Ambient energy in the form of mechanical kinetic energy is mostly considered waste energy. The process of scavenging and storing such energy is known as energy harvesting. Energy harvesting from mechanical vibration is performed using resonant energy harvesters (EH) with two major goals: enhancing the power scavenged at low frequency sources of vibrations, and increasing the efficiency of scavenging energy by increasing the bandwidth near the resonant frequency. Toward such goals, we propose a piezoelectric EH of a composite cantilever beam with a tip magnet facing another magnet at a distance. The composite cantilever consists of a piezoelectric bimorph with an extended polymer material. With the effect of the nonlinearity of the magnetic force, higher amplitude can be achieved because of the generated bi-stability oscillations of the cantilever beam under harmonic excitation. The contribution of the this paper is to demonstrate lowering the achieved resonant frequency down to 17 Hz compared to 100 Hz for the piezoelectric bimorph beam without the extended polymer. Depending on the magnetic distance, the beam responses are divided to mono and bi-stable regions, for which we investigate static and dynamic behaviors. The dynamics of the system and the frequency and voltage responses of the beam are obtained using the shooting method.