A continuous-scan LDV is a convenient means for measuring the response mode shape (ODS) of a vibrating surface, particularly in view of the fact that the ODS is automatically derived as a spatial polynomial series. Second spatial derivatives of the deflection equations are therefore easily derived, and these should, in principle, give curvature equations from which, for a beam or plate of known cross-section, stresses and strains can be obtained directly. Unfortunately, the stress and strain distributions depend critically on higher terms in the original ODS series, which are not accurately measured. This problem can be avoided by a method described here, which enables accurate stress and strain distributions to be derived, from a straight-line LDV scan along a uniform beam, using only five terms in the mode-shape polynomial series. A similar technique could be applied to uniform plates but the analysis and the governing equations are rather more complicated.
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