Elastic Strain Produced by Sudden Application of Pressure to One End of a Cylindrical Bar. II. Experimental Observations

Abstract

Measurements are presented which show that the elastic strain produced in a cylindrical bar by stepfunction end-loading corresponds closely to predictions of the theory presented in Part I. In particular, even at large distances from the end of the bar, there is an observable strain moving faster than the bar velocity determined by Young's modulus. The theoretical shape for the head of the pulse conforms to experiment, and the head is followed by oscillations having the correct periods and amplitudes. Second-mode oscillations appear at the times predicted and with the expected periods and amplitudes.

Saint-Venant’s Principle in Dynamics of Structures

“…Cherukuri and Shawki [96] confirm, by using finite difference solutions, the results obtained by Fox and Curtis [48], according to which beyond two diameters off the impacted end the type of BC (either mixed of pure) has no effect. The same conclusion, based on energy partition among propagating modes, was derived by Karp [74] with the aid of bi-orthogonality relations for an elastic strip.…”

“…They indicate that the initial disturbance, and the phenomena occurring just behind it, are of three-dimensional character and are relatively unimportant several diameters from the source." [47, p. 244] Fox and Curtis [48] devised an experiment aimed to confirm the asymptotic solution of step pulse excitation of a bar obtained by Folk et al [49] for strains far from the loaded end. Since the asymptotic solution is valid only beyond a distance of 10-20 diameters from the end, the experimental results do not include data for strains at distances smaller than 20D from the excited end.…”

Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism

“…Orazov (1983) investigated the validity of DSVP in an elastic semiinfinite waveguide with free or clamped surfaces subjected to displacement or stress on the near end and zero displacement at the remote end (at infinity). Cherukuri and Shawki (1996) confirm, by using finite difference solutions, the results obtained by Fox and Curtis (1958), according to which beyond two diameters off the impacted end the type of BC (either mixed of pure) has no effect. It is noted that in general, such conditions give rise also to non-evanescent waves radiating energy to infinity, resembling Sommerfeld's condition.…”

An Impact Test to Determine the Wave Speed in SHPB: Measurement and Uncertainty

“…Both are affected by dispersion (see [14], §2.5.4 and §8.4.1). Fox and Curtis [24] however introduced a change in variable ((t − x/c 0 )/x 1/3 , where x is the propagation distance) which "should reduce the beginning portions of all strain-time records to a single curve". This was also used by Kaul and McCoy [25].…”

“…This was also used by Kaul and McCoy [25]. It is interesting to note that "the time of initial rise should vary inversely as the cube root of the distance of travel" [24]: that is why the starting points of the wave are not suitable for the transit time-method.…”