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- W2034497227 abstract "The geometrical stability of the non-linear normal mode vibrations of a class of two degree of freedom dynamical systems is studied by utilizing the definitions and analysis of Synge's “Geometry of Dynamics.” It is shown that instabilities can occur for small amplitudes of vibration only if (a) one of the associated linear normal modes possesses a frequency which is nearly a multiple of the frequency of the other linear normal mode, or (b) the frequency of one linear normal mode is nearly zero. Die geometrische Stabilität der nichtlinearen Eigenschwingungen einer Klasse dynamischer Systeme mit zwei Freiheitsgraden wird an Hand der Definitionen und der Berechnung in “Geometry of Dynamics” von Synge untersucht. Es wird gezeigt, dass für kleine Schwingungsamplituden Instabilitäten nur dann auftreten können, wenn (a) eine der zugehörigen linearen Eigenschwingungen eine Frequenz besitzt, die nahezu ein einzahliges Vielfaches der Frequenz der anderen linearen Eigenschwingung ist, oder wenn (b) die Frequenz einer linearen Eigenschwingung nahezu gleich null ist. ИccлeдoвaHa гeoмeтpичecкaя ycтoйчивocть HqopмaльHыч мoд HeлиHeйHыч кoлeбaHий клacca диHaмичecкич cиcтeм c двyмя cтeпeHями cвoбoды. Иccлeдoвaяиe ocHoвaHo Ha aHaлизe и oпpeдeлeяияч, дaHHыч в кHигe cиягa «Гeoмeтpип дияaмпкиå. ПoкaзaHo, чтo в cлyчae мaлыч aмплитyД кoлeбaHий яeycтoйчивocти мoгyт вoзяикHyть лищь в cлeдyющич cлyчaяч: (a) ecли oдпa из cвязaHыч c Hимп лиHeйHыч HopмaльHыч мoд имeeт чacтoтy, кoтopaя мaлo oтличaeтcя oт кpaтHocти чacтoты дpyгoй лиHeйяoй HopмaльHoй мoвы, йли (б) ecли чacтoтa oдHoй из лиHeйHыч HopмaльHыч мoд близкa к Hyлю." @default.
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- W2034497227 date "1973-04-01" @default.
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- W2034497227 title "The geometrical stability of non-linear normal modes in two degree of freedom systems" @default.
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- W2034497227 doi "https://doi.org/10.1016/0020-7462(73)90033-4" @default.
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