Flow-Induced Motion (FIM) of elastically-supported oscillators with "circle-polygon-attachments"sections are experimentally investigated in a water channel to examine the effects of combined sections on hydrokinetic energy harnessing. The incoming flow velocity considered is U = 0.55 – 1.35 m/s, corresponding to reduced velocity Ur = 5.3 –13. A controllable magnetic damping system is applied to change the total damping ratio (ζtotal) of the flow-induced motion energy conversion system (FIMECS) by varying excitation voltages VB (VB = 0 – 108 V, ζtotal = 0.037 – 0.398). Particularly, to calculate fluid force with experimental results, a torque sensor is introduced into FIMECS. The amplitude, frequency, fluid force, active power and efficiency are analyzed. Results suggest that an oscillator with symmetric sharp attachments and no vortex reattachment is conducive to galloping with self-excitation under large damping, and the circle-T-attachments oscillator is optimum. Its best branch for energy conversion is the galloping branch, the peak of active power is Pharn is 19.28 W and the peak of efficiency is ηharn is 26.22% (VB = 99 V, Ur = 11.28). Under the same condition, the circular-T-attachments oscillator has a better energy conversion capacity than the existing ones (triangular prism).