Estimation of Rotational Degrees of Freedom Using Spline Functions
Date
2011-01-25
Authors
Ng'andu, Namasamu Alvert
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Abstract
Structural Dynamics Modification work often requires the inclusion of rational degrees of freedom in the modal data. These are not usually directly measurable because suitable transducers are not yet readily available. This work investigates the estimation of rotations from computed or measured translational data using spline functions for curve and surface fitting.The estimation accuracy is found to depend on a number of factors including the spatial distribution of data points, the level of error in the original data and the degree of smoothing applied. Analysis on beam and plate structures show that an interpolating spline gives the best results on error-free data, but that some degree of smoothing is required when dealing with noisy data. It is shown that structural boundary conditions provide a useful basis for judging the level of smoothing required. For clamped structures, the approximation which minimises the slope at the clamped boundary is found to be acceptable . For free boundaries, the approximation which minimises the second derivative of the fit function there gives the best overral results. The accuracy of the rotation estimates is found to depend on the general level of error in the origainal data but is influenced to a much lesser extent by the distribution of error between data points. The error in the rotation from data with a maximum error of 1% of the largest modal translation are shown to be generally below 10% provided there are atleast two maesurement points between modal lines for the highest mode of interest.As the consequence of errors in the rotations, the errors in the structural dynamics modification predictions are found to be broadly less than 5% when rotational errors are of the order of 10%. Further, it is shown that estimates of rotations which are within 20% of the correct value yield frequency prediction errors which are under 10%. Thus it is concluded that the proposed method is a quick ,simple, versatile and effective tool for estimating rotations yielding comparable performance with existing methods on similar structures. An addition benefit is that there is no requirement for performing finite element analyses of the structure.
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Keywords
Rational degrees of freedom-modal data , Spline functions for curve and surface fitting