Vibrations of plate with boundary “hinged attachment” conditions

In the paper, the initial problem for the equation of vibrations of a rectangular plate with boundary conditions of the “hinged attachment” type is studied. An energy inequality is established, from which the uniqueness of the solution of the stated initial-boundary problem follows. The corresponding existence and stability theorems for the solution of the problem in the classes of regular and generalized solutions are proved. The existence of a solution to the problem posed is carried out by the method of spectral analysis and it is constructed as the sum of an orthogonal series over a system of eigenfunctions corresponding to a two-dimensional spectral problem, which is constructed by the method of separation of variables. A complete substantiation of the convergence of the constructed three-dimensional series in the class of regular solutions of the considered equation is given. The generalized solution is defined as the uniform limit of the sequence of regular solutions of the initial boundary value problem.