Dynamics of a Rigid Body Moving on an Elastic Base with a Single Point of Contact
The paper considers the dynamics of a body moving along an elastic beam. The aim of the work is mathematical modeling of the dynamics of the “solid body — elastic beam” system, taking into account the force interaction of these bodies at one point of contact. Based on the Euler–Bernoulli beam theory...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
National Academy of Sciences of Belarus, State Scientific Institution “The Joint Institute of Mechanical Engineering"
2025-06-01
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| Series: | Механика машин, механизмов и материалов |
| Subjects: | |
| Online Access: | https://mmmm.by/en/readers-en/archive-room-en?layout=edit&id=2026 |
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| Summary: | The paper considers the dynamics of a body moving along an elastic beam. The aim of the work is mathematical modeling of the dynamics of the “solid body — elastic beam” system, taking into account the force interaction of these bodies at one point of contact. Based on the Euler–Bernoulli beam theory and general dynamics theorems, partial differential equations of motion of the “solid body — elastic beam” system are constructed. Using the Bubnov–Galerkin method, ordinary differential equations (ODEs) for the weight coefficients of the approximate solution of the partial differential equation are obtained. Based on the results of numerical integration of the ODE, the dependences of the deflection and the angle of rotation of the elastic beam cross section on time are obtained. Unlike the previously used models, the developed model makes it possible to take into account the effect of the force action of a moving solid on the bending of the elastic beam. The results of the work can be used in the design and manufacture of new transport systems. |
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| ISSN: | 1995-0470 2518-1475 |