Evaluation of the transition frequency characterizing the deterministic and statistical behaviour of structures

It is becoming a general feeling that the model of a particular member of a population is not always appropriate to describe the vibrational behaviour of the whole set of similar structures. In fact, uncertainties on the boundary conditions, joints' and physical parameters affect the response of each member of the population, leading to different dynamic behaviours, that sometimes become quite dramatic. This observation implies that the use of a dterministic model to describe the whole polulation is not correct, and rather a statistical description would be required, depending on the role of the parameters' uncertainties and the frequency range of interest. A simple n degrees of freedom mass-spring system is here proposed to show how each of the system's parameters affect the system response in any of the frequency ranges, focusing when a deterministic or statistical model would be necessary. On the base of these results, a simple criterion is proposed indicating the need of a statistical approach.