Sensitivity and robustness analyses of non-linear bladed disc dynamics

There are two major causes of vibrations in gas-turbine structures: (i) excitation by time-varied external forces applied to a structure and (ii) self-excitation, which can occur, for some fluttering vibration modes, due to interaction of a vibrating structure with gas flow. Gas-turbine structures are typically assembled structures, which comprise friction, gap and other types of the contact interfaces: such as damper devices, interlock shrouds and root joints in bladed discs, etc. Forces occurring at these interfaces are strongly nonlinear because of friction forces, unilateral interaction forces acting along normal to a contact interface, closing and opening clearances during vibrations, etc. The nonlinear contact interfaces can have dominant influence or affect significantly the amplitude levels and resonance frequencies for forced vibrations and can suppress the exponential growth of flutter amplitudes to form a periodic motion of limit cycle oscillations for flutter-excited vibrations. The nonlinear vibration regimes can be highly sensitive to variation of the parameters of contact interfaces and design parameters of the structure. Appropriate choice of parameter values can reduce the levels of vibration amplitudes to those when they cannot cause immediate failure and, even, do not contribute practically to the accumulation of high-cycle fatigue damages. The effective choice and control of the vibration levels require methods for quantitative assessment of their sensitivity to variation of structural and contact interface parameters. Moreover, in addition to finding parameters providing the acceptable vibration levels, inevitable variability and scatters of design parameters and operating conditions during manufacture and during gas-turbine engine operation require determination the parameters which ensure the robustness of the design: when changes of design parameters within ranges of their variability do not affect significantly the vibration amplitudes In this paper, efficient frequency-domain methods are discussed which allow direct and efficient calculation of the sensitivity coefficients for: (i) the nonlinear forced response and (ii) amplitudes and frequencies of flutter-excited limit-cycle oscillations for structures with friction and gap contact interfaces. The methods use realistic large-scale finite element models of structures and multiharmonic representation of the periodic vibrations. The approaches are developed to calculate design parameters maximising the design robustness. A set of representative examples of the application of these methods are given.