The transient mixed problem for an elastic semi-strip is investigated in this article. The semi-strip is loaded by a transient load at the center of its short edge. The longitudinal sides of the semi-strip are fixed. The initial problem is reduced to a one-dimensional problem with the help of Laplace and Fourier transforms. The analytical solution of the one-dimensional boundary problem is constructed with the help of matrix differential calculation apparatus. The original functions are found with the help of mutual inversion of Laplace–Fourier transform. Here the Laplace originals were derived by the new approach based on expansion of Laplace transform in a multiple series. The wave field of the semi-strip was investigated depending on time and geometric parameters.

本文研究了弹性半带的瞬态混合问题。半带钢在其短边的中心受到瞬态载荷的作用。半条的纵向侧是固定的。借助拉普拉斯（Laplace）和傅里叶（Fourier）变换，将初始问题简化为一维问题。借助矩阵微分计算装置构造一维边界问题的解析解。原始函数是在拉普拉斯-傅立叶变换的相互求逆的帮助下找到的。在此，拉普拉斯原图是通过在多个序列中扩展拉普拉斯变换的新方法得出的。根据时间和几何参数研究了半带的波场。