Scanning Laser Doppler Vibrometer measurements for vibrating beam model updating

The response mode shape of a uniform beam is, in general, a polynomial function of distance along the beam, of which, as is shown, only four of the polynomial coefficients are independent. Ratios involving the other coefficients can therefore, in principle, be used to determine its density/stiffness ratio, and to confirm that it is, indeed, uniform. A scanning Laser Doppler Vibrometer is particularly useful for measuring mode shapes because the required polynomial coefficients can be derived directly. Practical trials on uniform and non-uniform beams have shown some promise. The lowest frequency modes of vibration are not normally satisfactory, because the mode shapes do not involve higher polynomial components. The process is one of limited accuracy and is affected by numerical instabilities, the paper includes some investigation of these problems.