The theories of the vibrational dampers in turbomachineries are studied and the dynamic response characteristics of bladed disc systems with dry friction damper devices are investigated both by theoretical analysis and numerical approach.The HBM (harmonic balance method) is used to linearize the nonlinear dynamic behaviors of the systems effectively.The nonlinear behaviors are caused by the discontinuity of the displacement that occurs between two contact interfaces.The equivalent linearized damping and stiffness of the systems are obtained.Numerical approach of dynamic response characteristics is adopted.The calculation and analysis of dynamic response characteristics of aeroengine examples are executed by applying ANSYS finite element software.The rotor discs with shrouded blades and with lacing rod blades are selected as the engineering cases.The concepts of optimal normal pressure and critical damping characteristics between contact interfaces of dry friction damper are derived from a set of response amplitude versus frequency curves under different friction damping values.The conclusions of this dissertation can be applied to the optimal design of dry friction dampers for the future turbomachineries.