Spectral element-based method for a one-dimensional damaged structure with distributed random properties

Stochastic methods have received considerable attention because they address the randomness present in structural numerical models. Uncertainties represent important events in dynamic systems regarding vibration response prediction, especially in the mid- and high-frequency ranges, when responses have higher dispersions. The spectral element method (SEM) is suitable for analysing wave propagation problems based on large frequency ranges. It is a powerful tool for structural health monitoring. This paper unifies these two techniques to use the SEM with distributed randomness in the system parameters to model structural damage. Parameters are assumed to be distributed along the structure and expressed as a random field, which are expanded in the Karhunen-LoSve spectral decomposition and memoryless transformation. A frequency-dependent stochastic stiffness and mass element matrices are formulated for bending vibration. Closed-form expressions are derived by the Karhunen-LoSve expansion. Numerical examples are used to address the proposed methodology.