Improved Frequency Equations for Calculating the Young’s Modulus of Bars of Rectangular or Circular Cross Section from Their Flexural Resonant Frequencies

Abstract

Abstract New analyses of the frequency equations relating Young’s modulus to the flexural resonant frequencies of bars of uniform rectangular, square, or circular cross section have expanded the practical slenderness ratio range, over which these equations can be used, while maintaining the precision of the older equations. The original experimental data obtained on steel bars of cylindrical, square, and rectangular cross sections were also used here.