The problem of infinite plate loaded with normal force following a complex trajectory

Introduction. A method for solving the problem of an infinite plate on an elastic foundation is proposed. The plate is affected by a periodic load in the form of a force following an arbitrary closed path. The work objective is to develop a numerical method for solving problems of the elasticity theory for bodies under a moving load. Materials andMethods. Given the periodicity of the load under consideration, it is decomposed in a Fourier series in a time interval whose length is equal to the load period. The solution to the original problem is constructed by superposition of the solutions to the problems corresponding to the load specified by the terms of the Fourier series described above. The final solution to the problem is presented as a segment of a series. In this case, each term corresponds to the solution of the problem of the impact on an infinite plate of a load distributed along a closed curve (the trajectory of the force motion). To find these solutions, the fundamental solution to the equation of vibration of an infinite plate lying on an elastic base is used...