The dynamic responses of TTRs in the deep water were studied considering coupled the random heave of platform and VIV. The random parametric excitation is set up considering the random motion of platform. The vortex lift force is calculated with the time-varying lift coefficient based on the Van der Pol drafting oscillator model. The equation of coupled VIV and parametric excitation vibration (PEV) is established and the program of solving coupled PEV and VIV is developed. The coupled dynamic response induced by random parametrical excitation and VIV is calculated for the TTR of Truss Spar, and the dynamic characteristics are investigated. The results show that the random parametrical excitation can magnify the dynamic response of TTRs, and it will change the main frequency of TTRs vibration.

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