Variations in steepness of the probability density function of beam random vibration

Dynamic behaviour of a beam, subjected to stationary random excitation, has been investigated for the situation in which the response is different from the model of a Gaussian random process. The study was restricted to the case of symmetric non-Gaussian probability density functions of beam vibrations. There are two possible causes of deviations of the system response from the Gaussian model: the first, nonlinear behaviour, concerns the system itself and the second is external when the excitation is not Gaussian. Both cases have been considered in the paper. To clarity the conclusions for each case and to avoid interference of these different types of system behaviour, 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 integration of the generalised coordinate equations. Probability density functions of the beam response were analysed and approximated making use of different 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 Fourier expansion and fed to a shaker input. To generate a non-Gaussian excitation a special procedure of harmonic phase adjustment was implemented instead of the random choice. In so doing, the non-Gaussian kurtosis parameter of the beam response was controlled.