Nonlinear Two-to-One Internal Resonance for Broadband Energy Harvesting

The transformation of waste vibration energy into low-power electricity has been heavily researched to enable self-sustained wireless electronic components. Monostable and bistable nonlinear oscillators have been explored by several researchers in an effort to enhance the frequency bandwidth of operation. Linear two degree of freedom (2-DOF) configurations as well as combination of a nonlinear single-DOF harvester with a linear oscillator to constitute a nonlinear 2-DOF harvester have also been explored to develop broadband energy harvesters. In the present work, the concept of nonlinear internal resonance in a continuous frame structure is explored for broadband energy harvesting. The L-shaped beam-mass structure with quadratic nonlinearity was formerly studied in the nonlinear dynamics literature to demonstrate modal energy exchange and the saturation phenomenon when carefully tuned for two-to-one internal resonance. In the current effort, piezoelectric coupling is introduced, and electromechanical equations of the L-shaped energy harvester are employed to explore the primary resonance behaviors around the first and the second linear natural frequencies for bandwidth enhancement. Simulations using approximate analytical frequency response equations as well as time-domain numerical solutions reveal that 2-DOF configuration with quadratic and two-to-one internal resonance could extend the bandwidth enhancement capability. Both electrical power and shunted vibration frequency response curves of steady-state solutions are explored in detail. Effects of various electromechanical system parameters, such as piezoelectric coupling and load resistance, on the overall dynamics of the internal resonance energy harvesting system are reported.