Abstract
The propagation of thermally generated stress waves in a dispersive elastic rod was investigated both experimentally and analytically.
In the experimental investigation, the end of a circular colored-glass rod was heated very rapidly by the deposition of luminous energy from a Q-switched ruby laser. The light from the laser was directed parallel to the axis of the rod and deposited on the polished end of the rod. The depth of deposition was of the same order as the radius of the rod. The length of the energy pulse from the laser was 20 nsec. This results in heating at such a rate that it can be considered as instantaneous when compared to the mechanical response of the material used. The resulting stress wave was measured using a thin quartz crystal in a Hopkinson pressure-bar arrangement.
Radial inertia precluded the use of the simple wave equation; Love's modified wave equation was used to describe the motion. The thermoelastic problem was reduced to a homogeneous partial differential equation with appropriate initial and boundary conditions which is solved by the separation of variables technique. The experimental results are in good agreement with Love's theory. The amplitude of the stress waves was found to be directly proportional to the total energy deposited.
The very short stress pulses generated by Q-switched laser deposition on the end of the thin rod gave rise to the higher modes of longitudinal wave propagation. The existence of wave propagation in a thin rod at near dilatational velocities was experimentally confirmed. It is concluded that the experimental techniques developed can be used to model stress-wave generation due to electromagnetic-energy depositions. Also, laser deposition provides an efficient means for generating the higher modes of longitudinal wave propagation in thin rods.
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This work was supported by the U. S. Atomic Energy Commission at University of California, Lawrence Radiation Laboratory, Livermore, Calif.
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Percival, C.M., Cheney, J.A. Thermally generated stress waves in a dispersive elastic rod. Experimental Mechanics 9, 49–57 (1969). https://doi.org/10.1007/BF02326674
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DOI: https://doi.org/10.1007/BF02326674