Analysis of randomly vibrating structures under hybrid uncertainty

In the analysis of several structural systems some parameters always suffer from a level of scattering and others have an intrinsic unpredictable nature. In these circumstances, conventional deterministic-based approaches can lead to excessive approximations and the final results may be very far from the real ones. In this paper, a hybrid approach for the analysis of randomly vibrating structures is presented, to take into account both stochastic processes and epistemic variables. In detail, the dynamic loading has been modelled as a random process whereas the parameters for describing the input process as well as the structural systems are treated as fuzzy variables. This hypothesis has been performed to describe the random meanings and behaviours of some dynamic loads (i.e. earthquake, wind or sea waves) but also to incorporate “non-conventional” sources of uncertainties in the adopted mathematical models. Some numerical examples are presented at the end of the paper in order to illustrate the consequences of the developed methodology. First, the problem regarding a linear tuned mass damper under non-stationary excitation is presented and a sensitivity analysis is conducted for the structural response by considering different values of the input parameters. The second example deals with the dynamic analysis of a broadcasting antenna subject to double filtered stationary base motion. Numerical results demonstrate that the proposed methodology provides an efficient support for assessing the dynamic response under hybrid uncertainty.