Construction of the shape functions of beam vibrations for analysis of the rectangular plates by Kantorovich-Vlasov

For analysis of the plates and membranes by numerical or analytical methods, the question of choice of the system of functions satisfying the different boundary conditions remains a major challenge to address. It is to this issue that is dedicated this work based on an approach of choice of combinations of trigonometric functions, which are shape functions of a bended beam with the boundary conditions corresponding to the plate support mode. To do this, the shape functions of beam vibrations for strength analysis of the rectangular plates by Kantorovich-Vlasov\'s method is considered.Using the properties of quasi-orthogonality of those functions allowed assessing to differential equation for every member of the series. Therefore it\'s proposed some new forms of integration of the beam functions, in order to simplify the problem.