APPROXIMATION OF A CLOSELY SPACED MODE SUBSPACE BY A REPEATED MODE SUBSPACE IN VIBRATION CONTROL OF FLEXIBLE STRUCTURES

The necessary conditions under which a closely spaced mode subspace mi ght be substituted by a repeated mode subspace from the point of view of the control and dynamics are presented in this paper. The definitio ns of the controllability degree and observability degree are first su ggested. Based on these definitions and dynamical analysis, the necess ary conditions are obtained for the approximation of a closely spaced mode subspace by a repeated mode subspace, namely not only the deviati on of the natural frequencies epsilon should be small, but also epsilo n/xi(0) should be small enough, where xi(0) is the relative coefficien t of the damping. (C) 1997 Elsevier Science Ltd.