National Repository of Grey Literature 125 records found  previous11 - 20nextend  jump to record: Search took 0.01 seconds. 
Numerical solution of a stochastic model of a ball-type vibration absorber
Fischer, Cyril ; Náprstek, Jiří
The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplifcation, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can negatively influence efficiency of the absorber.
Stability of a bar influenced by small and large imperfections
Náprstek, Jiří ; Fischer, Cyril
The geometrical and physical imperfections of systems can drastically reduce their critical loading. These imperfections are usually of stochastic character and, therefore, they act as random parametric perturbations of coefficients of corresponding differential equations. In this paper, the imperfections are introduced as multidimensional statistics on the set of a large number of realizations of the same system. As far as the amount of information is small or the imperfections themselves cannot be considered small, the convex analysis is preferable. The paper compares results obtained by both stochastic and convex analyses for hyperprism and demonstrates when each of them is more convenient to be used. Besides of the hyper-prism, the possibilities and properties of other modifications of convex method are considered, especially those based on the definition of imperfection zone marked as a centric hyper-ellipsoid or as an eccentric hyper-ellipsoid. The analytical background was brought up to the level when only a few configurations of imperfections are sufficient to be evaluated numerically. These configurations are obtained by means of the convex analysis as points of extreme critical loading using the Lagrange method of constrained extremes.
Multifold stationary solutions of an auto-parametric non-linear 2DOF system
Fischer, Cyril ; Náprstek, Jiří
A non-linear 2DOF model of a bridge girder with a bluff cross-section under wind loading is used to describe the heave and pitch self-excited motion. Existence conditions of stationary auto-parametric response for both the self-excited case and an assumption of a harmonic load form a non-linear algebraic system of equations. Number of distinct solutions to this algebraic system depends on the frequencies of two principal aero-elastic modes and other system parameters. Thus, the system may possess none, one, or several stationary solutions, whose stability has to be checked using the Routh-Hurwitz conditions. If all quantities entering the system are continuous functions, individual solutions may exhibit (piecewise) continuous dependence on selected system parameters. Thus, multiple identified solutions to the system for a given set of parameters may actually belong to a single solution branch and their values can be determined from the knowledge of the solution branch. Such a situation may significantly simplify assessment of stability of the particular solutions and/or provides an applicable overall description of the system response.
Random response of a dynamic system under polynomial of a white noise
Náprstek, Jiří ; Fischer, Cyril
Many types of external additive random excitation of dynamic systems admit to be modelled as a combination of powers of a Gaussian noise. Such a type of excitation produces a non-Gaussian response even if the dynamic system is linear and the excitation is additive only. Although the excitation as a whole is non-Gaussian, the problem can be transformed into the form of a linear system with an additive and multiplicative white noise excitation which _nally produces a non-Gaussian response. The general method of transformation, the respective FPK equation, basic stochastic moments of the response, and a demonstrative example are discussed.
System response with random imperfections in coefficients on the space of realizations
Náprstek, Jiří ; Fischer, Cyril
The contribution is concerned with the analysis of the simultaneous effect of a random perturbation and a white noise in the coefficient of the system. The excitation of the system of the 1-st order is described by the sum of a deterministic signal and an additive white noise which is partly correlated with the parametric noise. The random perturbation in the parameter is considered as a statistics in a set of realizations. It reveals that the density of probability of perturbations must be limited in the phase space, otherwise the system would lose the stochastic stability in probability. The width of the permissible zone depends heavily on the intensity of the parametric noise, the extent of correlation with the additive excitation noise and the type of probability density. The general explanation is demonstrated on cases of normal, uniform and truncated normal densities of probability.
Sensitivity of the generalized van der Pol equation to sub- or super-harmonic resonance
Fischer, Cyril ; Náprstek, Jiří
Vortex induced vibrations in aeroelasticity of slender structures are often described using the generalized van der Pol equation. This equation provides a good analytical model which is able to reproduce the complex non-stationary behaviour of the structure. Due to the non-linear character of the underlying physical system, the effect of sub- or super-harmonic synchronization can be encountered. The contribution presents results of a numerical study aimed at detailed identification of sub- or super-harmonic resonance effects in the model. This way it supplements the previous works by the authors.
Local stabilization of the quasiperiodic response of the generalized van der Pol oscillator
Fischer, Cyril ; Náprstek, Jiří
The generalized van der Pol equation is often used for description of various effects originating in the aero-elasticity of large slender engineering structures. This applies mainly to the quasiperiodic beatings that can be encountered especially in lock-in regimes when the vortex frequency becomes close to the structure eigenfrequency with a small detuning. The current paper presents numerical analysis of influence of the subor superharmonic excitation on the character of the response of a generalized van der Pol oscillator. This way it complements two previous papers of the authors dealing with stability analysis of certain types of the stationary periodic or quasiperiodic response of the system under study.
Stochastic resonance in dynamics and related disciplines
Náprstek, Jiří ; Fischer, Cyril
Stochastic resonance (SR) is a phenomenon which can be observed in some nonlinear dynamic systems under combined excitation including deterministic harmonic force and random noise. This phenomenon was observed the first in the early 1940s when investigating the Brownian motion. Later several disciplines in optics, plasma physics, biomedicine and social sciences encountered effects of this type. However, the actual discovery and start of intensive period of investigation is dated in early 1980s when the idea of SR initiated remarkable inter disciplinary interest including most areas of physics, chemistry and neuro-physiology with a significant overlap to engineering and industrial area. Promising opportunities to employ SR in mechanics emerged only recently to model certain post-critical effects in non-linear dynamics and simultaneously to develop new vibration damping devices, energy harvesting facilities, sophisticated measuring technics and others. The aim of the paper is to present information about a new challenging discipline offering a large field of basic research and possibilities for practical applications.
Strategies for computation of Lyapunov exponents estimates from discrete data
Fischer, Cyril ; Náprstek, Jiří
The Lyapunov exponents (LE) provide a simple numerical measure of the sensitive dependence of the dynamical system on initial conditions. The positive LE in dissipative systems is often regarded as an indicator of the occurrence of deterministic chaos. However, the values of LE can also help to assess stability of particular solution branches of dynamical systems. The contribution brings a short review of two methods for estimation of the largest LE from discrete data series. Two methods are analysed and their freely available Matlab implementations are tested using two sets of discrete data: the sampled series of the Lorenz system and the experimental record of the movement of a heavy ball in a spherical cavity. It appears that the most important factor in LE estimation from discrete data series is quality of the available record.
Probability density determination by means of Gibbs entropy probability density
Náprstek, Jiří ; Fischer, Cyril
A method of random response investigation of a nonlinear dynam-ical system is discussed. In particular, the solution of the probability density of a single/multi-degree of freedom (SDOF/MDOF) system response is investigated. Multiple stable equilibrium states with possible jumps of the snap-through type among them are considered. The system is Hamiltonian with weak damping excited by a set of non-stationary Gaussian white noises. The solution, which is based on the Gibbs principle of the maximum entropy of probability, can be employed in various branches of engineering. The search for the extreme of the Gibbs entropy functional is formulated as a constrained optimization problem. The secondary constraints follow from the Fokker-Planck equation (FPE) for the system considered or from the system of ordinary di_erential equations for the stochastic moments of the response derived from the relevant FPE

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