Response probability density function for multi-cracked beams with uncertain amplitude and position of cracks

Abstract

This paper addresses the determination of the response of beams under static loads, in presence of multiple cracks. The crack is modeled as a rotational internal spring. Both the amplitude and position of the spring are taken as uncertain variables. In particular, its random position characteristic has been modeled as Poisson law distribution along the axial coordinate. By using the theory of generalized functions, the probability transformation method (PTM) has been easily applied to the beam equilibrium equations. The PTM, employing the space transformation laws of random vectors, allows determining the probability density function (PDF) of the system response directly and easily. The results of some numerical applications have confirmed the goodness of the proposed stochastic procedure.