Variations in steepness of the probability density function of beam randomvibration

Dynamic behaviour of a beam, subjected to stationary random excitation, has been investigated for the situation in which the response is different fro m the model of a Gaussian random process. The study was restricted to the c ase of symmetric non-Gaussian probability density functions of beam vibrati ons. There are two possible causes of deviations of the system response fro m the Gaussian model: me first, nonlinear behaviour, concerns the system it self and the second is external when the excitation is not Gaussian. Both c ases have been considered in the paper. To clarity the conclusions for each case and to avoid interference of these different types of system behaviou r, two beam structures, clamped-clamped and cantilevered, have been studied . A numerical procedure for prediction of the nonlinear random response of a clamped-clamped beam under the Gaussian excitations was based on a linear modal expansion. Monte Carlo simulation was undertaken using Runge-Kutta i ntegration of the generalised coordinate equations. Probability density fun ctions of the beam response were analysed and approximated making use of di fferent theoretical models. An experimental study has been carried out for a linear system of a cantilevered beam with a point mass at the free end. A pseudo-random driving signal was generated digitally in the form of a Four ier expansion and fed to a shaker input. To generate a non-Gaussian excitat ion a special procedure of harmonic phase adjustment was implemented instea d of the random choice. In so doing, the non-Gaussian kurtosis parameter of the beam response was controlled. (C) 2000 Editions scientifiques et medic ales Elsevier SAS.