Stability of vehicles under nonstationary crosswind excitation

Strong crosswind gusts have great influence on the stability of railway and road vehicles. They may lead to accidents and also to a discomfort for the road vehicle driver. Risk assessment for overturning of railway and road vehicles is usually calculated based on the stationary situation or at least on wind-tunnel experiments that are mostly carried out with a static vehicle model. Nonstationary excitation due to wind turbulence occurs if the vehicle accelerates or decelerates. Increasing vehicle speed relative to wind speed will move the energy content of the spectrum to a higher frequency range. It has been realized that nonstationary wind has a great influence on vehicle stability especially when the vehicle speed is high. Thus in order to assess the overturning risk in a more realistic way, a nonstationary wind model together with its interaction with the vehicle should be taken into consideration.This paper proposes a nonstationary wind turbulence model for the investigation of crosswind stability of ground vehicles. A wind model with nonstationary turbulence as well as the wind effects to the moving vehicle in a nonstationary situation (acceleration/deceleration) is described. Nonstationary aerodynamic forces are considered together with the interaction between the moving vehicle system and the wind turbulence. Failure probabilities are computed and reliability analyses are carried out. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the performance of ground vehicles under the influence of stochastic wind loads

The influence of aerodynamic loads on the performance of ground vehicles is an important economical, safety and comfort issue. For the safety and comfort matters, especially the crosswind behavior of the ground vehicles is of great interest, as strong lateral winds can cause major accidents or at least make the driver and the passengers feel very uncomfortable and insecure. Two different failure scenarios dominate the safety aspect. The most important one is the risk of overturning, which happens not very often but if it occurs it leads in most cases to serious personal damages and the second one is the sudden lane change of road vehicles and the associated driving instabilities because of unforeseen gusts. As most of the design and excitation parameters of the system are uncertain, they are recognized as stochastic variables. Taking the mentioned failure scenarios into account the probability of failure of a freight vehicle has been computed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of wave–wind interaction at a seawall using a numerical wave channel

This paper presents the study on wind and waves interactions at a seawall using a numerical wave channel. The numerical experiments were conducted for wave overtopping of a 1/4 sloping seawall using several conditions of incident waves and wind speeds. The numerical results were verified against laboratory data in a case for wave overtopping without wind effects. The interaction of waves and wind was analyzed in term of mean wave quantities, overtopping rate and variation of wind velocity at some selected locations. The results showed that the overtopping rate was strongly affected by wind and the wind field was also significantly modified by waves. There exists an effective range of wind speed in comparison with the local shallow wave speed at the breaking location, which gives significant effects to the wave overtopping rates. The maximum of wind adjustment coefficient f_w for wave overtopping rate was strongly related to the mean overtopping rate in the case for no wind. This study also showed that when the mean overtopping rate was greater than 5 × 10⁻⁴ m³/s/m, the maximum of wind adjustment coefficient f_w approached to a specific value of about 1.25.     

On the influence of crosswind on the overturning stability of railway vehicles

In recent years modern railway vehicle design shows a trend to faster, lighter and more energy efficient railway systems. These developments unfortunately alter the crosswind stability in a negative manner and so the risk of overturning of railway vehicles during operation in strong winds becomes a critical issue. The risk of overturning is quantified by the probability that a railway vehicle capsizes. To improve the crosswind stability it is very important to know the influence of the design and excitation variables on the wheel unloading of the railway car. Sensitivity coefficients of the design and excitation variables with respect to the probability of failure are calculated and the most influential variables are accentuated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the stochastic response of a fractionally-damped Duffing oscillator

A numerical method is presented to compute the response of a viscoelastic Duffing oscillator with fractional derivative damping, subjected to a stochastic input. The key idea involves an appropriate discretization of the fractional derivative, based on a preliminary change of variable, that allows to approximate the original system by an equivalent system with additional degrees of freedom, the number of which depends on the discretization of the fractional derivative. Unlike the original system that, due to the presence of the fractional derivative, is governed by non-ordinary differential equations, the equivalent system is governed by ordinary differential equations that can be readily handled by standard integration methods such as the Runge–Kutta method. In this manner, a significant reduction of computational effort is achieved with respect to the classical solution methods, where the fractional derivative is reverted to a Grunwald–Letnikov series expansion and numerical integration methods are applied in incremental form. The method applies for fractional damping of arbitrary order α (0 < α < 1) and yields very satisfactory results. With respect to its applications, it is worth remarking that the method may be considered for evaluating the dynamic response of a structural system under stochastic excitations such as earthquake and wind, or of a motorcycle equipped with viscoelastic devices on a stochastic road ground profile.     

