Stanisław Żukowski

Vibrations of the beam due to a load moving with stochastic velocity

The aim of this work is to give an approach for obtaining the probabilistic characteristics of the beam response due to a load moving with stochastic velocity. It is assumed that the load is modelled by a set of point forces of random amplitudes, the inter-arrival times are random variables that constitute the Poisson stochastic process and the forces are moving along the beam with velocities that are also stochastic. The effective solution in such a case can be obtained by applying the Ito integral and the Ito differentiation rule. In this paper, the theoretical basis for such an approach is given. Analytical expressions for calculating the probabilistic characteristics of the beam response and numerical results are shown.

Optimization of absorbers in the highway bridges due to traffic flow

The problem of reducing the level of vibrations in various constructions is considered for many years and numerous ways and means of preventing unacceptable vibrations are known [1]. One of this ways are various vibration absorbers. Their application play a special role because they can be used during the construction design and also when unsatisfactory dynamic properties appear in a construction during operation. Absorbers are applied in various engineering structures such as shipbuildings, steel chimneys, TV towers, bridges [2, 3], etc. Vibrations of some of this structures are excited by load of random nature. In this cases damped vibration absorbers (DVA) are used to mitigate the random excitation [3] and their parametres are optimized on the condition of the main mass’s. The minimum variance of the displacement corresponds to the maximum reliability of the system. The traffic flow is such type of load which causes complicated stress and displacement states in bridges and also causes the material fatigue that ultimately can damage the structure. The application of absorbers can greatly extend its lifetime.

Design Sensitivity Random Eigenvalue Problem in Dynamics and Buckling of Structures

In the paper, the problem of the sensitivity of the probabilistic characteristics of the eigenvalue problem and buckling is considered. Using the linearization method, relationships defining the sensitivity of the expected values of eigenvalues and eigenvectors and of the covariance and the standard deviation of eigenvalues to changes in structural parameters and in the probabilistic characteristic of these parameters are derived.