The spectral elements of the Lobatto family provide desirable characteristics of convergence and accuracy using a diagonal mass matrix in dynamic analysis. These characteristics might be expected to render the spectral element method with the use of an explicit time integration scheme effective for the transient analysis of wave propagations. In this paper we study the use of the central difference method and the recently proposed Noh-Bathe method for explicit time integration in the use of the spectral finite element method. The Noh-Bathe scheme is a second-order accurate procedure with small solution errors in the required frequency range while suppressing spurious high frequencies. We calculate appropriate CFL numbers for the time integrations and give an analysis of the dispersion errors for different orders of spectral elements. Finally, we demonstrate the capabilities of the Noh-Bathe scheme compared to the central difference method through the solution of several numerical examples of wave propagations.

Lobatto 系列的光谱元素在动态分析中使用对角质量矩阵提供所需的收敛性和准确性特征。预计这些特性将使光谱元素方法使用显式时间积分方案有效地进行波传播的瞬态分析。在本文中，我们研究了使用中心差分法和最近提出的 Noh-Bathe 方法在使用谱有限元方法进行显式时间积分的情况。Noh-Bathe 方案是一种二阶精确程序，在所需的频率范围内具有较小的解算误差，同时抑制寄生高频。我们为时间积分计算了适当的 CFL 数，并分析了不同阶光谱元素的色散误差。最后，