Discussion. The Flow Induced Oscillation of Marine Structures.

Abstract

There are one or two points of correction and slight elaboration which I would like to make to the text of the Paper. I have been asked questions about equations (7)-(12). These are dimensionally stable provided M is recognized as a unit of mass and that E is recognized as a unit of force. There is, however, a dimensional error in Table 1. The lines for M 1 and 2/pD2 have unfortunately been left in units of weight. The later non-dimensional lines are, of course, correct, because the missing g has been cancelled out on the top and bottom lines, so the lines in which you have probably been most interested are still absolutely correct.107. The values of K,, towards the bottom, have been achieved by using an assumed value for 6 , of 0.07, which was taken at the time to be as good a guess as could be made of a value typical of the sort of structures which we were considering. Mr KingI would like to comment on Fig. 16. While the fundamental pile frequency can be fairly readily calculated the sway loads are more ephemeral. The fundamental sway frequencies are included in the diagram to build up a complete picture. All figures on the outer two lines have been calculated from actual results, but the others, referring to sway, are guesstimates, as is the uncoupled sway frequency in Fig. 15. 109.In 5 85 reference is made to the comparison between the direct determination of the eigenvalues by the QL method and the results of the more elaborate Sturm sequence analysis; Table 2 gives actual figures. The comparison of cols 1 and 2 appeared satisfactory, but at the time we were working fast and did not do a direct comparison of identical cases. The fit is not as good as it might be, particularly on the second mode. The pile mode was not located exactly by the Sturm sequence, hence the query. Since then a colleague, Mr Kent, has done more work (cols 3 and 4) introducing extra degrees of freedom into the centre of the piles. Introducing a horizontal rotational degree of freedom (col. 4) gave a much closer fit. Had we been able to include both 8, and 0, rotations the 'fit' would probably have been exact.110. This points to the danger of oversimplification. While calculations should be simple, if possible, this fact led to a 15% overestimate. If, as in this case, a safe upper bound is to be established, this could be a serious error.