Numerical methods for analyzing the effects of uncertainties on the dynamics of periodic structures

Various approaches are proposed and compared for analysing the e¤ects of structural irregularities and parameter uncertainties on the dynamics of Þnitely long, one-dimensional, mono-coupled, nearly periodic assemblies with and without structural damping. Computational concerns are raised in regard to the classical method of modal analysis, and alternative methods are formulated which allow for the numerically e¦cient determination of the exponential decay constant. While modal analysis and CramerÕs rule require the solution of an eigenvalue problem, the matrix inversion and matrix partitioning approaches avoid costly eigenvalue computations and require only cost-e¤ective algebraic manipulations. Therefore, implementation of either the direct inversion technique or matrix partitioning both simpliÞes the analysis and cuts computational costs substantially.