The article is devoted to the development of a mathematical model of the process of geometric nonlinear deformation of thin magnetoelastic plates of a complex structural shape based on the Hamilton-Ostrogradsky variational principle, and conducting computational experiments. In this case, the three-dimensional mathematical model was transferred to a two-dimensional view using the Kirchhoff-Liav hypothesis. Cauchy's relationship, Hooke's law, Lawrence's force and Maxwell's electromagnetic tensor were used to determine kinetic and potential energy and work done by external forces. The effects of the electromagnetic field on the deformation stress state of the magnetoelastic plate were observed, as a result, a mathematical model was created in the form of a system of differential differential equations with initial and boundary conditions for displacement. To solve the equation, a calculation algorithm was developed using the R-function, Bubnov-Galerkin, Newmark, Gaussian, Gaussian squares, and Iteration number methods. Calculation experiments were carried out in various mechanical states of the magneto-elastic plate, its borders were tightly fixed, one side was hinged and the other side was free, and numerical results were obtained. A comparative analysis of the results of the calculations was presented.
In this paper, we proved the unique solvability of the local boundary value problem with the Frankl condition for a degenerating of mixed type equation with a fractional derivative