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 beam's 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 beam's 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.