Piezoelectric patches with adapted electrical circuits or viscoelastic dissipative materials are two solutions particularly adapted to reduce vibration of light structures. To accurately design these solutions, it is necessary to describe precisely the dynamical behaviour of the structure. It may quickly become computationally intensive to describe robustly this behaviour for a structure with nonlinear phenomena, such as contact or friction for bolted structures, and uncertain variations of its parameters. The aim of this work is to propose a non-intrusive reduced stochastic method to characterize robustly the vibrational response of a structure with random parameters. Our goal is to characterize the eigenspace of linear systems with dynamic properties considered as random variables. This method is based on a separation of random aspects from deterministic aspects and allows us to estimate the first central moments of each random eigenfrequency with a single deterministic finite elements computation. The method is applied to a frame with several Young’s moduli modeled as random variables. This example could be expanded to a bolted structure including piezoelectric devices. The method needs to be enhanced when random eigenvalues are closely spaced. An indicator with no additional computational cost is proposed to characterize the ”proximity” of two random eigenvalues.