An. Kounadis et Gj. Simitses, NONCONSERVATIVE SYSTEMS WITH SYMMETRIZABLE STIFFNESS MATRICES EXHIBITING LIMIT-CYCLES, International journal of non-linear mechanics, 32(3), 1997, pp. 515-529
Non-conservative dissipative systems under partial follower loading, w
ith stiffness matrices that are symmetrizable, are reexamined with the
aid of non-linear analysis. In this work, the conditions under which
the above autonomous systems may experience a limit cycle response, st
able (periodic attractor) or unstable (dynamic instability via flutter
) in a certain region of existence of adjacent equilibria (region of d
ivergence instability) are properly established. This region where a l
imit cycle response may occur is defined by an interval of values of t
he non-conservativeness loading parameter eta with lower bound eta = e
ta(0) (boundary between existence and non-existence of adjacent equili
bria) and upper bound eta = 0.50 (being invariant with respect to all
other parameters). In this region although the set of buckling eigenve
ctors is complete (associated with distinct eigenvalues) there is one
postbuckling equilibrium path passing through two consecutive branchin
g points. Hence, only non-conservative systems with eta > 0.50 (having
all postbuckling equilibrium paths independent of each other) behave
dynamically like symmetric (conservative) systems. These findings are
verified with the aid of various numerical examples. (C) 1997 Elsevier
Science Ltd.