Dynamic tension of cables in a random sea: analytic approximation for the envelope probability density function

Abstract

When a random sea is filtered by the transfer function of a floating system a narrow banded excitation at the suspended end of risers and mooring lines is, in general, obtained. Using then this gaussian narrow banded signal as input and the algebraic expression for the dynamic tension derived in Aranha and Pinto [Dynamic tension in risers and mooring lines: an algebraic approximation for harmonic excitation (2001), submitted], the probability density function (pdf) for the envelope of the dynamic tension in the risers and mooring lines can be analytically approximated. The obtained expression differs, in general, from the Rayleigh distribution and it is compared, in the present work, with numerical results in the time domain, the agreement being fair even in the cases where the risers become dynamically compressed. From a more practical point of view, given then the transfer function of the floating body and the wave energy spectrum, the statistics of the dynamic tension can be estimated directly from some few integral parameters of the static configuration introduced in Aranha and Pinto [Dynamic tension in risers and mooring lines: an algebraic approximation for harmonic excitation (2001), submitted], avoiding the simulation in time of the riser's dynamics.