The Acoustic Black Hole (ABH) phenomenon exhibits obvious wave retarding and energy focusing when bending waves propagate inside a structure whose thickness is tailored according to a power-law relationship. These appealing features offer new opportunities for effective wave manipulation and energy harvesting (EH). Using a PZT-coated ABH beam as a benchmark, this paper proposes an improved semi-analytical model based on Timoshenko deformation assumption. The model considers the high-frequency shear effects of the beam alongside the full electromechanical coupling between the host beam and the PZT patches. Comparisons with FEM and experimental results show the model offers improved accuracy as compared with the previous Euler-Bernoulli model. This improved accuracy, which can be achieved through including a small number of decomposition terms relating to the rotational angle of the cross section of the beam, proves to be necessary to truthfully describe the increasing dynamics of the ABH beam, especially near the tip region, which is a critical area for EH. Meanwhile, the model allows straightforward integration of any external electrical modules, conducive to studies such as their interaction with the host ABH structures as well as the design of efficient energy harvesting systems.