Fast methods based on modal stability procedure to evaluate natural frequency variability for industrial shell-type structures

• Methods are proposed to take into account variability in dynamic finite element analysis.
• They are based on a mechanical assumption.
• They are fast and non-intrusive.
• They are relevant for a large number of degrees of freedom and a large number of random variables.

This paper proposes a set of parametric numerical methods to predict the effect of uncertainties in the input parameters on the natural frequencies of structures. The first method, called MCS–MSP, involves the Monte Carlo simulation (MCS) and the modal stability procedure (MSP). Here the weak sensitivity of the mode shape to variations in the input parameters of the model is exploited. A single finite element analysis is required for the MCS–MSP, leading to a fast Monte Carlo simulation. Next, two first order methods are presented that rely on the calculation of frequency sensitivity to random variables using either the finite element method (FOFE) or the MSP (FOMSP). These first order methods require only as many finite element or MSP analyses as the number of random variables. These fast and non-intrusive methods are intended to be used with industrial-size models with a large number of degrees of freedom and a large number of random variables. Finally, two applications are presented: a spot welded plate assembly and a car body in white. The stochastic results obtained (mean value, standard deviation, coefficient of variation, statistical distribution) with the three presented methods are compared to those obtained using the direct MCS as a reference. For both examples, the quality of the results obtained with these fast methods is satisfactory. Moreover, the gains are very valuable: the computation time involved in the proposed approaches based on MSP assumption is lower than the computation time needed for six deterministic finite element analyses.