A mathematical model for calculating the vibrations of three-layer rods under spatial loading is developed in the article. Variations of kinetic and potential energies and the work of external forces, substituted into the Ostrogradsky-Hamilton variational principle, are compiled. A system of vibration equations for a three-layer rod with corresponding generalized initial and natural boundary conditions is obtained. The problem is solved for six unknowns. To solve it, the authors used the central finite-difference relations of the implicit scheme of the finite-difference method of the second-order accuracy, considering the features of the boundary and initial conditions. By setting specific boundary conditions, several practical problems can be solved. A methodology and computational algorithm for calculating static and dynamic strain processes of spatially loaded threelayer rods are given.
| Mualliflar | Anarova, Sh.A., Shokirov, D.A., Анарова, Ш.А., Шокиров, Д.А. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2024-07-19 |
| Son | 3 |
| Betlar | 57-76 |
| Til | Rus |
algorithm, three – layer rod, finite difference method, Ostrogradsky – Hamilton principle, dimensionless parameter, rod oscillation, алгоритм, трехслойный стержень, метод конечных разностей, принцип Остроградского – Гамильтона, безразмерного параметр, колебания стержня
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