Institute of Fundamental Technological Research

In the paper we show how some basic informational quality measures (e.g. the Shannon entropy and the relative entropy/Kullback-Leibler divergence) defined for stochastic dynamical systems change in time and how they depend on the system properties and intensity of random disturbances. First, the Liouvillian systems (when randomness is present in the initial states only) are discussed and then various (linear and nonlinear) systems with random external excitations are treated in detail. Both, general and specific systems are considered, including numerical and graphical illustrations.

stochastic dynamics, information, entropy, relative entropy, information gain, non-Gaussian prediction, maximum entropy approximation

In this paper, the basic methodology for the fatigue reliability assessment of randomly vibrating multidegree-of-freedom systems is presented within the coupled response-degradation model. The fatigue process in the system components is quantified by the fatigue crack growth equations which—via the stress range—are coupled with the system response. Simultaneously, the system dynamics is affected by fatigue process via its stiffness degradation so that it provides the actual stress values to the fatigue growth equation. In addition to the general coupled response-degradation analysis, its special case of noncoupled fatigue crack growth is treated as well for the wide-band stationary applied stress by the use of its first four spectral moments and the approximate, empirically motivated, Dirlik’s probability distribution for the stress range. Both, the general analysis and the illustrating exemplary problems elaborated in the paper provide the route to the fatigue reliability estimation in complex–hierarchical vibratory systems under random loading.

Fatigue, Crack growth, Random vibration, System reliability, Stiffness degradation

In this paper, the analytical approach to quantitative characterization of random microstructural residual stress field in brittle elastic materials is presented. The analysis consists of two parts. First, we expound the basic features of random microstructural stresses and show how the eigenstrain approach (of “classical” micromechanics) can be extended to the situations where randomness of the initial eigenstrains has to be taken into account. The second part of the paper deals with the effects of random microstresses on crack growth phenomena. The stress intensity induced by random dilatant transformation eigenstrains and by thermally-induced random microstresses are treated in detail, including numerical and graphical illustrations of specific crack problems

Random residual microstresses, Random eigenstrain model, Stress intensity factor, Toughening effect, Thermal microstresses

The paper presents a method for quantitative characterization of random hydrogen-induced stresses. The method is based on randomized diffusion-elasticity equations. Also a stochastic parametric model, suitable for representing relevant empirical data, is outlined. The general considerations are illustrated by two particular examples. The first one concerns the effect of random hydrogen concentration on material failure time in a half-space, whereas the second one shows its effect on the Mode-I stress intensity factor for a crack in a circular cylinder.

In the paper a coupled response–degradation problem for a nonlinear vibrating system is analyzed. The analysis allows to account for the effect of stiffness degradation (during the vibration process) on the response and, in the same time, gives the actual stress values for estimation of damage accumulating in the system. The paper constitutes an extension of the approach (a sequential characterization of the degradation random process) presented in [4] to vibrating systems with nonlinear restoring term.

In this paper the basic methodology of the coupled response-degradation modelling of stochastic dynamical systems is presented along with the effective analysis of selected problems. First, the general formulation of the problems of stochastic dynamics coupled with the evolution of deterioration process is given. Then some specific degrading oscillatory systems under random excitation are analyzed with a special attention on the systems with fatigue-induced stiffness degradation. Both, the general discussion and the analysis of selected exemplary problems indicate how the reliability of deteriorating stochastic dynamical systems can be assessed

stochastic dynamics, fatigue induced stiffness degradation, hysteretic systems, systems with varying/random structure

This paper provides a methodology for optimal prediction of the response of randomly vibrating structures using information from a limited number of measurements. The objective is to optimize the locations of sensors for the purpose of making the most accurate predictions of the response at unmeasured locations in structural systems. The kriging method is used to find the response predictions and the corresponding mean-square errors at unmeasured locations. The mean-square errors in the predictions depend on the locations of sensors and the correlation characteristics of the response evaluated from the model of dynamics and the characteristics of the excitation. The response predictions depend also on the information contained in measurements. The optimal sensor locations are selected to minimize the total mean-square error of the response predictions at unmeasured points. This leads to a complicated non-convex optimization problem in which multiple local and global optima may exist. A hybrid optimization method based on evolution strategies is used to determine a global minimum. The optimal experimental design method presented in the paper is illustrated by designing the optimal sensor locations for an elastic beam and a plate subjected to a class of random stationary loads.

Structures, Random vibrations, Sensor locations, Kriging, Evolution strategies

Opracowanie pt. „Strategia nauk technicznych do roku 2020” powstało z inicjatywy przewodniczącego Wydziału Nauk Technicznych PAN, który powołał zespół (zaakceptowany następnie przez zgromadzenie członków Wydziału w dniu 25 marca 2004 r.) złożony z członków PAN z IV Wydziału. Zadaniem zespołu było przygotowanie najpierw wstępnych założeń, a następnie pełnego opracowania dotyczącego najważniejszych – w opinii zespołu – problemów badawczych z zakresu nauk technicznych na najbliższą przyszłość (w przybliżeniu do roku 2020), które powinny być przedmiotem szczególnej troski państwa podczas ich finansowania z budżetu. Nie oznacza to, iż mają to być jedyne obszary badawcze, na których ma się koncentrować wysiłek uczonych.

Zespół przyjął również założenia, że badania prowadzone zgodnie z priorytetami problemowymi w dużych zespołach badawczych będą przyczyniać się do integracji w tych zespołach, ale również winny przyczyniać się do podejmowania prac indywidualnych, a nawet powinny stanowić źródła inspiracji dla uzdolnionych badaczy do podejmowania takich badań dzięki przyznawaniu grantów i zatwierdzaniu zamawianiu projektów badawczych. (...)

The problem of propagation of plane harmonic waves in an infinite elastic solid containing a random configuration ofN identical scatterers of finite size is considered. The paper presents the general formalism of the analysis of mean (or coherent) elastic waves for an arbitrary shape of the scatterers and the solutions of some specific problems in the case of spherical scatterers. The equations expressing the average total field in terms of the probability density function and scattering properties of individual scatterers are presented. These equations concern an arbitrary shape of the scatterers and include the effects of single and multiple scattering. In the case of dilute and uniform distribution of spherical scatterers the more detailed analysis of average total field leads to the determination of the equivalent homogeneous medium in which the mean wave propagates. For the limit of the low frequences the effective parameters of the medium are given and they turn out to be the same as those obtained within effective modulus theory in static case.

The free transverse vibrations of elastic rectangular plates with random material properties are considered. On the assumption that the fluctuations of random bending rigidity are sufficiently small, the perturbation technique is applied and statistical characteristics of the random eigenvalues are determined. For illustration, the exponential form of correlation function of the random inhomogeneities is assumed and variance of the first eigenvalue is estimated; the result is that this variance is very sensitive to the degree of statistical dependence of the values of random rigidity at two points of the plate and it decreases exponentially when the correlation length increases.