Free Vibrations of Rigid Kinematic Support of Yu.D. Cherepinsky

DOI: 10.37153/2618-9283-2020-2-18-31

Authors:  
Rubric:     Theoretical and experimental studies   
Key words: kinematical rolling support, free vibrations, Lagrange equation
Annotation:
The author derives the equation of free vibrations for kinematical rolling support of Yu.D.Cherepinsky. Both support and the surface below are assumed rigid. It is shown that Lagrange equation is similar to the equation of motion for rotational oscillator where the rotation centre, rotational inertia and stiffness are changing every moment, depending on displacements. This equation can be further simplified to the linear form with the error proportional to the second degree of displacements. This equation looks somewhat like the equation for classical pendulum, but effective length in our case is controlled by curvature radii of support and of the rolling surface, as well as by the position of vertical load relative to the centre of the support. Non-linear characteristic is soft. The main nonlinearity is in the inertial term, and not in the stiffness term. Used Books:
1.Cherepinskii Yu.D., Zhunusov T.Zh., Gorvic I.G. Aktivnaya sejsmozashchita
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sistemah sejsmoizolyacii s vklyuchayushchimsya suhim treniem // Tezisy
dokladov respublikanskoi konferencii «Seismostoikoe stroitel'stvo v Uzbekskoi
SSR». Tashkent: Fan. 1974. [In Russian]
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seismoizoliruyushchih fundamentov. M.: VNIINTPI. 1997. 76 p. [In Russian]
4.Vibracii v tekhnike. Spravochnik. V 6-i t./T.1. Kolebaniya linejnyh system / Pod
red.V.V.Bolotina. M: Mashinostroenie. 1978. 352 p. [In Russian]