Τhe piezoelectric energy harvesting from nonlinear vibrating structures has greatly attracted the attention of scientific community over the last decades, as it seems to provide one of the more promising ways for high electromechanical energy conversion. Current study deals with the development of a robust and accurate numerical tool capable of modelling and designing piezoelectric structures undergoing severe nonlinear vibrations. Specifically, a coupled multi-field generalized nonlinear mechanics framework for piezoelectric beams and plates subjected to initial stresses and large rotations, extended to include passive external electric circuits in order to predict the dynamic response of the structure and the power generated at the external resistive load. An experimental setup was also developed providing great correlations with the numerical results in case of a vibrating axially prestressed composite beam under the prebuckling regime. At the end, a computational investigation was performed studying the complex dynamic behavior of the piezoelectric beam, in the postbuckling regime. The model successfully captures the measured energy harvesting response of the beam including additional effects induced by the asymmetric configuration of the piezoelectric film.