Internal resonance in axially loaded beam energy harvesters with an oscillator to enhance the bandwidth

Internal resonance is explored as a possible mechanism to enhance the bandwidth of vibratory energy harvesters. To demonstrate the improved performance, an axially loaded beam energy harvester with an oscillator is considered. Based on the equations governing the vibration measured from a stable equilibrium position, the method of multiple scales is applied to derive the amplitude-frequency response relationships of the voltage and the power in the first primary resonances with a two-to-one internal resonance. The optimal resistance is determined to achieve the maximum of the power. The amplitude-frequency response curves of the voltage and the power under the optimal load resistance have two peaks bending to the left and the right, respectively. The amplitude-frequency response curves bend more to the right, indicating hardening-type nonlinearity. The numerical simulations support the analytical results. The results demonstrate that the internal resonance design can improve bandwidth of the energy harvester. Numerical simulations indicate the appearance of chaos under sufficiently strong excitation.