We present a piezoelectric nonlinear energy sink (NES) framework for attenuation of nonlinear vibrations in a cantilever beam. The NES acts as a nonlinear piezoelectric shunt that implements linear components along with op-amp and multiplier nonlinear circuit elements to enable NES dynamics in the electrical domain. The piezoelectric NES was recently shown to provide wideband vibration attenuation in a cantilever undergoing linear mechanical vibrations. Following these recent efforts, we implement the piezoelectric NES to broadband attenuations of nonlinear vibrations of a thin cantilever beam. The model makes use of the linear modal parameters for the bimorph cantilever (PZT-5H patches connected in parallel) for the fundamental natural frequency obtained using the Rayleigh-Ritz method. Circuit parameters for the linear bimorph cantilever target frequency are obtained using harmonic balance analysis. The performance of the piezoelectric NES for broadband attenuation of nonlinear vibrations is evaluated and simulations are performed by modifying the structure (with a tip mass to move its resonance frequency) without tuning the NES circuit components. Simulations are presented for a range of acceleration levels and frequency ranges to demonstrate the broadband attenuation of the nonlinear vibrations using a single circuit configuration.