Forming the first part of a two-part paper, the methodology of an efficient frequency-domain approach for predicting the forced response of turbomachinery blades is presented. The capability and computational efficiency of the method are demonstrated in Part Two with a three-stage transonic compressor case. Interaction between fluid and structure is dealt with in a loosely coupled manner, based on the assumption of linear aerodynamic damping and negligible frequency shift. The Finite Element (FE) package ANSYS is used to provide the mode shape and natural frequency of a particular mode, which is interpolated onto the CFD mesh. The linearised unsteady Navier-Stokes equations are solved in the frequency domain using a single-passage approach to provide aerodynamic excitation and damping forces. Two methods of obtaining the single degree-of-freedom forced response solution are demonstrated: the Modal Reduction Technique, solving the modal forced response equation in modal space; and a new Energy Method, an alternative method allowing calculations to be performed directly and simply in physical space. Both methods are demonstrated in a preliminary case study of the NASA R67 transonic fan blade with excitation of the 1st torsion mode due to a hypothetical inlet distortion.

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