Typical vibrational harvesters using a high-permeability beam in a cantilever configuration exploit the field generated by a couple of counter-polarized permanent magnets facing the vibrating strip at the free end. Such a canonical position of the magnets does not permit one, however, to highlight the importance of the bias field pattern. A proof of concept archetype is realized in this work, by which the influence of the magnetization profile along the length of the vibrating ferromagnetic beam is put in evidence. It demonstrates, in particular, that significant variations, even by a factor of three, of the output power can be obtained by a modification of the magnets arrangement. We discuss in this paper the behavior of a cantilever-based generator, where a Fe-Co high-permeability beam is made to vibrate inside an inhomogeneous magnetic field generated by permanent magnets, whose arrangement can modified in order to vary the magnetization profile along the vibrating laminae. The effects of such a profile are measured and analyzed by means of a simple 2D numerical model, showing that the generated power can be enhanced by conveniently acting on the magnets configuration. The measurements show that, with a host acceleration of 5g rms (g = 9.81 m/s2), a 6.72 mW time average output power is obtained for operating frequencies around 60 Hz.