Stick balancing with reflex delay in case of parametric forcing

The effect of parametric forcing on a PD control of an inverted pendulum is analyzed in the presence of feedback delay. The stability of the time-periodic and time-delayed system is determined numerically using the first-order semi-discretization method in the 5-dimensional parameter space of the pendulum’s length, the forcing frequency, the forcing amplitude, the proportional and the differential gains. It is shown that the critical length of the pendulum (that can just be balanced against the time-delay) can significantly be decreased by parametric forcing even if the maximum forcing acceleration is limited. The numerical analysis showed that the critical stick length about 30 cm corresponding to the unforced system with reflex delay 0.1 s can be decreased to 18 cm with keeping maximum acceleration below the gravitational acceleration.     

Computational modelling of fluid structure interaction at nano-scale boundaries with modified Maxwellian velocity distribution

The soft collisions among fluid–fluid and fluid-wall molecules are modeled from first principles. In particular, the assumption of Maxwellian distribution of velocities for thermalized molecules, in both parallel and perpendicular directions to the wall, has been re-evaluated with supporting experimental and/or numerical evidence.It is proposed that the normal component of molecular velocity post collision is conserved for all fluid molecules. The slip effect at the wall boundary, introduced by the surface roughness, is accounted by an accommodation coefficient f. A moving least square method is used to calculate macroscopic velocity values. The influence of molecular interaction on the macroscopic velocity distribution is investigated at 40 MPa and 300 K for slit pore, inclined and stepped wall configurations. The accommodation coefficient values f = 0, 0.07, 0.257, 0.45, 0.681 and 1; and acceleration values ranging from zero to 1 × 10¹¹ m/s² and 250 × 10¹¹ m/s² are used for comparison.The distribution of macroscopic velocity parallel to the wall is studied to observe the effect of the slip behaviour. The detailed study of average of velocity values at various magnitudes of acceleration has shown an evidence of characteristic low and high speed of molecular flows that is considered as significant and a comparison is sought with an equivalent laminar and turbulent flow style behaviour. The two dimensional vector and contour plots of macroscopic velocity provide further insights in understanding Continuum velocity distributions resulting from molecular fluid-wall interaction at nanoscale. The research has highlighted the need to develop molecular dynamics simulation techniques for non-periodic boundary conditions.     

Explicit series solution of travelling waves with a front of Fisher equation

In this paper, an analytic technique, namely the homotopy analysis method, is employed to solve the Fisher equation, which describes a family of travelling waves with a front. The explicit series solution for all possible wave speeds 0 < c < +∞ is given. Such kind of explicit series solution has never been reported, to the best of author’s knowledge. Our series solution indicates that the solution contains an oscillation part when 0 < c < 2. The proposed analytic approach is general, and can be applied to solve other similar nonlinear travelling wave problems.     

A cartographic study of the phase space of the elliptic restricted three body problem. Application to the Sun–Jupiter–Asteroid system

This work deals with numerical investigations of the phase space of the planar elliptic restricted three body model. The Sun–Jupiter–Asteroid system is considered and the fast Lyapunov indicator (FLI) is used as a tool to examine various types of orbits on which the infinitesimal mass can undergo. The FLI is computed on given grids of initial conditions regularly spaced in the domain 1.5 AU ? a ? 6 AU and 0 ? e ? 0.5 and for various choices of initial angles: the argument of perihelion ω and mean anomaly M. On the obtained charts the stability regions, the chaotic zones and the geography of resonances are clearly displayed. Moreover, the ‘V’ shaped layers associated with the mean motion resonances of low order with its chaotic zones due to separatrix splitting and libration regions are clearly distinguished. Their size is discussed as a function of the resonance order and the parameters entering into the perturbing function. The results are discussed and compared with analytical studies concerning the subject.     

Numerical analysis of pressure field on curved self-weighted metallic roofs due to the wind effect by the finite element method

In this paper, an evaluation of distribution of the air pressure is determined throughout the curved and open self-weighted metallic roof due to the wind effect by the finite element method (FEM) [K. Bathe, Finite Element Procedures, Prentice-Hall, Englewood Cliffs, New York, 1996]. Data from experimental tests carried out in a wind tunnel involving a reduced scale model of a roof was used for comparison. The nonlinearity is due to time-averaged Navier–Stokes equations [C.A.J. Fletcher, Computational Techniques for Fluid Dynamics, Springer, Berlin, 1991] that govern the turbulent flow. The calculation has been carried out keeping in mind the possibility of turbulent flow in the vicinities of the walls, and speeds of wind have been analyzed between 30 and 40 m/s. Finally, the forces and moments are determined on the cover, as well as the distribution of pressures on the same one, comparing the results obtained with the Spanish and European Standards rules, giving place to the conclusions that are exposed in the study.     

