Postgraduate, School of Naval Architecture and Maritime, Zhejiang Ocean University

Postgraduate, School of Naval Architecture and Maritime, Zhejiang Ocean University

Schematic of a 2-noded straight tether element experiencing rigid body motion in NPFEM

1.  Dynamic modelling of an elastic pendulum using 3-DOF Nodal Position Finite Element Method (2020.02~2020.06)

    At the first beginning, I preliminary learn the finite element method by G. Q. Li. (2015), in which the 3-DOF Nodal Position FEM was used to model the motion of a tether spacecraft. Based on the mastering of numerical algorithms, a FORTRAN based program was developed. 

    The oscillation of an elastic pendulum was investigated in this program. First,  the simple pendulum motion with an initial velocity at the free end was tested. Then, the results of free-falling elastic pendulum was carried out. The results are shown as follows.

P.s. : The detailed expressions and matrixes can be seen in G. Q. Li. (2015) (Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration)

Fig. 1 Schematic diagram of elastic pendulum
Table. 1 Main parameters of the pendulum
Case 1. Simple pendulum motion with an initial velocity at the free end
    In this case, one end of the pendulum was fixed to a pin joint to restrict the motion, and a horizontal velocity along the positive direction of the Y axis of 3 m/s was applied to the free end. The simple simulation animation can be seen as follows, the time of simulation was 20 s.
Fig. 2 A simple pendulum motion with an initial velocity
Case 2. Free-falling of the elastic pendulum
    In this section, a horizontally orientated elastic pendulum in air is arranged initially to have one end connected to a fixed pin while the other end is free for induced motion, the time of simulation was set to be 20 s.
Fig. 3 Free-falling of an elastic pendulum in the air
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