comments on “Vibration of simply supported beams under a single moving load: A detailed study of cancellation phenomenon” by C.P. Sudheesh Kumar, C. Sujatha, K. Shankar [Int. J. Mech. Sci. 99 (2015) 40–47, doi: 10.1016/j.ijmecsci.2015.05.001]
“…• The verification of serviceability limits in terms of dynamic displacement can be verified using the conventional moving load model. Museros et al (2013), Museros and Moliner (2017), and Doménech et al (2014) agreed to the fact that the moving load model provides a good estimate where the prediction of bridge response is of prime importance.…”
Section: Mathematical Formulationsupporting
confidence: 61%
“…Museros et al (2013), De Roeck et al (n.d.), and Museros and Alarcón (2002) also reported that the vehicle–track interaction is of little importance as the frequency ratio of simply supported bridges is far from unity resulting in a considerable reduction in peak responses during resonances.• The verification of serviceability limits in terms of dynamic displacement can be verified using the conventional moving load model. Museros et al (2013), Museros and Moliner (2017), and Doménech et al (2014) agreed to the fact that the moving load model provides a good estimate where the prediction of bridge response is of prime importance.Figure 1.Idealization of the opposite traversing vehicles in an elastically supported beam as per Eurocode EN 1991-2 load models (Gulvanessian, 2001; ERRI, 1999): (a) HSLM-B and (b) HSLM-A.…”
The design of high-speed simply supported bridges in critical conditions, such as road or canal crossings, is a matter of concern, particularly under two-way crossings with sequential wheel loads. Contrarily to simple classical support, elastic bearings can serve towards vibration mitigation under high speed. In this paper, a non-dimensional framework is developed to understand the impact mechanism of an elastically supported (ES) beam under the action of single as well as opposite traversing loads. A good agreement with the available literature has been confirmed for the one-way crossing using the present methodology. Moreover, a parametric study is conducted for an ES beam, in which the effects of speed parameter ( η), speed parameter ratio between two trains ( R), interspatial distance between loads to the length of the bridge ( ϵ), damping ζ, stiffness parameter ( κ), and traversing time difference between two trains ( t os) are investigated. The theoretical results suggest the effective use of the ES beam under higher values of η for one-way and R for two-way traffic. Additionally, various resonances and cancellation speed ratios under particular values of ϵ have been identified under varying values of κ.
“…• The verification of serviceability limits in terms of dynamic displacement can be verified using the conventional moving load model. Museros et al (2013), Museros and Moliner (2017), and Doménech et al (2014) agreed to the fact that the moving load model provides a good estimate where the prediction of bridge response is of prime importance.…”
Section: Mathematical Formulationsupporting
confidence: 61%
“…Museros et al (2013), De Roeck et al (n.d.), and Museros and Alarcón (2002) also reported that the vehicle–track interaction is of little importance as the frequency ratio of simply supported bridges is far from unity resulting in a considerable reduction in peak responses during resonances.• The verification of serviceability limits in terms of dynamic displacement can be verified using the conventional moving load model. Museros et al (2013), Museros and Moliner (2017), and Doménech et al (2014) agreed to the fact that the moving load model provides a good estimate where the prediction of bridge response is of prime importance.Figure 1.Idealization of the opposite traversing vehicles in an elastically supported beam as per Eurocode EN 1991-2 load models (Gulvanessian, 2001; ERRI, 1999): (a) HSLM-B and (b) HSLM-A.…”
The design of high-speed simply supported bridges in critical conditions, such as road or canal crossings, is a matter of concern, particularly under two-way crossings with sequential wheel loads. Contrarily to simple classical support, elastic bearings can serve towards vibration mitigation under high speed. In this paper, a non-dimensional framework is developed to understand the impact mechanism of an elastically supported (ES) beam under the action of single as well as opposite traversing loads. A good agreement with the available literature has been confirmed for the one-way crossing using the present methodology. Moreover, a parametric study is conducted for an ES beam, in which the effects of speed parameter ( η), speed parameter ratio between two trains ( R), interspatial distance between loads to the length of the bridge ( ϵ), damping ζ, stiffness parameter ( κ), and traversing time difference between two trains ( t os) are investigated. The theoretical results suggest the effective use of the ES beam under higher values of η for one-way and R for two-way traffic. Additionally, various resonances and cancellation speed ratios under particular values of ϵ have been identified under varying values of κ.
