The propagation of a longitudinal elastic strain pulse in a wide rectangular bar is considered on the basis of approximate plane-stress equations of motion. Asymptotic expressions are obtained which, for large distances of travel, describe the pulse propagation in a semi-infinite strip with stress-free lateral edges, subject to the conditions that a uniform normal stress with a step-function time dependence is applied to the end and that the end is laterally constrained. Particular emphasis is given to describing the warping of plane sections during passage of the strain pulse.
The plane-stress theory presented in Part 1 is shown to predict qualitatively the warping of plane sections observed in transient fringe patterns obtained using birefringent coatings and in dynamic photoelastic pictures obtained in other investigations. Measurements using conventional techniques are described in which wide rectangular bars were subjected to a longitudinal step-function pressure loading produced by a shock tube. Comparisons show that the gross features of the experimental records for the head of the pulse are qualitatively predicted by the theory. Both theory and experiment show that short-wavelength, second-mode disturbances arrive very early. Experimentally it is observed that these disturbances are accomplished by thickness-mode activity which cannot be accounted for by the plane-stress theory.
Longitudinal Strain Pulse Propagation in Wide Rectangular Bars: Part 1—Theoretical Considerations
