Equation of planar vibrations of rigid structure on kinematic supports after A.M. Kurzanov

DOI: 10.37153/2618-9283-2020-5-19-31

Authors:  
Rubric:     Theoretical and experimental studies   
Key words: kinematical rolling support after A.M. Kurzanov, free vibrations, seismic response
Annotation:

The author derives the equation of planar vibrations of rigid structure resting on kinematical pendulum supports with planar bottom (after A.M. Kurzanov). Both support and the surface below are assumed rigid; no sliding assumed. One of the coefficients in the equation (i.e. coordinate of the rotation center) proves to be piece-wise constant. The equation is of the hyperbolic type with parametric terms. Even linearization of this equation does not bring it to the conventional equation of the SDOF oscillator. Principal difference is that the free vibration period depends on the amplitude. The equation is checked for free and forced vibrations. Similar problem is for the seismic response of the unanchored items. For the further research the experimental data about damping are of great importance: both for rotation and the gap closing.

Used Books:

1. Tyapin A.G. Svobodnye kolebaniya zhestkoi kinematicheskoi opory Yu.D. Cherepinskogo. Seismostoikoe stroitel'stvo. Bezopasnost' sooruzhenii. 2020, no. 2, pp. 18-31. (In Russ.) doi: 10.37153/2618-9283-2020-2-18-31

2. Tyapin A.G. Kolebaniya zhestkogo sooruzheniya na kinematicheskikh oporakh Yu.D. Cherepinskogo. Seismostoikoe stroitel'stvo. Bezopasnost' sooruzhenii. 2020, no. 3, pp. 5-18. (In Russ.) doi: 10.37153/2618-9283-2020-3-5-18

3. Tyapin A.G. Ploskie kolebaniya zhestkogo sooruzheniya na kinematicheskikh oporakh: obshchii sluchai geometrii. Seismostoikoe stroitel'stvo. Bezopasnost' sooruzhenii. 2020, no. 4, pp. 41-54. (In Russ.)     doi: 10.37153/2618-9283-2020-4-41-54

4. Izmenenie № 1 k SP 14.13330.2018 «SNIP II-7-81* Stroitel'stvo v seismicheskikh rajonakh». FAU FCCS. 2019. (In Russ.)