Variability analysis of frequency dependent visco-elastic three-layered beams

The modal stability procedure is combined with Monte-Carlo simulations to estimate the variability of natural frequencies and damping ratios of frequency dependent visco-elastic sandwich structures. In the pre-processing phase, the Diamant approach is used, at nominal, to compute complex eigenvalues and eigenmodes. Then, in the on-line phase i.e within the Monte-Carlo simulation loop, a non-linear equation is solved with Newton-Raphson algorithm to obtain perturbed complex eigenvalues. The low computational times of the method enable the use of large scale Monte-Carlo simulations yielding accurate estimates of means and coefficients of variation of frequencies and damping ratios. The method is illustrated on a three-layered sandwich rectangular beam with visco-elastic core. A frequency dependent visco-elastic material 3M ISD112 is used and two different set of boundary conditions are considered. The stochastic variables are the Young modulus of the elastic faces and the delayed elasticity shear modulus. In particular, it is shown that the mechanism of uncertainty propagation affects mostly damping ratios that experience higher coefficients of variation than natural frequencies.