On the calculation of rectangular plates by the method of trigonometric series

In the article calculations of rectangular plates by the method of trigonometric series are presented. In the case of the plate, which have free or hinged bearing along the whole contour, the solution is determined in the double trigonometric series (the solution of the Navier). In the more general case of a plate in which only two opposite edges are hinged bearing, and the other two edges are arbitrary boundary conditions, the solution is sought in the form of the single trigonometric series (the solution of the M. Levi). The comparative analysis of the results is obtained.