Abstract: 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.
