<p>The critical coupling condition of acoustic black hole structures, which leads to a zero-reflection coefficient, can significantly enhance the energy absorption efficiency of the system. Traditional enumeration-based methods for designing these critical coupling conditions are inefficient and struggle to pinpoint them precisely at target frequencies. This paper proposes a general optimization framework for designing critical coupling conditions of acoustic black hole beams using the piezoelectric shunt damping. To support the design process, the semi-analytical model of the reflection coefficient of flexural waves is derived via a hybrid wave/Rayleigh-Ritz method. Reflection coefficients at single and multiple frequencies are minimized using single and multiple resonance shunt circuits, respectively. Design results demonstrate that multiple critical coupling conditions can be achieved at specified frequencies by adjusting the shunting inductors and resistors. Additionally, numerical simulations show that the multi-resonance shunt circuit can effectively achieve a specific number of critical coupling conditions.</p>