The N-p-q Periodic Movement Of The Vibro-impact System With Two-sided Constraints

The research on the vibro-impact vibration system has been carried out for nearly 50 years. It is well known, that vibro-impact vibration system can be the cases with one-sided constraint or two-sided constraints. At present, research results concern mainly the case with one-sided constraint and little achievement are obtained about two-sided constraints. However,the current knowledge indicates the vibration characteristics of the vibro-impact system with one-sided constraint are quite different with two-sided constraints.In this paper, Integrally Shrouded Blade (ISB) with two-sided constraints is studied. First,employing the finite element modeling method, the dynamical model of ISB with two-sided constraints is established, considering the gas flow excitation force. Using real mode transformation method, the coupling motion differential equations obtained are decoupled and transferred into the equations with mode coordinate. And the criterion of vibro-impact of the system with two-sided constraints is given. Then, the analytical solutions of the vibro-impact system are deduced by the ordinary differential equation theory, and at same time their matrix expression is obtained which will be used at the stability analysis subsequently. And the motion process of impact system is described in detail by mathematical expressions. Finally,applying the time history, phase diagram and Poincare mapping diagram, the n-p-q periodic motion and the nonlinear behavior of the vibro-impact system with two-sided constraints are investigated. And the stability of the system is analyzed based on the variational expression of the differential equation and Floquet theory.