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In this paper, a new approach is presented to prove the efficiency of the direct Monte Carlo method combined with the Elementary Effect method to quantify structural data uncertainty under uncertain input parameters of a beam structure. Normally, the application of the direct Monte Carlo method requires high computational cost when all input parameters are taken into account. It is proposed to use a combination of the direct Monte Carlo method and the Elementary Effect method for the variance-based sensitivity analysis, named the combined Monte Carlo method. By the application of the Elementary Effect method as a screening method, the truely influential input parameters are identified. Then, the parametric uncertainty is analyzed only under these influential input parameters’ uncertainty by the use of the Monte Carlo method. Through a combination of these two methods, the number of simulations can be significantly reduced due to the reduction of the number of analyzed input parameters.

The novelty of this paper is to investigate the accuracy and the efficiency of this combined approach by the use of a beam structure with piezo-elastic supports for buckling and vibration control as a reference structure. The uncertain structural input parameters are the geometric, material, and stiffness parameters of the piezo-elastic supports. The output variable is the first lateral resonance frequency of the beam structure. Its uncertainty will be analyzed by the application of the combined Monte Carlo method applied for only a few but influential input parameters and will also be analyzed by the application of the direct Monte Carlo method for all input parameters. The results by the two methods will be compared based on the analysis accuracy to estimate the sensitivity of the input parameters on the first lateral resonance frequency and the minimal required number of the simulations.