Governing Equations and Numerical Solutions of Tension Leg Platform with Finite Amplitude Motion

It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

Analysis of Spacecraft Relative Motion and Applicability of Hill's Solution

研究了空间飞行器编队中最具基础性的问题之一,即相对运动的解析表达及Hill方程的适用条件。通过建立相对运动的通解公式,针对不同性质的初值深入地分析了其相对运动轨迹的本质特征,并给出了Hill方程的适用条件。此外,文中还给出了一个新的编队设计简化公式。

Two-time scales inner solutions and motion of a geostrophic vortex

Based on the authors' previous work, in this paper the systematical analyses on the motion and the inner solutions of a geostrophic vortex have been presented by means of thematched asymptotic expansion method with multiple time scales (S/gh001/2 and α S/gh001/2) and space scales. It has been shown that the leading inner solutions to the core structure in two-time scales analyses are identified with the results in normal one-time scale analyses. The time averages of the first-order solutions on short time variable τ are the same as the first-order solutions obtained in one normal time scale analyses. The geostrophic vortex induces an oscillatory motion in addition to moving with the background flow. The period, amplitude andthe deviation from the mean trajectory depend on the core structure and the initial conditions. The velocity of the motion of vortex center varies periodically and the time average of the velocity on short time variable τ is equal to the value of the local mean velocity.

A unified law of motion of lithospheric plates and the driving mechanism

From observed data on lithospheric plates, a unified empirical law for plate motion,valid for continental as well as oceanic plates, is obtained in the following form: The speedof plate motion U depends linearly on a geometric parameter T_d, ratio of the sum of effectiveridge length and trench arc length to the sum of area of continental part of plate and total areaof cold sinking slab. Based on this unified law, a simple mechanical analysis shows that, themain driving forces for lithospheric plates come from push along the mid-ocean ridge andpull by the cold sinking slab, while the main drag forces consist of the viscous traction beneaththe continental part of plate and over both faces of the sinking slab. Moreover, the specific-push along ridge and pull by slab are found to be of equal magnitude.