The acoustic characteristics of 2D single-oscillator, dual-oscillator, and triple-oscillator acoustic metamaterials were investigated based on concentric ring structures using the finite element method. For the single-oscillator, dual-oscillator, and triple-oscillator models investigated here, the dipolar resonances of the scatterer always induce negative effective mass density, preventing waves from propagating in the structure, thus forming the band gap. As the number of oscillators increases, relative movements between the oscillators generate coupling effect; this increases the number of dipolar resonance modes, causes negative effective mass density in more frequency ranges, and increases the number of band gaps. It can be seen that the number of oscillators in the cell is closely related to the number of band gaps due to the coupling effect, when the filling rate is of a certain value.