DETERMINATION OF STATIC STIFFNESS OF MECHANICAL STRUCTURES FROM OPERATIONAL MODAL ANALYSIS

The experimental determination of static stiffness is an important task in structural design. The two current methods include clamping the structure, applying pre-defined loads, and measuring the displacements, or performing EMA and interpolating the frequency response function to 0 Hz. Both methods require high experimental effort in laboratory setup. This paper presents a new idea, whereby the structure is measured during normal operating conditions, and OMA is used to reconstruct the stiffness matrix. The challenge of unsealed eigenvectors in operational modal analysis is overcome using mass modification scaling, whereby the structure is measured at a baseline and mass modified condition. Three different models were investigated: a basic discrete model, a laboratory ladder frame and a car body. Investigations were conducted into the effects of the position and magnitude of the mass modification, the number of assigned degrees of freedom of the system, the mode shape error effect and the effect of modal truncation. Key findings include significantly reduced reconstruction errors when the mass modification is a scalar multiple of the mass matrix. It was' also found that the accuracy of the reconstructed stiffness matrix is strongly dependent on the uncertainty in the eigenvectors, as well as how the model is truncated. A finite element model of the ladder frame was used to test different modification strategies and to compare to results from operational modal analysis. A key finding which was not revealed by the discrete model was the importance of including the RBM in the stiffness matrix reconstruction. Finally experimental modal analysis and operational modal analysis were conducted on an Audi TT. The reconstructed stiffness matrices, bending and torsion static stiffness are then compared and discussed.