A method of determining modal residues using an improved residual model and least squares
A new approach to determining mode vectors is presented which uses predetermined global parameters and an improved residual model to iteratively determine modal residues. The motivation for such a technique is to determine modal parameters rapidly so that, as data acquisition techniques become faster, more structural degrees of freedom can be measured without significantly slowing down the parameter estimation process.
The technique requires an accurate determination of the global parameters of natural frequency and damping by means of an FRF curve fit. More than one structural point is recommended to determine the global parameters since they will be used in determining the mode vectors. A structurally damped curve fitter which uses one or two FRFs is described and can be used for determining the global parameters. Examples of curve fitting simulated and measured data are presented and a comparison is made to a commercially available curve-fitter.
Once a frequency range-of-interest is selected, frequencies will be chosen at which the mobility is measured using sine excitation. The in-range modal response is represented by a matrix-vector product where the vector contains the residues for the modes of interest. The out-of-range modal content is also represented by a matrix-vector product and forms the improved residual model. The residual content is removed from the measured mobility by an iterative technique which allows for an accurate determination of the residues of interest.
An evaluation of the technique is carried out by simulating a dynamic system including the shaker and power supply. The simulated system is closely modeled after a real system used to evaluate the technique on experimental data. Convergence rates are shown for cases of close modes, low amplitude modes and errors in the global parameters. The results of using the technique on experimental data shows that convergence typically occurs in under 15 iterations. Regenerating the FRF from the modal parameters shows close agreement to the original FRF and better agreement than the regeneration from modal parameters derived from a commercially available curve fitter.>