This manuscript brings the derivation of influence functions for a three-dimensional full-space under bilinearly-distributed time-harmonic loads. The differential equations describing the medium are decomposed in terms of uncoupled vector fields. A double Fourier transform allows the system of equations to be solved algebraically in the transformed space, where the bilinear-loading boundary conditions are imposed. The resulting displacement and stress solutions are presented in terms of double improper integrals to be evaluated numerically. The manuscript brings selected results from the evaluation of these solutions. These influence functions can be used in boundary element models of elastodynamic problems to yield computationally-efficient solutions and improved representation of sharply-varying contact traction fields.

这份手稿带来了双线性分布时谐载荷下三维全空间影响函数的推导。描述介质的微分方程根据非耦合矢量场进行分解。双傅立叶变换允许在变换空间中对方程组进行代数求解，其中施加了双线性加载边界条件。由此产生的位移和应力解以双不适当积分的形式呈现，以进行数值评估。手稿带来了对这些解决方案的评估结果。这些影响函数可用于弹性动力学问题的边界元模型，以产生计算效率高的解决方案并改进对急剧变化的接触牵引场的表示。