Abstract: Objectives The acoustic black hole (ABH) structure exhibits wide-frequency wave-gathering performance, but it only functions when the size of the acoustic black hole exceeds the wavelength of the bending wave, indicating that the acoustic black hole has a cutoff frequency. To enhance the vibration suppression performance of the acoustic black hole structure in the low-frequency range below the cutoff frequency, a periodic acoustic black hole beam model incorporating a piezoelectric structure is proposed. Methods The virtual spring technique is employed to handle periodic boundary conditions, and the equivalent medium method is used to equate piezoelectric structures with external circuits to homogeneous materials. This forms the virtual spring energy method, which can be used to solve the vibration of periodic piezoelectric acoustic black hole beams. The accuracy of this method is verified through the finite element method. Results The periodic arrangement of acoustic black hole structures can form a vibration attenuation zone below the cutoff frequency; furthermore, by designing appropriate external circuit parameters, the vibration amplitude of the structure can be suppressed at a specified frequency.Conclusions Finally, a periodic piezoelectric acoustic black hole beam with low-frequency broadband vibration suppression capability can be formed, providing insights into improving the low-frequency vibration suppression performance of acoustic black hole structures.