DEVELOPMENT OF COMPUTATIONAL ALGORITHMS FOR THE STUDY OF WAVE PROCESSES IN DISCRETE MEDIA

Abstract

In the provided article, the task was practically implemented to develop the principles of limiting transition from discrete models to continual models in problems concerning the dynamics of elastic structures; to study discrete models and existing methods for solving problems on this topic more thoroughly; to improve already existing solutions by constructing such discrete models that would be maximally close to known continual models and would have some significant advantages in problem solutions. To develop a software module for further application in the project, which allows for the construction of such discrete models of the system under study that would ensure system stability under the action of the applied force, regardless of the set initial conditions, as well as the absence of calculation errors at the stage of problem solution. To achieve the goal, all characteristic dependencies of forces acting on the system were considered, including forces that depend on time, system position, and velocity. The architecture of the DiscretModels software product is presented, which combines subsystems for the graphical visualization of the oscillations of the system under study, a calculation subsystem that implements the proposed approach for constructing discrete models of the system under dynamic loading, and a subsystem for setting and editing the main system parameters. The following were built: the Form subsystem – the main subsystem of the project, which is a container for the graphical and calculation subsystems. The main function of this component is the user's connection with all the possibilities provided by the developed project. The Param subsystem – a project subsystem that ensures the input and editing of the main system parameters, according to the selected problem. The Graf subsystem – a developed dynamic library that is part of the software project, intended for forming a new type of graphical component based on System.Windows.Forms.Control. The term "system under study" in this context refers to a one-dimensional oscillator and a rod, represented as a chain of masses with discrete springs, under dynamic loading. During the execution of this research, a new approach to constructing discrete models of the system under study was proposed, based on already existing solutions. A software product was developed that successfully implements the proposed approach and compares the obtained results with the results of existing solutions to confirm the project's effectiveness. Any software product has limitations in its use and the scope of solvable problems. In this method, it is proven that some limitations can be overcome by applying additional checking conditions and error detection criteria to the implementation. Conclusions were drawn regarding the advantages and disadvantages of each of the methods of continual and discrete models. It is shown that the most promising is the discretization method with a constant step change of forces acting in the system. However, the use of this option requires a corresponding software algorithm to determine the moments of abrupt force changes, which defines the prospects for the project's further development.