In this work, a time domain spectral element-based wave finite element method is proposed to analyze periodic structures. Time domain spectral element-based formulation reduces the total degrees of freedom and also renders a diagonal mass matrix resulting in substantial reduction in computation time for the wave finite element method. The formulation is then considered to obtain the stop band characteristics for a periodic bar and a Timoshenko beam considering geometric as well as material periodicity. The impact of geometric parameters on the stop bands of 1-D structures is then investigated in detail. It is shown that the stop bands can be obtained in the frequency range of interest, and its width can be varied by tuning those geometric parameters. Also, the effect of material uncertainty is studied in detail on the stop band characteristics of periodic 1-D structures, and the same formulation is utilized for Monte Carlo simulations. Results show that randomness in density influences more the bandwidth of the stop bands than that of elastic parameters.

在这项工作中，提出了一种基于时域频谱元素的波有限元方法来分析周期结构。基于时域频谱元素的公式化减少了总的自由度，并且还绘制了对角质量矩阵，从而大大减少了波有限元方法的计算时间。然后考虑到几何以及材料的周期性，考虑该公式以获得周期棒和Timoshenko光束的阻带特性。然后详细研究几何参数对一维结构阻带的影响。结果表明，可以在感兴趣的频率范围内获得阻带，并且可以通过调整那些几何参数来改变其宽度。还，详细研究了材料不确定性对周期性一维结构的阻带特性的影响，并且对蒙特卡洛模拟采用了相同的公式。结果表明，密度的随机性比弹性参数对阻带带宽的影响更大。