Investigating the multiple scales method based on a new scaling for energy harvesting from a double cantilever beam with internal resonance

Nowadays, energy harvesting by piezoelectric materials has become one of the important fields for researchers. In this research, energy harvesting from double cantilever beams is investigated by an approximate analytical solution based on the multiple scales method (MMS). First, the technique to solve the equations of motion by the method of multiple scales is explained, which is performed based on two different scalings. MMS based on scaling 1 is similar to those reported by other researchers, but MMS based on scaling 2 solution has been solved based on a new scaling. The results show that the MMS based on scaling 2 has higher speed and accuracy than the MMS based on scaling 1 with respect to the numerical reference solution. This is due to the correct selection of scaling parameters. Next, the experimental results are compared with the MMS based on scaling 2 results. Finally, the effect of adding a magnet on the bandwidth of the system is comprehensively investigated. The results show that by proper selection of system parameters, it is possible to have a system with wide bandwidth or high voltage peak depending on the values of the initial distance between the magnets and electrical resistance.