Numerical study of the vertical vibration of a vehicle model with variable speed

The paper deals with the numerical analysis of the general model of vehicle oscillations considering the non-stationarity of random excitation. The model parameters of the applied railway vehicle are deterministic functions. The non-stationary random function will be modelled by the variable speed of the vehicle and the vertical unevenness of the track. The so-called evolutionary Gaussian random process will be considering. The proposed comparative study of the dynamics of the vertical motion of the analysed railway vehicle will be realized using Monte Carlo simulation and a numerical procedure based on the theory of Markov processes. The originality of the article can be found in the implementation and algorithmization of the principles of solving non-stationary oscillation problems of machines. A universal methodology applicable in the dynamics of machines of various purposes is presented.

Excitation of decayless kink oscillations by random motion

We study kink oscillations of a straight magnetic tube with a transitional region at its boundary. The tube is homogeneous in the axial direction. The plasma density monotonically decreases in the transitional region from its value inside the tube to that in the surrounding plasma. The plasma motion is described by the linear magnetohydrodynamic equations in the cold plasma approximation. We use the ideal equations inside the tube and in the surrounding plasma, but take viscosity into account in the transitional region. We also use the thin tube and thin transitional or boundary layer (TTTB) approximation. Kink oscillations are assumed to be driven by a driver at the tube footpoint. We derive the equation describing the displacement in the fundamental mode and overtones. We use this equation to study kink oscillations both in the case of harmonic as well as random driving. In the case of random driving we assume that the driver is described by a stationary random function. The displacements in the fundamental mode and overtones are also described by stationary random functions. We derive the relation between the power spectra of the fundamental mode and all overtones and the power spectrum of the driver. We suggest a new method of obtaining information on the internal structure of coronal magnetic loops based on the shape of graphs of the power spectrum of the fundamental mode.

Evaluation of the reliability of reinforced concrete beams on a stochastically inhomogeneous elastic foundation under the action of a non-stationary random load

The results of the evaluation of the reliability of reinforced concrete beams lying on an elastic foundation are presented. The load on the beam is considered as a non-stationary random function, the elastic properties of the foundation are described as a stationary random function. Beam stiffness is considered as a random variable depending on the cubic strength of concrete. To solve the beam bending equation on an elastic foundation with random properties and a loaded non-stationary random load, the small parameter method and the method of spectral representations are used. The obtained probability characteristics of the probability density distribution of bending moments allow us to find the probability of failure of a reinforced concrete beam on an elastic stochastically inhomogeneous foundation.

Scattering of internal tides by irregular bathymetry of large extent

We present an analytical theory of scattering of tide-generated internal gravity waves in a continuously stratified ocean with a randomly rough seabed. Based on a linearized approximation, the idealized case of constant mean sea depth and Brunt–Väisälä frequency is considered. The depth fluctuation is assumed to be a stationary random function of space, characterized by small amplitude and a correlation length comparable to the typical wavelength. For both one- and two-dimensional topographies the effects of scattering on the wave phase over long distances are derived explicitly by the method of multiple scales. For one-dimensional topography, numerical results are compared with Bühler & Holmes-Cerfon (J. Fluid Mech., vol. 678, 2011, pp. 271–293), computed by the method of characteristics. For two-dimensional topography, new results are presented for both statistically isotropic and anisotropic cases.

Spectral representation of a Banach-valued stationary random function on a locally compact abelian group

Let

Transition length of two stationary random functions in investigation of railway stability

In this paper the scientific justification for determination of transition length of two stationary random functions is presented on the basis of the weight function and properties of stationary random function in wide sense. The application of the results for practice gives the transition lengths of straight and curved railway, which it is necessary to throw away in measurement of initial horizontal displacement of railway in its stability estimation under action of longitudinal compression load.

Fonctions Certaines Admettant des Répartitions Asymptotiques et Fonctions Aléatoires Stationnaires

In the article below, we consider sets of non-random functions of time t admitting certain asymptotic distributions. Purely temporal and deterministic considerations lead us to associate to a set , say, of functions H(t) of this type, a space Ω of samples ω.To each function H(t) ⊂ , there corresponds a random variable h (ω). To the set of translated functions H(t + λ) of a function H(t) ⊂ , there corresponds a stationary random function of the translation parameter λ, say, h(λ, ω). We study the transposition to the set of non-random functions H(t) of such properties as moments, gaussian character, independence, harmonic analysis, and others, of the random variables h (ω) and of the random functions h (λ, ω).Some remarks are made concerning the links between ergodicity and the above problems.