P. Śniady

Vibration of a beam due to a random stream of moving forces with random velocity

Abstract The problem of dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes and velocities is considered. Force arrivals at the beam are assumed to constitute the point stochastic process of events. Thus, the excitation process is an idealization of vehicular traffic loads on a bridge. An analytical technique is developed to determine the response of the beam. Explicit expressions for the expected value and the 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.

LIFE EXPECTANCY OF HIGHWAY BRIDGES DUE TO TRAFFIC LOAD

Abstract In this paper the life expectancy of highway bridges to traffic flow is studied. It is assumed that the traffic is a composition of different types of vehicle models. Each type of vehicle is modeled by one or more concentrated random forces. In this idealization the vehicles are regarded as being of random weight and traveling with the same constant speed. The interarrival times of the vehicles are regarded as random variables. For estimation of the life expectancy of the structure one needs to find the joint probability density function of the displacement, velocity and acceleration of the vibrating beam. In the paper the damage process of the bridge is determined by the Palmgren-Miner rule. As an example, the covariance function, the spectral density function and the life expectancy of a bridge modeled as a simply supported beam are determined.

Dynamic response of linear structures to a random stream of pulses

Abstract The vibration of a linear structure caused by a random series of pulses is considered. Some different aspects of a point stochastic process characterizing a stream of pulses are taken into account. It is assumed that the occurrence process may be a general point stochastic process, a Poisson process, a renewal process, or a double point stochastic process. The case of loading of the structure by two streams of pulses is also considered. An analytical technique is developed to determine the probabilistic characteristics: i.e., the response of the structure as the expected value, the covariance, the cumulants, the characteristic function and the probability density function of the response. One general conclusion follows from these results: the variance of the response is smaller in the case of a general point stochastic process and a renewal process than for a Poisson process.

Random vibration of a suspension bridge due to highway traffic

The problem of dynamic non-linear response of a suspension bridge to the passage of a train of concentrated forces with random weight is considered. Force arrivals at the bridge are assumed to constitute a Poisson process of events. Thus, the excitation process idealizes vehicular traffic loads on a bridge. By use of both iterative and linearization methods the solution for the expected value and variance of the bridges deflections is determined. As an example, the response of a bridge to a stationary stream of forces is obtained. A numerical technique is developed to compute the solution for a particular bridge and some practical cases of the loading.

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.

Dynamics of machine foundations with random parameters

Solution of the problem of free and forced vibration of a discrete system with random parameters, as a model of a machine foundation, is considered. Expressions for the expected values and correlation functions of the solution are formulated, in terms of the probabilistic characteristics of the structure, initial conditions and excitation, which are assumed to be known. The stochastic linearization method is used. The solution is illustrated by an example of a block foundation with random parameters.

Spectral density of the bridge beam response with uncertain parameters under a random train of moving forces

The paper presents the spectral analysis of the beams vibration with uncertain parameters under a random train of moving forces which forms a filtered Poisson process. It is assumed that natural frequencies of the bridge beam are uncertain and are modelled by fuzzy numbers, random variables or fuzzy random variables. In order to obtain general solutions for the spectral density function of the beams response the normal mode dynamic influence function has been introduced. As an example the spectral density functions of a bridge modelled as a simple supported beam are determined.

Stochastic vibration of linear structures due to sample discontinuous load

Abstract Random vibrations of linear structures subject to real loads with possible nearly discontinuous amplitude changes, lasting for various time intervals, are described. It has been assumed that these changes occur at random moments and they have been described as birth processes. Analysis of the structural vibrations has been carried out by using correlation theory. Several selected particular cases have been studied and the solutions obtained have been evaluated by numerical computation. The solutions presented here may be applied in the dynamics of structures loaded by a group of machines working in a discontinuous way.

Dynamic response of linear structures to random streams of arbitrary impulses in time and space

The dynamic response of continuous structures to a stream of arbitrary impulses is considered. The impulses commence at random times and are located at random points on the surface of the structure. The shapes of the impulses can be arbitrary and can have a deterministic or stochastic nature, both in time and in space. The respective time durations and amplitudes of the impulses are also random. An analytical technique is developed to determine the response of the structure, and explicit expressions are provided for the expected value and covariance of the structure deflection. The results presented in the work can be used, for example, in estimating the reliability of bridge loading by traffic flow.

Dynamic response of linear structures to a stream of random impulses in a “space-time” system

Abstract The dynamic response of continuous structures subjected to a stream of random impulses in a “space-time” system is considered. The impulses reach the structure at random points on the surface and at random time intervals. It is assumed that the stream can be correlated in respect to space and time. Explicit expressions are provided for the expected value and covariance of the structure deflection.