Abstract The wave finite element method has been developed for waveguides and periodic structures with advantages in the calculation time. However, this method cannot be applied easily if the structure is subjected to complex or density loads and this is the aim of this article. Based on the finite element method, the dynamic equation of one period of the structure is rewritten to obtain a relation between the responses (DOF and nodal loads) on the left and right boundaries. This relation presents an additive term which links to the loads applying on the period. Then, by using WFE technique, we can compute the wave modes of the period and the wave decomposition. Because of the periodicity, we can also obtain a relation between the response and the left and right ends of the structure. Afterwards, the responses of the structure are calculated by using the wave decomposition in the dynamic stiffness matrix (DSM) approach or the wave analysis (WA). For the DSM approach, this technique shows that the external loads have no contribution to the global matrix but they lead to an equivalent force in the dynamic equation. Meanwhile, the external loads create waves propagating to the left and right of the structure in the WA approach.

中文翻译：

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任意载荷作用下波导和周期结构的波浪有限元方法

摘要 波有限元方法已被开发用于波导和周期结构，在计算时间上具有优势。但是，如果结构承受复杂载荷或密度载荷，则无法轻松应用此方法，这是本文的目的。基于有限元方法，重写结构一个周期的动力方程，得到左右边界响应（自由度和节点载荷）之间的关系。这种关系提供了一个附加项，它与施加在该期间的载荷相关联。然后，通过使用 WFE 技术，我们可以计算周期的波浪模式和波浪分解。由于周期性，我们还可以得到响应与结构左右端之间的关系。然后，结构的响应是通过使用动态刚度矩阵 (DSM) 方法或波浪分析 (WA) 中的波浪分解来计算的。对于 DSM 方法，该技术表明外部载荷对全局矩阵没有贡献，但它们会导致动态方程中的等效力。同时，在 WA 方法中，外部载荷会产生向结构左侧和右侧传播的波浪。