A general model of road traffic accidents

A general model that relates road traffic accidents to the number of vehicles involved, and the number of primary causes of such accidents, is presented. The model considers traffic accidents as failures of a road traffic network system to meet social and economic constraints, and therefore as a measure of the unreliability of such a system. The equations apply to accidents in the real time domain as well as to mean values per unit of vehicle exposure time or vehicle distance. They also apply to single vehicles and drivers, groups of drivers and fleets of vehicles, and the entire vehicle and driving population. They can be used for sections of a network or for a whole network.The equations used have a large number of terms, hence bias errors are common in road accident investigations.     

On the crosswind stability of high speed railway vehicles

The crosswind stability against overturning is a major national design criterium for high-speed railway vehicles. Due to the increasing interoperability in Europe it has also become an important international task. Especially modern light-weight trains are at risk to fail and counter-measures as for example wind-fences or adding extra weight in the underbelly are always very expensive. In recent years efforts were made to derive an uniform rule in certifying railway vehicles. In this case especially probabilistic methods were proposed. These probabilistic technics are common design criteria for wind turbines. This paper presents a sophisticated method to compute the reliability of railway vehicles under strong crosswind. In consideration of the given gust signal and the high-frequency, turbulent fluctuations of the wind the response of a simplified train model is computed. The major failure criterium to determine the reliability is the lowest wheel-rail contact force of the railway vehicle. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new formulation and an exact approach for the many-to-many hub location-routing problem

An important problem of the freight industry is the parcel delivery network design, where several facilities are responsible for assembling flows from several origins, re-routing them to other facilities where the flows are disassembled and the packages delivered to their final destinations. In order to provide this service, local tours are established for the vehicles assigned to each of the processing facilities, which are then responsible for the pickup and delivery tasks. This application gives rise to the many-to-many hub location routing problem that is the combination of two well known problems: the vehicle routing problem and the single assignment hub location problem. In this work, a new formulation for this important problem is proposed and solved by a specially tailored Benders decomposition algorithm. The proposed method is robust enough to solve instances up to 100 nodes having 4 million integer variables.     

On the stability of fractional neutron point kinetics (FNPK)

The aim of this work is investigate the stability of fractional neutron point kinetics (FNPK). The method applied in this work considers the stability of FNPK as a linear fractional differential equation by transforming the s − plane to the W − plane. The FNPK equations is an approximation of the dynamics of the reactor that includes three new terms related to fractional derivatives, which are explored in this work with an aim to understand their effect in the system stability. Theoretical study of reactor dynamical systems plays a significant role in understanding the behavior of neutron density, which is important in the analysis of reactor safety. The fractional relaxation time (τ^α) for values of fractional-order derivative (α) were analyzed, and the minimum absolute phase was obtained in order to establish the stability of the system. The results show that nuclear reactor stability with FNPK is a function of the fractional relaxation time.     

Spread of disease in a patchy environment

For a two patches SIR model, it is shown that its dynamic behavior is determined by several quantities. We have shown that if R₀ < 1, then the disease-free equilibrium is globally asymptotically stable, otherwise it is unstable. Some sufficient conditions for the local stability of boundary equilibria are obtained. Numerical simulations indicate that travel between patches can reduces oscillations in both patches; may enhances oscillations in both patches; or travel switches oscillations from one patch to another.     

The new airfoil model NACA0015, modal analysis and flutter properties

The experimental airfoil model NACA0015 was used to study aeroelastic phenomena during self-excited profile vibration. It provides data for control of aeroelastic calculation programs at subsonic speeds of the stream. The model movability is two-dimensional with two-degree of freedom dynamic system, one in pitch and the second in plunge, and is proposed to be a dynamic system having two near corresponding eigenfrequencies. To quantitatively evaluate flow field using interferometry, a special test section design and profile was constructed. It utilized a large visual field for the optical system together with the option of changing support stiffness for both degrees of freedom. In this paper experimental results from the range of Reynolds numbers Re = (2.63–2.83) 10⁵ are published. The identified eigenvalues and eigenmodes for zero flow velocity are compared with measured flutter properties (frequency, modes and time evolutions) of the airfoil.     

