Application of sensitivity analysis and uncertainty quantification methods on the dynamic response of general nonlocal beams

Abstract

There is a gap to be filled in the literature regarding uncertainties that may exist in nanobeams’ material and geometric properties, such as the nonlocal parameters, Young's modulus, Poisson ratio, density, and beam's length, width, and height. Considering the fact there are so many input parameters that can affect the response of the system, parametric studies that only focus on single parameters may limit the usefulness of the obtained output. Thus, in this effort, local and global sensitivity analysis and uncertainty quantification techniques are applied to determine the most influential parameters on the acoustic dispersion curves and the linear response of nanobeams which are modeled utilizing Euler–Bernoulli beam theory and the general nonlocal theory. The sensitivity analysis and uncertainty quantification methods include expanded parametric studies around an ideal or baseline system configuration, the Morris method elementary effects, Sobol’ sensitivity indices, Pearson correlation coefficients, and output distribution curves. Various input probability distributions are used for the input parameters uncertainties and the effects of all parameters on the ideal configurations are investigated for both acoustic dispersions and first natural frequency. For this study, there is great agreement in input parameter ranking between the methods. The introduced methodologies can be used for many other complex dynamical systems to show the limits of applicability of each method and determine the most influential input parameters and dominant output configurations.