Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2220310.22363/2658-4670-2019-27-2-124-132Modeling and SimulationМатематическое моделированиеResearch ArticleSeismic stability of oscillating building on kinematic supportsСейсмостойкость колеблющегося здания на кинематических опорахKarnilovichSergei PКарниловичСергей Петрович

Associate Professor, Ph.D., Assistant Professor Institute of Physical Research and Technology

karnilovich-sp@rudn.ruLovetskiyKonstantin PЛовецкийКонстантин Петрович

Associate Professor, Ph.D., Assistant Professor of Department of Applied Probability and Informatics

lovetskiy-kp@rudn.ruSevastianovLeonid AСевастьяновЛеонид Антонович

professor, Doctor of Physical and Mathematical Sciences, professor of Department of Applied Probability and Informatics

sevastianov-la@rudn.ruShchesnyakEugene LЩеснякЕвгений Леонидович

professor, Doctor of Economics, First Vice-Rector, Vice-Rector for Economic Activity

shcheasnyak-el@rudn.ruPeoples’ Friendship University of Russia (RUDN University)Российский университет дружбы народов15122019272VOL 27, NO2 (2019)ТОМ 27, №2 (2019)12413222112019Copyright ©; 2019, Karnilovich S.P., Lovetskiy K.P., Sevastianov L.A., Shchesnyak E.L.Copyright ©; 2019, Карнилович С.П., Ловецкий К.П., Севастьянов Л.А., Щесняк Е.Л.2019Karnilovich S.P., Lovetskiy K.P., Sevastianov L.A., Shchesnyak E.L.Карнилович С.П., Ловецкий К.П., Севастьянов Л.А., Щесняк Е.Л.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/22203

The design of kinematic supports is considered, which allows to damp the oscillation energy of seismic waves during earthquakes. The building rests on supports that have the geometry of straight cylinders. When horizontal ground oscillations occur, the supports are deflected at a small angle . At the same time, their centre of gravity rises and tends to return to its original position under the action of two forces on each support: the weight of the building evenly distributed over all the supports, and the weight of the support itself. The first force is applied to the highest point of the support, the second one is applied to the centre of gravity of the support, so that the rotational moments of two forces act on the support. It should be noted that under very strong vibrations of the ground, the projection of the centre of gravity could move beyond the base of the support. In this case, the supports will begin to tip over. We confine ourselves to considering such deviations that the rotational moments of the forces of gravity still tend to return the supports to their initial state of equilibrium.

Рассмотрена конструкция кинематических опор, позволяющая демпфировать энергию колебаний сейсмических волн при землетрясениях. Здание опирается на опоры, которые имеют геометрию прямых цилиндров. Когда происходят горизонтальные колебания грунта, опоры отклоняются под небольшим углом. В то же время их центр тяжести поднимается и стремится вернуться в исходное положение под действием двух сил на каждую опору: вес здания, равномерно распределенного по всем опорам, и вес самой опоры. Первая сила применяется к самой высокой точке опоры, вторая - к центру тяжести опоры, так что на опору действуют моменты вращения двух сил. Следует отметить, что при очень сильных колебаниях грунта проекция центра тяжести может выходить за пределы основания опоры. В этом случае опоры начнут опрокидываться. Мы ограничимся рассмотрением таких отклонений, что вращательные моменты сил гравитации все еще стремятся вернуть опоры в исходное состояние равновесия.

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