Relation between Strain and Velocity in Resonant Vibration

In a recent paper Hunt examined the relation between strain and velocity in forced resonant motion for a wide variety of elastic bodies. He found that the maximum strain was always proportional to the ratio of the maximum vibratory velocity to the velocity of sound in the body and that the constant of proportionality appeared to be constrained to remain in a narrow range extending about an order of magnitude. Similar results were obtained independently by Ungar [see E. E. Ungar, “Maximum Stresses in Beams and Plates Vibrating at Resonance,” J. Eng. Ind. Trans. ASME 84B, 149–155 (1962)] for uniform beams and plates. In this note a similitude argument is used to establish the form of these results. It is also pointed out that because of both strain and velocity concentrations the range of possible values for the proportionality constant can be very much wider than the range found by Hunt.