Structural Harmonic analysis with random modal damping parameters

Assigning deterministic values to damping parameters in many numerical simulations of structural dynamics is a very difficult task owing to the fact that such parameters possess significant uncertainty. In this paper, the modal damping parameters are considered as random variables. The generalized polynomial chaos (gPC) expansion is employed to capture the uncertainty in the parameters and frequency responses. The response functions are considered as random process having unknown deterministic frequency-dependent coefficients. Finite element model of damped vibration analysis of fiber-reinforced composite plates is served as deterministic black-box solver to realize frequency responses. The range of uncertainties and the probability distributions of the parameters are identified from experimental modal tests. A set of random collocation points are generated for which the constructed gPC expansions are used to generate samples of damping parameters as deterministic inputs to the FEM model. This yields realizations of the frequency responses which are then employed to estimate the unknown coefficients. The results show while the responses are influenced from the damping uncertainties at the mid and high frequency ranges, the uncertainty impact at lower modes can be safely ignored. Furthermore, the method indicates also a very good agreement compared to the sampling-based Monte Carlo FEM simulations with large number of realizations. This leads to a very efficient simulations in term of computational times.