A Comparison of Experimental and Theoretical Relations Between Young’s Modulus and the Flexural and Longitudinal Resonance Frequencies of Uniform Bars

The relations from which Young’s modulus may be computed from mechanical flexural and longitudinal resonance frequencies have been established by an empirical method using two sets of steel bars. Both sets contained rectangular and cylindrical specimens. For longitudinal vibration of cylindrical specimens, the agreement between the empirical curves and Bancroft’s corresponding theoretical relation was within experimental error if Poisson’s ratio for both sets is taken to be 0.292. For flexural vibrations, the agreement between the empirical curve and the corresponding theoretical relation developed by Pickett is also within experimental error for about the same value of Poisson’s ratio for the rectangular specimens of both sets; but for cylindrical specimens, the empirical values are somewhat lower than those predicted by the theory.