ON THE CUMULATIVE DISTRIBUTION FUNCTION OF OUTPUT RANDOM VARIABLES IN THE STUDY OF DYNAMIC SYSTEMS

The method presented in the article enables us to easily determine the cumulative distribution function of certain relevant quantities that depend on the solution of a dynamic process, which includes some random variables as input parameters. The article provides three examples. In the first two examples, the obtained solution is compared with the explicit one. The third example deals with a masonry tower that was subjected to an acceleration recorded during the 2013 Fivizzano earthquake. Assuming that Young’s modulus of the material and the PGA of the earthquake are random variables whose probability density function is known, the cumulative distribution functions of both the attained maximum tower top displacement and the maximum cracked volume are determined.