QUALITATIVE AND NUMERICAL APPROACHES TO STUDY OF NONLINEAR MATHEMATICAL MODELS OF TECHNICAL OSCILLATORY SYSTEMS - PUKACH, PETRO; SLIUSARCHUK, OLHA; PUKACH, PAVLO (Herald of Khmelnytskyi National University. Technical sciences, 2024)
In this paper, we consider important classes of one-dimensional media whose bending stiffness can be neglected. It is not possible to apply approximate analytical methods for constructing solutions in mathematical models of dynamic processes in these cases. Therefore, the existence and uniqueness of solutions are substantiated here; their qualitative evaluation is carried out; on the basis of numerical analysis, the above is confirmed and the peculiarities of dynamic processes of some of the classes of systems under consideration are analysed. The technique allows not only prove the correctness of the model solution, but also has an opportunity in its study to apply various approximate methods.
Keywords: qualitative methods; nonlinear oscillations; nonlinear wave equation; Galerkin method; monotonicity method; compactness method; nonlinear elastic properties