The novel method to investigate the interaction between plane harmonic waves and plates under arbitrary boundary conditions in elastic soil environments

This article discusses the issue of how a harmonic plane wave interacts with an infinite homogeneous steel plate in a soil environment, specifically an elastic environment. The load compensation method is used to address this problem. The Kirchhoff-Love equation describes the equation of motion for the plate. The soil motion equations may be described using several mathematical frameworks, including elastic theory equations, Cauchy relations, physical equations, and Lame equations. The boundary conditions for the contact between the plate and the soil medium include ensuring that the normal displacements at the boundary of the obstacle and the soil medium are equal. Additionally, it is assumed that the pressure amplitudes and normal stresses are also equal. Calculate the influence functions of the displacement perpendicular to the infinite plate when subjected to a concentrated force in the form of the Dirac delta function. Once the value of compensatory loads has been established based on the boundary conditions. The normal displacement values of the plate may be calculated by summing the convolution of the influence function with the compensating loads and displacements of the infinite plate that are influenced by plane harmonic waves.