Numerical Investigation of Modal Parameter Statistics of Random Rods

In this article, the ensemble statistics of the modal parameters of longitudinal rods with non-deterministic parameters were investigated through the statistical results of metric functions of the Random Matrix Theory (RMT). The levels of agreement with the Poisson and Gaussian Orthogonal Ensemble (GOE) models were evaluated for natural frequencies and corresponding mode shapes. The mean and relative variance values of kinetic energy density responses were calculated and compared to analytical predictions based on the Poisson and GOE models. The main effects on the energy response statistics due to incomplete establishment of GOE (or Poisson) statistics were systematically assessed for each modal parameter considering the single point-loading and spatially-averaged excitation. The numerical results also allowed the identification of the possible impact on the performance of analytical predictions of the relative variance when the modal parameter statistics do not conform completely to the GOE (or Poisson) model. An improved understanding was obtained regarding the relationship between the modal parameter statistics expected for one-dimensional engineering systems and those described by the GOE and Poisson models.