On the destabilizing effect of non-linear damping in non-conservative systems with follower forces

In this paper, a mechanical model with two degrees of freedom previously studied by Ziegler [1] is examined, but Ziegler's linear damping is replaced by a non-linear term, as is usual for structural damping. In the critical case, the stability problem must then be solved by the second method of Liapunov. The undamped system is also examined, but in this case the stability question in the critical case cannot be decided by the terms of lowest order. Non-linear damping gives rise to a behaviour similar to that due to linear damping; however, the stability of the zero position depends only on the ratio of the two damping coefficients.B paбoтe пccлeдyeтcя мeчaничecкця мoдeль co двyмя cтeпeнями cвoбoды paccмaт pпвaeмaя yзe Циглepoм (1), oдпaкo здecь лпнeйпoe дeмпфпpoвaнпe зaмeпeпo пeшнeйпым, кoтopoe oбычнo в cлyчaяч cтpyктypнoгo дeмпфиpoвaнпя.B кpнтпчecкoм cлyчae, пpoблeмa ycтoйчивocти. дoлзпa быть зaтeм peшeпa втopым мeтoдoм ляпyнoвa. Paccмaтpивaeтcя тoзe пeзaтyчayщaя cпcтeмa, oдпaкo в этoм cлyчac вoпpoc ycтoйчпвocти в кpптичecкoм cлyчae пe мoзeт быть peшeн c пoмoщьy члeпoв мaлeйшeгo пopядкa. пeлипeйпoe дeмпфиpoвaнпe выэывaeт пoвeдeпиe пoчoзee пзвecнoмy c линeйнoгo дeмПфиpoвaпия, oднaкo ycтoйчивocть нyлeвoгo пoлoзeпия зaвиcит тoгдa тoлькo oт cooтнoпeния двyч кoзффициeптoв дeмПфиpoвaния.