Conventional harvester systems usually have linear behavior. One of the great matters in these systems is that energy is harvested in a low frequency bandwidth. In this study, double cantilever beams are used for energy harvesting. Two beams are connected at the end of them through a linear spring. The bimorph piezoelectric patches are attached to the top beam using double-sided tape for energy harvesting. A pair of the magnet is applied for adding a nonlinear effect to the system. One of the magnets is mounted at the end of the bottom beam, and another is on the system's base. The whole system is designed based on the internal resonance phenomenon. Base excitation of the acceleration type is used for exciting system. The governing equations of the system's vibration are derived using the energy method by the Euler-Bernoulli assumptions. Next, the system is discretized by the assumed modes approach. Two cases are investigated, including the absence and the presence of the magnetic force. In the absence of the magnetic force, the magnet mounted on the system's base is removed, and thus the system shows a linear behavior. In the presence of the magnetic force, the nonlinearity and internal resonance effects on the energy harvesting are investigated. The obtained equations of motion are solved with numerical and method of multiple scales (MMS) solutions. For the first time in this study, MMS is derived based on new scaling for a two-degrees-of-freedom system with quadratic and cubic nonlinear terms. MMS solution based on our proposed scaling is more accurate than the MMS solution based on conventional scaling that others have used. It predicts the frequency response peaks and their corresponding frequencies more precisely compared to the numerical solution. A test rig was designed and fabricated for experimental studies. The experimental results show that the performed modeling is in good agreement with the experimental data. The obtained results show that in the presence of the magnetic force, energy is usually harvested in a broader frequency bandwidth in comparison to the absence of magnetic force. However, its peak voltage can be higher or lower than the absence of the magnetic force. Depending on need, the system's parameters in the case of the presence of magnetic force can be selected in such a way that the bandwidth, or peak voltage, or both increase compared to the absence of magnetic force. Keywords energy harvesting, double cantilever beams, nonlinear vibration, internal resonance, assume mode, method of multiple scale