Bifurcation and chaos in discrete-time predator–prey system

The discrete-time predator–prey system obtained by Euler method is investigated. The conditions of existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory. And numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including period-3, 5, 6, 7, 8, 9, 10, 12, 18, 20, 22, 30, 39-orbits in different chaotic regions, attracting invariant circle, period-doubling bifurcation from period-10 leading to chaos, inverse period-doubling bifurcation from period-5 leading to chaos, interior crisis and boundary crisis, intermittency mechanic, onset of chaos suddenly and sudden disappearance of the chaotic dynamics, attracting chaotic set, and non-attracting chaotic set. In particular, we observe that when the prey is in chaotic dynamic, the predator can tend to extinction or to a stable equilibrium. The computations of Lyapunov exponents confirm the dynamical behaviors. The analysis and results in this paper are interesting in mathematics and biology.     

Implementación eficiente de una formulación semirrecursiva para la dinámica de sistemas multicuerpo de gran tamaño

This article shows an efficient implementation of a dynamic semi-recursive formulation for large and complex multibody system simulations, with interesting applications in the automotive field and especially with industrial vehicles. These systems tend to have a huge amount of kinematic constraints, becoming usual the presence of redundant but compatible systems of equations. The maths involved in the solution of these problems have a high computational cost, making very challenging to achieve real-time simulations.In this article, two implementations to increase the efficiency of these computations will be shown. The difference between them is the way they consider the Jacobian matrix of the constraint equations. The first one treats this matrix as a dense one, using the BLAS functions to solve the system of equations. The second one takes into account the sparse pattern of the Jacobian matrix, introducing the sparse function MA48 from Harwell.Both methodologies have been applied on two multibody system models with different sizes. The first model is a vehicle IVECO DAILY 35C15 with 17 degrees of freedom. The second one is a semi-trailer truck with 40 degrees of freedom. Taking as a reference the standard C/C + + implementation, the efficiency improvements that have been achieved using dense matrices (BLAS) have been of 15% and 50% respectively. The results in the first model have not improved significantly by using sparse matrices, but in the second one, the times with sparse matrices have been reduced 8% with respect to the BLAS ones.     

On “P” property and the column-W property

P-matrices play an important role in the well-posedness of a linear complementarity problem (LCP). Similarly, the well-posedness of a horizontal linear complementarity problem (HLCP) is closely related to the column-W property of a matrix k-tuple.In this paper we first consider the problem of generating P-matrices from a given pair of matrices. Given a matrix pair (D, F) where D is a square matrix of order m and matrix F has m rows, “what are the conditions under which there exists a matrix G such that (D + FG) is a P-matrix?”. We obtain necessary and sufficient conditions for the special case when the column rank of F is m ? 1. A decision algorithm of complexity O(m²) to check whether the given pair of matrices (D, F) is P-matrisable is obtained. We also obtain a necessary and an independent sufficient condition for the general case when rank(F) is less than m ? 1.We then generalise the P-matrix generating problem to the generation of matrix k-tuples satisfying the column-W property from a given matrix (k + 1)-tuple. That is, given a matrix (k + 1)-tuple (D₁, … ,D_k, F), where D_js are square matrices of order m and F is a matrix having m rows, we determine the conditions under which the matrix k-tuple (D₁ + FG₁, … ,D_k + FG_k) satisfies the column-W property. As in the case of P-matrices we obtain necessary and sufficient conditions for the case when rank(F) = m ? 1. Using these conditions a decision algorithm of complexity O(km²) to check whether the given matrix (k + 1)-tuple is column-W matrisable is obtained. Then for the case when rank(F) is less than m ? 1, we obtain a necessary and an independent sufficient condition.For a special sub-class of P-matrices we give a polynomial time decision algorithm for P-matrisability. Finally, we obtain a geometric characterisation of column-W property by generalising the well known separation theorem for P-matrices.     

Lower bounds for minimum semidefinite rank from orthogonal removal and chordal supergraphs

The minimum semidefinite rank (msr) of a graph is the minimum rank among positive semidefinite matrices with the given graph. The OS-number is a useful lower bound for msr, which arises by considering ordered vertex sets with some connectivity properties. In this paper, we develop two new interpretations of the OS-number. We first show that OS-number is also equal to the maximum number of vertices which can be orthogonally removed from a graph under certain nondegeneracy conditions. Our second interpretation of the OS-number is as the maximum possible rank of chordal supergraphs who exhibit a notion of connectivity we call isolation-preserving. These interpretations not only give insight into the OS-number, but also allow us to prove some new results. For example we show that msr(G) = |G| ? 2 if and only if OS(G) = |Gzsfnc ? 2.