This work describes the application of a piezo-shunt absorber for robust vibration suppression on a cantilever beam with two piezoelectric patches. The cantilever beam is submitted to harmonic excitation forces containing several harmonic components. In particular, the implementation of the Resistance-Inductance-Capacitance circuit is employed for vibration absorption at the first four mode-shapes of the beam and, by using the Frequency Response Function of the arrangement, the modal parameters of such dominant mode-shapes can be used to synthesize an adaptive-like piezo-shunt absorber for damping injection at specific modes. Some experimental results are presented to validate the good dynamic performance of the piezo-shunt absorber for adaptive damping injection to the cantilever beam.