Kinematic support modeling in Sage

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Abstract

The article discusses the kinematic support, which allows reducing the horizontal dynamic effects on the building during earthquakes. The model of a seismic isolation support is considered from the point of view of classical mechanics, that is, we assume that the support is absolutely solid, oscillating in a vertical plane above a fixed horizontal solid plate. This approach allows a more adequate description of the interaction of the support with the soil and the base plate of the building. The paper describes the procedure for reducing the complete system of equations of motion of a massive rigid body on a fixed horizontal perfectly smooth plane to a form suitable for applying the finite difference method and its implementation in the Sage computer algebra system. The numerical calculations by the Euler method for grids with different number of elements are carried out and a mathematical model of the support as a perfectly rigid body in the Sage computer algebra system is implemented. The article presents the intermediate results of numerical experiments performed in Sage and gives a brief analysis (description) of the results.

About the authors

Oleg K. Kroytor

Peoples’ Friendship University of Russia (RUDN University)

Email: kroytor_ok@pfur.ru
Postgraduate of Department of Applied Probability and Informatics 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Mikhail D. Malykh

Peoples’ Friendship University of Russia (RUDN University)

Email: malykh_md@pfur.ru
Doctor of Physical and Mathematical Sciences, assistant professor of Department of Applied Probability and Informatics 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Sergei P. Karnilovich

Peoples’ Friendship University of Russia (RUDN University)

Email: karnilovich_sp@pfur.ru
assistant professor, Ph.d., assistant professor of Institute of Physical Research and Technology 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

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