A finite element procedure is proposed for wave propagation in elastic media. The method is based on an alternative formulation for the equations of motion that can systematically be constructed for linear evolutionary partial differential equations. A weak formulation—corresponding to convolutional variational principles—is then defined, which paves the way for introducing a particular type of time-wise shape functions. Next, some mathematical characteristics of the method are investigated, and upon those properties, a new solution procedure for elastodynamics problems is proposed. Subsequently, several numerical examples are considered, including a single degree of freedom mass-spring-damper system as the prototype of structural dynamics along with 1d and 2d elastodynamics problems for the case of the wave motion in elastic solids. The present method can be considered as an alternative approach for time integration and time-marching algorithms, e.g., Newmark’s algorithm, to solve time-domain problems in elastic media.

为弹性介质中的波传播提出了一种有限元程序。该方法基于运动方程的替代公式，可以系统地构造线性演化偏微分方程。然后定义了一个与卷积变分原理相对应的弱公式，这为引入特定类型的时间形状函数铺平了道路。接下来，研究了该方法的一些数学特性，并根据这些特性，提出了一种新的弹性动力学问题求解程序。随后，考虑了几个数值示例，包括作为结构动力学原型的单自由度质量-弹簧-阻尼器系统以及弹性固体中波动情况下的一维和二维弹性动力学问题。