Identifying multiple axial load patterns using measured vibration data

Multiply redundant frames possess as many linearly independent axial load patterns as their degree of static indeterminacy. Any state of equilibrium can be described as the linear sum of these axial load patterns. As a frame is loaded in the multiple patterns, the changes in member axial loads affect the frame frequencies and mode shapes in a complicated way through geometric stiffening. By representing this behaviour in a finite element model (FEM), it is possible to measure the dynamic characteristics of a physical frame, update the axial loads in the FEM until the difference between measured and model frequencies is minimised and thus infer the member axial loads. What is updated is the factors on the axial load patterns and this is done iteratively using traditional model updating (Newtonʹs method). Thus, all member axial loads can be identified using just a set of updating parameters equal in number to the degree of static indeterminacy. A numerical simulation and, for the first time, an implementation on a physical realisation of a multiply redundant frame using measured vibration data are presented herein and show that member loads can be identified to an encouraging degree of accuracy. Beneficial strategies such as formulating the problem on an orthonormal basis for the axial load patterns and a ‘modal tagging’ scheme, which helps to conserve the strength of the necessary, but otherwise typically compromised, pairing of mode shapes of the FEM to those measured, are discussed.