Summary
The transient heave response of a freely floating cylinder with given initial conditions is obtained by a simultaneous time-domain solution of the fluid-motion and rigid-body dynamics problems. Volterra's method is used to derive the integral equation associated with the fluid motion. It is shown that the unit initial-velocity response is simply the time-derivative of the unit initial-displacement response multiplied by one half of the infinite-fluid virtual mass of the cylinder. Numerical evaluation of integrals related to the unsteady waterwave Green function is facilitated by expressing them in terms of the complex error function. Results for the transient motion of semi-circular, triangular, and rectangular cylinders are presented and discussed. Experimental measurements for the case of a semi-immersed circular cylinder agree excellently with the theoretical calculations.
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Yeung, R.W. The transient heaving motion of floating eylinders. J Eng Math 16, 97–119 (1982). https://doi.org/10.1007/BF00042549
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DOI: https://doi.org/10.1007/BF00042549