Torsional Resonance Vibrations of Uniform Bars of Square Cross Section

Relations by which the shear modulus may be computed from the fundamental and overtones of the torsional resonance frequencies of square bars have been established empirically. The results are analyzed in terms of a proportionality factor, R, defined by the equation G = (2l f(n)/n)(2)ρR. R is found to increase with increasing cross section to length ratio. Also, the overtones are less than integral multiples of the fundamental by an amount which increases with increasing cross section to length ratio.