The evaluation of the vibration behaviour of turbomachinery installations, where the model of the rotor support structure (foundation or casing) is unknown and the foundation has natural frequencies in or near the operating speed range, is still problematic. An attractive approach for identifying the foundation uses motion measurements of the rotor and the foundation at the bearing supports to indentify the parameters of an equivalent foundation, i.e. one which reproduces similar vibration responses over the operating speed range. Earlier work identified perfectly the modal parameters of a flexibly supported rigid foundation block, a situation involving only the six rigid body modes of the foundation, so that the equations of motion of the foundation could be written with a diagonal mass matrix. However, in practice, foundations such as gas turbine casings have flexural modes in or near the operating speed range, in which case it is unlikely that the foundation mass can be adequately represented by a diagonal mass matrix. Hence, this paper further develops the above identification technique to enable identification of a flexibly supported foundation block which has seven vibration modes in or near the operating speed range. It is shown by numerical experiments that the assumption of a diagonal mass matrix for the foundation does not result in a satisfactory equivalent foundation. On the other hand, when the identification procedure is enhanced to cater for a full symmetric foundation mass matrix, it is possible to identify the modal parameters of an equivalent foundation which, when substituted for the actual foundation of an unbalanced rotor bearing system, satisfactorily reproduces the system unbalance response. This is so even when the 'measurement' data used to identify the modal parameters is truncated to two digit accuracy to better represent practical measurement accuracy. It is concluded that the proposed foundation identification technique is likely to be applicable to practical field installations.
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