PLANAR VIBRATIONS OF RIGID STRUCTURE ON KINEMATIC SUPPORTS: GENERAL GEOMETRY

DOI: 10.37153/2618-9283-2020-4-41-54

Authors:  
Rubric:     Viewpoints   
Key words: kinematical rolling support, free vibrations, Lagrange equation
Annotation:
The author derives
the equation of planar vibrations for kinematical rolling supports of varying
curvature radius. Both support and the surface below are assumed rigid; no
sliding assumed. Generalization means arbitrary geometry of the support and
rolling surface (the building is attached to the supports by hinges, as
previously). The equation of motion developed is checked with free and forced
vibrations of the support with two curvature radii (great radius in the central
part and small radius in the side parts). Such a support in the limit case
(when great radius goes to infinity, and small radius goes to zero) models the
support after A.М.
Kurzanov with planar bottom and finite size in plan.  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 Russian].        DOI: 10.37153/2618-9283-2020-2-18-31

2. Tyapin A.G. Ploskie kolebaniya zhestkogo sooruzheniya na kinematicheskih oporakh Yu. D. Cherepinskogo. Seismostoikoe stroitel’stvo. Bezopasnost’ sooruzhenii. 2020, no.3, pp. 5-18 [In Russian].   DOI: 10.37153/2618-9283-2020-3-5-18

3.Vibratsii v tekhnike. Spravochnik. V 6-I t.T.1. Kolebaniya lineinyh system.Pod redaktsiei V.V. Bolotina. M.: Mashinistroenie.1978, 352 p. [In Russian]