The so-called " acoustic black hole " effect (ABH) is a passive vibration control technique based on the flexural waves properties in thin structure of varying thickness. A usual implementation consists in using a plate with tapered extremity with a power-law profile, covered with a thin damping layer. The inhomogeneity of the structure leads to a decrease of flexural wave speed and an increase of their amplitude, therefore resulting in an efficient energy dissipation if damping layer is placed where the thickness is minimal. The manufacture of an efficient extremity is difficult because of the small thickness, and often generates imperfections and tearing. Moreover , previous works suggest multiple that flexural modes are propagating across the width of the ABH tip. A model of an ABH multimodal waveguide taking into account an imperfect termination is developed. It shows that an elementary imperfection can affect the reflection coefficient of the extremity and reduce it. Scattering and propagation properties of the extremity are also studied. An incident mode excites several modes that are localised in the tapered region and local resonances explain the drops in the reflection coefficient. Experimental evidence of the influence of the imperfection on the reflection coefficient is provided. A key result of the paper is that manufacturing imperfections are not detrimental to the ABH effect.