This article investigates a new piezoelectric harvester for extracting energy from rotational motions. The harvester''s geometry is selected as a curve to increase the energy harvesting density. For its optimal performance across a wide range of rotational speeds, the harvester is excited by a non-linear magnetic force. Simultaneously with the rotation of the shaft and the attached magnet and creating a magnetic force, the magnet at the tip of the beam is excited, causing the curved piezoelectric element installed in the harvester to repeatedly deform and generate electrical energy. Electromechanically coupled differential equations are developed based on Hamilton''s principle, and the Lagrange equations and piezoelectric relationships are extracted and numerically solved. This research accurately calculates the force between the magnetic dipole and a new time and displacement-dependent correction factor. This model is used to investigate how the output voltage and power of the harvester are affected by the rotational speed, magnetic gap, number of excitation magnets, and circuit resistance in both the time and frequency domains. Most significantly, the theoretical modeling results are compared with experimental data obtained from constructing a prototype and conducting numerous tests. The results indicate that reducing the magnetic gap and increasing the number of magnets to a certain extent will increase the voltage and output power. The maximum power and maximum power density extracted during excitation with four magnets at a rotational speed of 986 rpm are 1523.5 μW and 11.37 μW/mm³, respectively, demonstrating the superior performance of the designed system.