NONCONSERVATIVE SYSTEMS WITH SYMMETRIZABLE STIFFNESS MATRICES EXHIBITING LIMIT-CYCLES

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.