The acoustic black hole(ABH) structure has a geometrical characteristic that becomes gradually thin from the root part to the tip, while maintaining the width. The smoothness criterion provides the basic principle for the vibration energy concentration at the tip of structure. In this work, an ABH structure with varying width is studied. The study concern is on the vibration and sound radiation characteristics according to the width change. The numerical simulations are performed on the several cantilevers: with constant thickness and width, conventional ABH with converging thickness, and converging ABH with converging thickness and width. The conventional ABH has more than 5 dB of transfer mobility compared to the cantilever, and the radiated sound pressure is large at the supersonic condition. The converging ABH has a transfer mobility of more than 10 dB larger than conventional ABH, and the radiation sound pressure is the smallest. The characteristics of the foregoing cantilevers are tested, and measured vibro-acoustic characteristics agree with the simulation. Numerical simulations are performed for parametric study of the ABH with varying width: diverging ABH, truncated converging ABH, and ABH with damping layer at the tip area. The diverging ABH has lower transfer mobility compared to conventional ABH, and the radiated sound pressure is large at low frequencies but small at high frequencies. The truncated converging ABH has the same transfer mobility as a conventional ABH, and the radiated sound pressure is largest. Attachment of a damping layer to the tip of the structure improves vibration damping performance, but does not depend on the area. The converging ABH has the same vibration damping performance as conventional ABH by only attaching a small damping layer. The ABH with varying width has a merit in its manufacturing difficulty, weight, and size. It is thought that the studied ABH structure with varying width can find its application on the area vibration amplification, sound reduction, and sound radiation.