Certain Problems of Statics and Dynamics of Point-Supported Elastic Rectangular Plates

The paper presents an algorithm, based on the finite Fourier transforms technique, making it possible to derive formally accurate solutions of the following engineering problems of statics and dynamics of elastic, isotropic plates: (1) Harmonic vibrations and statical bending of rectangular plates, loaded symmetrically with respect o both axes of symmetry of the plate, supported at four corners and, along the sides, on elastic ribs; (2) Statical bending of rectangular plates, loaded as before and supported at four or two points at equal distances from the opposite edges, or supported at a single point, at the center of symmetry of the plate; (3) Statical bending of a plate having the form of an isosceles rightangled triangle, the hypotenuse being either free or supported on an elastic rib, simply supported along the legs, and loaded symmetrically with respect to the symmetry axis. In the case of rectangular plates supported at four corners and on elastic ribs, the solution presented is confined to symmetric loadings for the sake of simplicity only, since it is easily observed that the formulae derived in the first part of the paper may be generalized to arbitrary static or dynamic loadings. All the considerations and formulae presented in the paper may easily be generalized to the case of orthotropy, as also to the practically important case of rectangular plates supported on columns having finite cross-sections, and located at certain distances from the edges of the plate, provided the loads are symmetric.