“…However, its amplitude is not predominant and the participation of several modal contributions different from the resonant mode are clearly perceptible. This fact can be attributed to the presence of a theoretical cancellation of the resonance condition in the vicinity of the circulation speed of S130 [28,29]. In addition, the frequencies associated to the vehicle system (car-bodies masses), as it is the case of the vertical frequency of the primary suspension system n p , which reaches 9.64 Hz for S130 train passenger coaches bogies [30], is close to the torsion mode frequency.…”
This work is devoted to the analysis of the railway-induced vertical vibrations of simplysupported double track bridges composed by pre-stressed concrete girder decks. Despite the low torsional stiffness that this particular deck configuration exhibits, several structures of this type do exist in both conventional and high-speed railway lines in Spain. Even though railway administrators recommend the construction of transverse or end beams bracing the longitudinal girders at the supports in girder bridges, in several occasions these elements are not built in order to accelerate the construction process. The aim of this study is to evaluate the beneficial effect of installing these transverse beams on the vertical dynamic response of the aforementioned structures and to determine what particular bridges are most affected by the presence of these elements. To this end, a representative ensemble of girder bridges covering a range of span lengths L between 10 m and 25 m has been predimensioned and their dynamic behaviour has been predicted by a finite element model that adopts common assumptions in engineering practice. Conclusions show that installing these elements is particularly relevant in the case of short (10-12.5 m) oblique bridges with a low number of longitudinal girders for a particular deck bending stiffness, leading to an important increase of the first torsion and first transverse bending natural frequencies and to a reduction of the structural response. Finally, experimental measurements on a real bridge belonging to the Madrid-Sevilla high-speed line are included in the final section to illustrate the theoretical derivations.
“…This well-known 1–3,26 mechanism of cancellation is referred in the paper as cancellation by addition , with a view to distinguish it from the zeroes of the influence line Γ max . Such zeroes of the influence line take place at particular speeds depending on the bridge characteristics, 17,20 and usually are designated simply as cancellations . It is important to notice that, since the d i values are fixed for each particular train, resonance will occur at given speeds when the time interval between the sinusoids coincides with integer multiples of T=1/f=2π/ω, being f the natural frequency in Hz. Cancellation (by addition) can be explained in much the same way, but adding or subtracting one half-period.…”
mentioning
confidence: 99%
“…This well-known 1–3,26 mechanism of cancellation is referred in the paper as cancellation by addition , with a view to distinguish it from the zeroes of the influence line Γ max . Such zeroes of the influence line take place at particular speeds depending on the bridge characteristics, 17,20 and usually are designated simply as cancellations .…”
The information contained in this paper will be of interest not only to bridge engineers, but also to train manufacturers. The article provides practical insight into the degree of coverage of real articulated trains (ATs) that Eurocode EN1991-2 guarantees. In both the design of new railway bridges, as well as in the assessment of existing ones, the importance of a detailed knowledge of the limits of validity of load models cannot be overemphasised. Being essential components of the rail transportation system, the capacity of bridges to withstand future traffic demands will be determined precisely by the load models. Therefore, accurate definition of the limits of validity of such models reveals crucial when increased speeds and/or increased axle loads are required by transportation pressing priorities. The most relevant load model for a significant portion of the bridges in high-speed railway lines is the so-called HSLM-A model, defined in EN1991-2. Their limits of validity are described in Annex E of such code. For its singular importance, the effects of vibrations induced by HSLM-A are analysed in this paper with attention to the response of simply supported bridges. This analysis is carried out in a view to determine whether the limits of validity given in Annex E of EN1991-2 cover the largest part of cases of interest. Specifically, the vibration effects of HSLM-A are compared with those of the ATs described in such Annex E, and the response is analysed in depth for simply supported bridges, which are structures especially sensitive to passing trains at high speeds. New theoretical approaches have been developed in order to undertake this investigation, including a novel, simplified expression of the train signature for ATs that is convenient for its low computational cost. The mathematical proofs are included in the first part of the paper and two separate appendices.
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