Summary
The energy approach is extended to cover the stability problem of nonconservative mechanical systems. The eigenvalue curve is obtained by the condition that a certain matrix be singular, and flutter loads follow from the requirement that the derivative of the determinant of this matrix with respect to the frequency of the motion be zero. In the case that the nonconservative forces of the system are being allowed to tend toward zero, all conditions of this general theory change into the well known conditions of the classical theory of stability of conservative systems. The here presented theory allows also for a post-buckling analysis and for the inclusion of nonautonomous systems.
Zusammenfassung
Die Energiemethode wird so erweitert, daß mit ihr Stabilitätsprobleme nichtkonservativer mechanischer Systeme erfaßt werden können. Die Eigenwertkurve wird mittels der Bedingung erhalten, daß eine gewisse Matrix singulär sei, und Flatterlasten folgen aus der Forderung, daß die Ableitung der Determinante dieser Matrix bezüglich der Frequenz der Bewegung gleich Null sei. In dem Fall, daß man die nichtkonservativen Kräfte des Systems gegen Null gehen läßt, gehen alle Bedingungen dieser allgemeinen Theorie in die wohlbekannten Bedingungen der klassischen Stabilitätstheorie konservativer Systeme über. Die hier dargestellte Theorie gestattet auch eine über-kritische Analysis und den Einschluß nichtautonomer Systeme in die Betrachtungen.
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Leipholz, H.H.E. On the application of the energy method to the stability problem of nonconservative autonomous and nonautonomous systems. Acta Mechanica 28, 113–138 (1977). https://doi.org/10.1007/BF01208793
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DOI: https://doi.org/10.1007/BF01208793