The first project is called "Developing and researching methods for solving vibration problems of loaded mechanical system" (grant number 19-31-90063). Project head, Associate Professor Sergey Solovyov, started working in this area back in 1981; as a student, he contributed to calculating vibrations of space mirror telescope. If external influence frequency correlates with the own vibrations of a mechanical construction, resonance arises, which poses the risk of destruction.
The other project is titled "Developing grid methods for solving spectral problems for systems of differential equations with applications in structural mechanics and plasma physics" (grant number 18-41-160029) and is also supervised by Solovyov.
"Own vibrations are important for designs of airplanes, rockets, spaceships, water and underwater vessels, and various construction. There are known cases of bridges collapsing under the feet of marching military units. Most often, such cases occur because of wind. In 2010, a bridge in Volgograd was seen vibrating visibly under a 16 km/h wind. Vibration amplitudes reached half a meter. After that, dampers were installed to attenuate wind waves.
"Mathematical modelling helps in this matter. The mathematical theory of such problems is very complex and abstract. So nowadays, more attention is paid to solutions and algorithms om computers without an appropriate mathematical basis. The projects supported by the RFBR concentrate on building a mathematical theory of such problems and setting up a mathematical basis for applied tasks," comments Solovyov.
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