COMMENTS ON “TRANSIENT AXISYMMETRIC STRESS WAVE PROPAGATION IN WEAKLY COUPLED LAYERED STRUCTURES”
✍ Scribed by M. El-Raheb
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 98 KB
- Volume
- 204
- Category
- Article
- ISSN
- 0022-460X
No coin nor oath required. For personal study only.
✦ Synopsis
The trapezoidal forcing function shown in Figure 3(a) of reference [1] has a duration of 7•5 ms. However, transient stress histories in Figures 16171819show that the response pulse of first arrival (before any reflections occur) has a width of approximately 20-25 ms. This indicates that the response is inconsistent with the time interval of the forcing function. The authors must have used a different forcing function than the one shown in Figure 3(a) to perform the numerical calculations.
Also, Figures 16 and18 indicate that during first arrival, results from the integral method have a magnitude smaller than results from the finite element analysis and not larger. This contradicts the statement in the third paragraph of page 410: ''In early times, the maximum stress values for s zz of the integral transform results are generally approximately 5% larger than those of the finite element analysis''. This sentence should be rectified.
Finally, dispersion lines of ''k'' versus ''v'' in Figures 4 and5 show that lines corresponding to different modes cross. This is inconsistent with the linearity of the problem which requires solutions to be unique; i.e., the dynamical system cannot assume two different states at the same frequency. In fact, these lines approach each other but never cross. This ''almost coalescence'' is characteristic of other problems in linear dynamics and acoustics. A note on this important issue is necessary for clarity.