Double grazing bifurcations of the non-smooth railway wheelset systems

There are numerous non-smooth factors in railway vehicle systems, such as flange impact, dry friction, creep force, and so on. Such non-smooth factors heavily affect the dynamical behavior of the railway systems. In this paper, we investigate and mathematically analyze the double grazing bifurcations of the railway wheelset systems with flange contact. Two types of models of flange impact are considered, one is a rigid impact model and the other is a soft impact model. First, we derive Poincaré maps near the grazing trajectory by the Poincaré-section discontinuity mapping (PDM) approach for the two impact models. Then, we analyze and compare the near grazing dynamics of the two models. It is shown that in the rigid impact model the stable periodic motion of the railway wheelset system translates into a chaotic motion after the gazing bifurcation, while in the soft impact model a pitchfork bifurcation occurs and the system tends to the chaotic state through a period doubling bifurcation. Our results also extend the applicability of the PDM of one constraint surface to that of two constraint surfaces for autonomous systems.

Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints

The dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation technique, and the different types of bifurcations are detected, such as grazing bifurcation, saddle-node bifurcation, and period-doubling bifurcation, which predicts the complexity of the system considered. Based on the grazing phenomenon obtained, the zero-time-discontinuity mapping is extended from the single constraint system presented in the literature to the two-sided elastic constraint system discussed in this paper. The Poincare mapping of double grazing periodic motion is derived, and this compound mapping is applied to obtain the existence conditions of codimension-two grazing bifurcation point of the system. According to the deduced theoretical result, the grazing curve and the codimension-two grazing bifurcation points are validated by numerical simulation. Finally, various types of periodic-impact motions near the codimension-two grazing bifurcation point are illustrated through the unfolding diagram and phase diagrams.

Cross-Bedding and Structural Mapping for Rockfall Assessment of a Tunnel using Hi-Resolution LiDAR (Fribourg, Switzerland)

<p>Lithology identification and discontinuity mapping are necessary for rockfall hazard assessment in tunnels. However, the restricted exposure and variability of rock face orientation in tunnels ought to be taken into account. Therefore, using Light Detection and Ranging (LiDAR) technique may significantly contribute to this task.</p><p>A historical carved tunnel in the Upper Marine Molasse (a poorly consolidated sandstone) of the City of Fribourg (Switzerland) was then investigated by fieldwork and LiDAR. Interestingly, it appears that in addition to joints and layering, some specific sedimentary structures, i.e. cross-bedding, have an important role in the tunnel roof stability. Cross-bedding is a sedimentary structure that can be identified clearly by the geometry of layer within one or more beds in a series of rock strata that does not run parallel to the plane of stratification.</p><p>In order to detect and analyse these sedimentary structures, the intensity of the backscattered LiDAR signal is analysed using the Oren-Nayar reflectance model, which considers range, incidence angle, scanned surface geometry (i.e. roughness). It provides corrected values of intensities that make possible to distinguish and identify geometry of cross-beddings in the tunnel.</p><p>An analysis of structural discontinuities was also performed using Coltop Software which identified joint sets developed inside the tunnel. Based on this approach, lithology characterizations, orientation of each discontinuity and bedding structures could be identified in point clouds confidently for understanding the mechanisms of potential rockfalls in the tunnel.</p>

Sliding Bifurcations in the Memristive Murali–Lakshmanan–Chua Circuit and the Memristive Driven Chua Oscillator

In this paper, we report the occurrence of sliding bifurcations admitted by the memristive Murali–Lakshmanan–Chua circuit [Ishaq & Lakshmanan, 2013] and the memristive driven Chua oscillator [Ishaq et al., 2011]. Both of these circuits have a flux-controlled active memristor designed by the authors in 2011, as their nonlinear element. The three-segment piecewise-linear characteristic of this memristor bestows on the circuits two discontinuity boundaries, dividing their phase spaces into three subregions. For proper choice of parameters, these circuits take on a degree of smoothness equal to one at each of their two discontinuities, thereby causing them to behave as Filippov systems. Sliding bifurcations, which are characteristic of Filippov systems, arise when the periodic orbits in each of the subregions, interact with the discontinuity boundaries, giving rise to many interesting dynamical phenomena. The numerical simulations are carried out after incorporating proper zero time discontinuity mapping (ZDM) corrections. These are found to agree well with the experimental observations which we report here appropriately.

Discontinuity Mapping using Terrestrial Laser Scanner and Kinematic Method

This study presents the results of discontinuity mapping using terrestrial laser scanning (TLS) survey and the kinematic method. The results provide the current site and slope condition of comprehensive geological study using terrestrial laser scanning and discontinuity survey at Simpang Pulai, Perak. From the results obtained, it can be concluded that the major potential failures in this area are wedge and plane failures, but there are some area had the potential of toppling failure. This study, however, constitutes a preliminary design consideration and not intended for use in final design or construction. The final design shall be made by the engineer based on the further detail site investigation (S.I.) and other design factors to be used in the actual design of the project.

Nonsmooth Vibration Characteristic of Gear Pair System with Periodic Stiffness and Backlash

As the most widely used power transmission device in mechanical equipment, the vibration characteristics of gears have a very important influence on the working performance. It is of great theoretical and practical significance to study the vibration characteristics of gear system. In this paper, a gear transmission system model is set up in a forcefully nonlinear form; the continuity mapping and discontinuity mapping are utilized to analyze the nonsmooth vibration. Then, the sliding dynamics of separation boundaries is studied by using the perturbation method and the differential inclusion theory. In addition, the periodic response of gear pair system is illustrated and Floquet’s theory is presented to confirm the stability and bifurcation of periodic response. Concurrently, the maximal Lyapunov exponent is obtained to accurately determine the chaotic state in gear pair system, which is consistent with the bifurcation diagram and Poincare section. Finally, a reasonable explanation is given for the jump phenomenon in bifurcation diagram.