Abstract: In order to study the vibro-impact response of an acoustic black hole (ABH) beam, a semi-analytical dynamic modeling and analysis method of response characteristics is proposed. Firstly, the motion equation of the system is established based on Euler-Bernoulli beam theory and Rayleigh-Ritz method, and the nonlinear impact force and contact stiffness are derived according to Hertz contact theory. Afterwards, the first-kind Chebyshev polynomials are used to construct the modal function, and the natural frequency and mode shape function of the system are obtained by solving the eigenvalue problem. On this basis, the Duhamel integral and time-stepping iteration method are used to calculate the vibro-impact response. The influences of key parameters such as the number of terms in the polynomial and the boundary spring stiffness on the natural frequency are studied. Comparison with experimental results shows that the proposed method can accurately solve the vibration response of ABH beams under continuous collision. Through numerical calculation, the influence of impact position and gap, base motion excitation frequency and amplitude on the vibro-impact response is analyzed. The results show that within the parameter range studied, the deflection of impact position and the impact force magnitude increase with the increment of the impact position and the base motion excitation amplitude, and increase first and then decrease with the increment of the impact gap and the base motion excitation frequency. By comparing with the uniform beam, it is verified that the ABH beam has advantages in piezoelectric energy harvesting and damping vibration reduction under impact.