Scaling operational modes by modal interpretation of static displacements

Operational modal analysis can only identify unscaled mode shapes, limiting further engineering applications. The widely-used mass-change method for modal scaling requires large mass perturbations to generate measurable natural frequency shifts in presence of noise, which however, is difficult and expensive to implement in practical engineering. This paper proposes a novel modal scaling strategy based on static measurement. The main idea of the strategy is to interpret the static displacements produced by a designated loading condition as a linear combination of the unscaled mode shapes. Consequently, the static and dynamic responses are linked together, from which the modal masses (scaling factors) can be identified. A numerically simulated bridge and an experimental cantilever beam demonstrate the effectiveness and superiority of the proposed strategy.