Uncertainty propagation analysis of multilayer plates with frequency-dependent viscoelastic damping layers

Viscoelastic multilayer structures exhibit notable variability in geometric and material parameters due to inevitable randomness in the processes of producing, manufacturing and assembling. The present study investigates the influence of inputs uncertainties on the modal parameters of the viscoelastic sandwich structure. The layer-wise theory is employed to model the multilayer structure and the nonlinear eigenvalue problem caused by frequency-dependent property of viscoelastic damping material is solved by the Implicitly Restarted Arnoldi Method. In the framework of uncertainty propagation, the formulated layer-wise finite element is combined with Direct Monte Carlo Simulation to evaluate the variability of modal frequency and damping ratio. The reason for selecting this method relies on the consideration about the compromise between computational efficiency and robustness and the simplicity of its implementation. A numerical example of the viscoelastic laminated sandwich structure is performed under uncertainty in material property, geometry size and the fiber orientation angle. Among the results, it is shown that the mean value of modal parameters keep equal to the deterministic result and the two critical input parameters for modal frequency and the damping ratio are material property and thickness.