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-Loève 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.

不确定性在动态系统中的振动和波传播行为中起着重要作用。随机方法已被用于解决数值模型中包含的随机性问题。谱元法（SEM）适用于基于大频率范围的振动和波传播分析，精度高，计算成本低。除了演示和量化材料固有随机性的影响之外，本文还探讨了考虑介质中不确定性的纵波传播。提出了随机 Love 棒光谱元素，并且假设参数在空间上分布在表示为随机场的结构旁边。它使用 Karhunen-Loève 谱分解和无记忆变换进行扩展。Wentzel-Kramers-Brillouin (WKB) 近似是评估局部阻抗缓慢变化的强大工具。它用于指示和量化与沿杆变化的材料特性相关的变化率。数值例子分析了具有分布参数的纵向波导中的波传播。