Paweł Śniady

Vibration of a Beam under a Random Stream of Moving Forces

ABSTRACT The problem of dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes is considered. Force arrivals at the beam are assumed to constitute a Poisson process of events. Thus, the excitation process idealizes vehicular traffic loads on a bridge. An analytical technique is developed to determine the response of the beam. This technique is based on the introduction of two influence functions, one of which satisfies nonhomogeneous, the other homogeneous differential equations for beam response. Explicit expressions for expected value and variance of the beam deflection are provided. As an example, the response of a beam to a stationary stream of forces is determined for some practical situations and discussed. The extension of the approach presented to the case of two-axle vehicles is also outlined

A train of pulses in load modelling

Abstract In the paper two problems connected with stochastic load models are considered. The first one is modelling of the load process by the superposition of many overlapping pulses. For this case the probability density function, cumulative distribution function and the mean upcrossing rate for the load has been obtained. The second problem is modelling of the train of non-overlapping pulses by using birth process. The pulse may have rectangular or stochastic shape. For rectangular shape pulses the problem of the superposition of two loads is solved. The solutions can be used to describe the load in warehouses or storerooms, the dynamic response of the structure under random series of pulses or the response of the bridge under traffic flow. They may be used in the stochastic earthquake model as well. Numerical examples have been provided.

Fuzzy Stochastic Vibrations of Double-Beam Complex System as Model Sandwich Beam with Uncertain Parameters

The dynamic behavior of a double Euler-Bernoulli beam system with uncertain parameters (fuzzy random variables) under a fuzzy stochastic excitation and axial compression is being considered. The beams are identical and parallel, one is above the other, and they are continuously coupled by a linear two-parameter (Pasternak subsoil) elastic element. This double Euler-Bernoulli beam system can be also treated as a theoretical model of a sandwich beam. The load process is fuzzy random both in space and time. The top beam carries a fuzzy stochastic load. The solution of the problem was found thanks to the fuzzy random dynamic influence function. The aim of the paper is to find the solution for the membership function of the probabilistic characteristics of the response of the structure.

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.