Three-dimentional problems of controlling the dynamics of incompletely observed thick elastic plates. Part I. The case of continuously specified desired condition
DOI:
https://doi.org/10.17721/1812-5409.2024/2.11Keywords:
spatially distributed dynamical systems, spatial problems of elasticity theory, thick elastic plates, control problemsAbstract
In the three-dimensional formulation for the first time complex problems of controlling the elastic plate’s dynamics on reaching by the field its elastic-dynamic displacements continuously for the spatially-temporal coordinates of a given desired state are solved. The classical equations of the three-dimensional theory of elasticity and the root mean- square control criterion were chosen as output data for solving the considered problems. Controlling can be volumetric, initial, surface and end external- dynamic disturbances, considered separately and in practical justified combination. The problems are formulated and solved on the condition of continuously defined initial-boundary observations for the plate’s state, which without restriction on their quantity and quality are defined functionally through linear differential operators of arbitrary order and structure. Observed system’s characteristics are modelled discretely and continuously defined by the simulation functions, numerical values and analytics of which are outside the considered spatial-temporal domain of functioning of the studied elastic body in the result of the construction of root mean-square approximations to linear algebraic, integral and functional equations’ solutions. Calculation formulas, which determine the set of admissible solutions of the considered problems are quite simple and accessible for computer implementation. The defined peculiarities of controlling the considered elastic object’s dynamics are determined for cases when the initial and boundary external-dynamic disturbances can be neglected, and the plate’s dynamics can be considered in unrestricted spatial and temporal domains. Assessment of the accuracy of control problems’ solving has been made, conditions for unambiguousness of the constructed solutions have been formulated.
Pages of the article in the issue: 65 - 71
Language of the article: Ukrainian
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