| Abstract: | This paper concerns the motion of different elastically coupled masses. One of the masses is subjected to a motive force, while the other mass is acted upon by friction. The motive force decreases linearly, while friction changes nonlinearly. The differential equations of motion are derived and are reduced to the standard form (after Bogolyubov). The averaging method is used to find steady-state solutions, one of which agrees with the exact steady-state solution of the initial system of equations. It is found that the actual conditions of stability of the steady-state solution are differ greatly from the conditions calculated on the basis of avaraged equations. These differences are due to the difference in the degrees of the characteristic Rouse-Hurwitz polynomials calculated on the basis of the initial and averaged equations. The analytical results are illustrated by modeling on a microcomputer. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev; Regional Scientific Research and Experimental Design Institute, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 94–100, August, 1999. |
