Energy Harvesting from the Greater Jakarta Commuter Rail Vibrations Using Piezoelectric Cymbal Transducers: Euler-Bernoulli Beam Analysis with Finite Difference Runge-Kutta Simulation

Harvesting energy from railway-induced vibrations poses challenges due to complex dynamic loads and the need for efficient conversion mechanisms. This study addresses these by developing a semi-empirical model for energy harvesting using piezoelectric cymbal transducers (PCTs), applied to the Jabodetabek electric rail commuter (KRL) system. To model rail deflection under a moving passenger-loaded train, we use Euler–Bernoulli beam equations combined with the finite difference method and Runge-Kutta techniques in MATLAB. The model identifies a natural frequency of 2.60 Hz for the rail beam and shows that a train speed of 1.5 m/s induces a contact force frequency of 2.50 Hz, creating near-resonance. This increases rail deflection to 0.55 mm and generates a peak contact force of 70.00 N on the PCT. As an original contribution, we show that under these conditions, the PCT can produce a voltage of 46.51 V and 0.25 mW power output at frequencies above 4 Hz. These findings demonstrate the potential of PCTs for sustainable energy harvesting to support self-powered monitoring or signaling systems in rail infrastructure.