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Radially self-accelerating acoustic beams (RSABs) with rotating field distributions enable three-dimensional manipulation of particles. Nevertheless, the generation of desired RSABs is always a challenge. In this study, we derive a general form for the RSABs with a rotating acoustic field. We investigate the correlation between acoustic intensity and phase distribution of the RSAB in-depth via theoretical calculations. Artificial structure plates carved with Archimedean spiral slits are designed to produce two-component RSABs (TRSABs). It is found that the number of main lobes, rotational speed, and initial position of the TRSAB can be modulated by simply changing the number of arms, initial radius, and relative angle of the two sets of spirals. The experimental and numerical demonstrations confirm the ability of artificial structure plates to generate TRSABs. Finally, simulations are performed to calculate the acoustic radiation force on Rayleigh polydimethylsiloxane particles in a TRSAB. The work presented here could greatly benefit acoustic particle three-dimensional trapping and manipulation.