О Трехмерных Начально-Краевых Задачах Динамики Толстых Упругих Плит

Abstract

Complex problems of three-dimensional elasticity theory for thick elastic plates with arbitrary geometry of their lateral surface are solved. Analytical dependencies of the components of the elastic dynamic displacements’ field of the plate’s inner points from the boundary-surface external-dynamic disturbing factors, defined by continuous functions or their values’ vectors, are constructed. It is assumed, that these disturbances have a classically defined powerful character, or are specified by a certain number of differential transformations of the field’s components of the plate’s dynamic displacement points. The absence of quantitative and qualitative restrictions on the determined transformations of the initial-boundary problems of the considered plates’ dynamics makes it incorrect and unsolvable by methods of classical and computational mathematics. The methodology of root-mean square mathematical modeling of discretely and continuously specified observations for the initial-boundary plate’s condition by the system of modeling functions and their values’ vectors is proposed in the paper. Constructed in this way field’s components of spatial-dynamic displacements of the plate’s points, precisely satisfying classical Lyame equation, with the available information on its initial-boundary condition, are agreed according to the root-mean square criterion. The problem of the obtained solutions’ ambiguity is investigated, their accuracy evaluation in accordance with the information on the external- dynamic condition of the investigated plate is conducted. The plate’s dynamics in the particular mode, for cases of information lack on external- dynamic influences on it and under the conditions of its geometric background according to spatial coordinates. The computer realization of the obtained mathematical results is engineeringly simple and can be easily implemented with the help of well-known methods of computational mathematics.