Analysis of nonlinear vibration energy harvesters using a complex dynamic frequency method

To understand the complicated dynamic behavior of a Nonlinear Piezoelectric Energy Harvester (NPEH), this paper develops an improved Complex Dynamic Frequency (CDF) method based on complex normal form. CDF introduces a dynamic frequency factor and establishes a set of algebraic equations in handling the effect of higher-order nonlinear terms in a wide frequency band to obtain periodic responses of NPEH. Numerical and experimental studies verify that the proposed CDF gives consistent and accurate predictions of the systems with both weak and strong nonlinearity. Furthermore, through an implicit relationship between magnet arrangement and output performance, one may effectively control the sweep frequency with softening and hardening characteristics. That is a major breakthrough toward the further nonlinear design for broad bandwidth harvesters. As the application, the experimental results reveal the high response profiles can be in a wide frequency range from 10.8 Hz to 24.5 Hz for the NPEH developed that allows an output power of 9 times higher than the conventional linear structure.