Uncertainties play an important role in dynamic systems regarding their vibration and wave propagation behaviour. Stochastic methods have been used to address the randomness incorporated in numerical models. The spectral element method (SEM) is suitable to perform vibration and wave propagation analysis based on large frequency ranges with accuracy and low computational cost. This paper explores the longitudinal wave propagation considering uncertainties in the media aside from demonstrating and quantifying the effect of randomness inherent in the material. The stochastic Love rod spectral elements are proposed, and the parameters were assumed to be spatially distributed alongside the structure expressed as a random field. It is expanded using the Karhunen-Loeve spectral decomposition and memoryless transformation. The Wentzel-Kramers-Brillouin (WKB) approximation is a powerful tool to evaluate local impedance changes slowly. It is used to indicate and quantify a changing rate related to material properties varying along the rod. Numerical examples analyse wave propagation in a longitudinal waveguide with distributed parameters.
