Abstract: In [1], by a transformation on the Liemrd equation system dx/dt=y-F(x), dy/dt=-g(x) (1) such that the trajectories of (1)on both left and right half-planes change into thoseintegral curves of the new equation system merely on the right half-plane,A.F.Hilippov shows that under some certain conditions the stable limit cycles of system (1) must exist.Applying the Filippov’s method on the more generalized system dx/dt=Q(x,y), dy/dt=P(x) (2) this paper provides a sufficient condition for the existence of the stable limit cycles oftvstem (2).

Key words: viscoelastic beam, differential equation of motion, Leaderman relation, Galerkin method, inner(outer) boundary, limit cycle, trajectory, annular region