A solution technique is developed whereby the problem of determining the synchronous unbalance response of general multi-degree of freedom rotor bearing systems is reduced to solving a set of as many simultaneous nonlinear equations in damper orbit eccentricities are there are dampers. It is shown how, in the case of a single damper, the resulting nonlinear equation may be solved directly to determine all possible orbit eccentricity solutions as a function of the rotor speed and bearing parameter, thereby ensuring completeness of solution, eliminating convergence problems and clearly indicating all multistable operation possibilities. Design maps portraying the effect of the relevant damper design parameters on system response may be conveniently obtained, allowing for optimal damper design. The technique is illustrated for the case of a simple squeeze film damped symmetric flexible rotor.

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