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Dynamic response of structures with statistical uncertainties in their stiffnesses

A considerable amount of research has been done recently on the effect of uncertainties in the mathematical model of a structure on its response. These uncertainties may be due either to imperfections in the physical structure unknown to the analyst, or to his lack of ability to correctly model certain structural elements such as joints, for example. The bulk of this research has focused on developing the sensitivity of the model natural frequencies to random perturbation introduced into the structural elements. The perturbations are chosen to represent the uncertainty in that part of the structure. In the present paper, a technique is derived to compute the transient forced vibration response of an undamped N‐degree‐of‐freedom structure to arbitrary driving functions when statistical uncertainties are allowed in the stiffnesses. The uncertainties can be either correlated or uncorrelated. For the case of impulsive input, simple bounds are derived showing the growth of response uncertainty with time as a f...