A Critical Assessment of the Cantilever Beam Method for the Determination of Dynamic Young's Modulus

Abstract

Abstract The application of a noncontacting optical transducer for the measurement of flexural resonant frequencies and normal mode shapes of a cantilever beam is described. Results on the resonant frequencies of cantilever beams, gripped at the fixed end by a vise, are compared with the Bernoulli-Euler and Timoshenko beam theories. Although the mode shapes agree well with the theories, there are large discrepancies between the experimental variation of resonant frequency with inverse slenderness ratio and that predicted by the theories. These discrepancies are attributed to imperfect clamping. It is concluded that for accurate Young's modulus calculations from the measured resonant frequencies of cantilever beams, tests must be restricted to long slender beams. For beams which cannot be fabricated to meet this criterion, an empirical method is presented which yields Young's modulus to within ±3 percent on the specimens tested. For increased accuracy the free-free reasonant beam method should be used.