Dry friction damping structures are simple and can be used in big range of working temperature, therefore varied kinds of friction contact damping structures have been widely used in turbomachine blades to reduce the forced vibration and improve dynamic stability. However, the dynamic analysis of such structures is still a challenging engineering task because the dry friction damping is a dynamic contact problem with complex boundary condition and strong nonlinear characteristics. A three dimensional numerical model for friction contact has been proposed to investigate the contact kinematics in the contact surfaces between adjacent blade shrouds. Microslip effects taken into account with a discretization of the contact surface with a mesh of contact elements, by altering the number of contact node can consider the effects of the area of the contact surface on forced response of shroud blade. The complex movement in the shroud contact surfaces was described by tracking the trajectory of the relative motion of the contact node. The model can consider the differences between the static friction coefficient and dynamic friction coefficient. The model has the mathematically tractable characteristic and can be easily used, and conforms to the engineering need. In order to decrease time consuming for computing the forced response, a reduced method is employed to condense all nonlinear degrees of freedom (DOF) to the nonlinear DOF on the contact surfaces, hence, iterative procedure of solution is limited in nonlinear degrees of freedoms. An alternating frequency/time domain method (AFT) which takes the advantages of both the time domain method and the frequency domain method is introduced to predict nonlinear vibration of shrouded blade systems. The developed friction model and calculated method of dynamic equation are applied to calculate nonlinear vibration for a real steam turbine blade. The effect of parameters on resonant frequency and response of the blade are investigated and discussed.

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