Modal scaling in operational modal analysis using a finite element model

• A methodology to scale mode shapes in operational modal analysis, using a finite element model, is proposed.
• The technique combines the experimental mode shapes and the mass matrix of a finite element model.
• Similar or better accuracy to that provided by the mass change method can be achieved.
• The methodology has been validated by numerical simulations and experimental tests carried out on a steel cantilever beam.
• The best results are obtained with a full finite element mass matrix and the expanded experimental mode shapes.

Operational modal analysis (OMA) is a technique that has been widely used on civil and mechanical structures in the last 10 years. As the force is unknown, mode shapes cannot be mass normalized from the responses used for modal identification. In the past few years, several formulations have been proposed to scale mode shapes using the mass-change method, which consists of repeating modal testing after changing the mass at different points of the structure where the mode shapes are known. This technique is easy to use in small systems but it has important drawbacks in medium and large structures due to the difficulties of applying masses of sufficient magnitude. In this paper a more simple methodology is proposed based on scaling the experimental mode shapes of a structure using the mass matrix of a finite element model. Two approaches are compared; one approach where the mass matrix is reduced to the set of measurement points using SEREP and a second approach where the experimental mode shapes are expanded to all DOFs in the model using a newly published principle called the local correspondence (LC) principle. The two approaches are compared in two case studies: a numerical example and a real experimental case. In the numerical example a finite element model was assembled in MATLAB, which was considered the experimental model, and then one thousand finite element models were simulated changing the material and the section properties of each element of the model, in order to study the accuracy provided by the different techniques. As regarding the experimental case, the scaling factors of a cantilever beam were estimated by the mass change method and with the equations that consider the mass matrix of the finite element model. The effect of discretization of the finite element model was studied by assembling several finite element models with different numbers of degree of freedoms.