Scaling mode shapes obtained from operating data

A set of scaled mode shapes is a complete representation of the linear dynamic properties of a structure. Mode shapes can be used for a variety of different analyses, including structural modifications, forced response simulations, excitation force calculations from measured responses, and frequency response function (FRF) synthesis for comparison with experimental data. When mode shapes are obtained experimentally from operating data, they are not properly scaled to preserve the mass and elastic properties of the structure. By operating data, we mean that only structural responses were measured - excitation forces were not measured. In this article, we review the traditional methods for scaling experimental mode shapes using FRFs, and also introduce two new methods that do not require FRF measurement. The new methods combine a search algorithm with the SDM (Structural Dynamics Modification or eigenvalue modification) algorithm to perform a series of structural modifications until proper scaling of the mode shapes is achieved. Details of the methods and examples of their use are included.