A direct variational method for nonconservative system stability
Abstract
Hamilton's principle is applied to analyze the problem of the stability of equilibrium of a discrete, holonomic, and scleronomic mechanical system under conservative and nonconservative (position and/or velocity dependent) forces. At the stability limit, the vanishing of the second order terms (in the deviations from equilibrium) of the total action change functional leads to the condition that the matrix of a certain quadratic form be singular; this yields the eigenvalue (frequencyload) curve. The flutter loads follow by setting the frequency derivative of the determinant of this matrix equal to zero; the energetic interpretation of this latter is also given. When the nonconservative forces go to zero it is shown that one recovers the wellknown discrete conservative system stability criterion. An application follows, and finally in an Appendix various relevant timeintegral equalities are summarized and interpreted.
 Publication:

Journal of Sound Vibration
 Pub Date:
 February 1982
 DOI:
 10.1016/0022460X(82)904928
 Bibcode:
 1982JSV....80..447P