Analytical and Experimental Studies of Random Vibration

Analytical and experimental investigations are made of the response of linear systems subject to magnitude-limited Gaussian broadband random excitation. A mathematical analysis for determining the statistical properties of this excitation is developed. Experimental studies on the probabilistic response of linear systems with magnitude-limited input are also presented. Secondly the peak characteristics of the response of linear systems subject to Gaussian broadband random excitation are investigated. It is shown that the number of peaks per unit time of the response of a single degree of freedom system increases as the frequency bandwidth of the excitation increases. Analytical and experimental techniques are developed to study the peak distribution characteristics of multi-degree of freedom systems and continuous systems. It is found that the normal mode random variables are statistically independent if the system damping is small, and the modal frequencies are sufficiently separated. Finally the method of Fokker-Planck is used to obtain the statistical properties of the response of a first order Coulomb damped system. The first order probability density function of displacement of this nonlinear system is determined. A simplified method for developing the autocorrelation function, and the power spectral density is discussed and applied to the above problem. The results are further substantiated by experiment. Experimental investigations are also carried out to determine the power spectral density of the response of a second order nonlinear system with Coulomb restoring force to white noise input. The results are compared with those given by Wolaver.