This paper presents a design methodology to determine the optimal circumferential placement of cylindrical probes upstream of a turbine stage for reduced excitation forces. The potential flow forcing function generated by the probes is characterized by means of a Fourier analysis. A finite difference formulation is used to evaluate the sensitivity of the forcing function to the probe positions. An optimization scheme, based on the linear programming method, uses the sensitivity analysis results to reposition the probes such that the Fourier amplitudes of critical excitation orders are reduced. The results for an example design situation are presented.
Efficient finite difference formulation of a geometrically nonlinear beam element
