This work proposes the implementation of a multimodal and fully passive piezoelectric tuned vibration absorber that mitigates several resonances of a nonlinear structure. By extending a principle of similarity, an analogous electrical network is designed in order to reproduce the dynamics of the mechanical structure. Several electrical resonances are simultaneously tuned to the mechanical resonances, thus providing the equivalent of a multimodal vibration absorber from electromechanical coupling through an array of piezoelectric patches. Furthermore, the use of a nonlinear capacitor in the analogous network generates an autonomous adjustment of the electrical resonance frequencies when the structure reaches the nonlinear domain. The interest of this method is proved experimentally by mitigating vibration over a wide frequency range that covers the first three modes of a beam with cubic nonlinearity.