SIMULATION OF OSCILLATIONS OF A MOVING ELASTIC FABRIC

The paper considers a model problem of one-dimensional small transverse vibrations of an elastic web moving at a constant speed. The oscillatory process is described by a linear differential equation of the 4th with constant coefficients. In the model under consideration, the Coriolis force is considered, which leads to the appearance of a term with a mixed derivative in the differential equation. This effect makes it very difficult to obtain an exact solution in the form of a Fourier series, but it is possible to propose an algorithm for constructing a family of exact solutions in the form of a special trigonometric series. For various conditions of fastening, it is established that the solution can be constructed in the form of a Fourier series according to the system of eigenfunctions of the auxiliary problem of beam oscillations. In the paper, the question of the convergence of the resulting series is investigated