The Use of Generalized Probability Density Functions in Random Vibration Theory 640340
Structural damage, fatigue, and many other dynamical theories utilize statistical approaches based upon classical probability density functions. It is the purpose of this paper to describe or fit mathematically the resulting nonclassical probabilistic functions arising in random vibration propositions. Pearson’s family, or as an alternative, Johnson’s transformation functions, meet all requirements of generality, relative simplicity, and contain members widely recognized and used in vibration theory. A new density function of wide generality and application is also investigated with favorable results. In addition to theoretical discussions, two example problems are given demonstrating the practical utility of these functions.