# Experimental Study and Parameter Optimization of a Magnetic Coupled Piezoelectric Energy Harvester
Among the linear optimization methods, a plurality of resonance frequencies are generated in the form of array or multi degrees of freedom. The array method utilizes a plurality of individual cantilever beams, which is simple to design. However, the volume and matching circuit of the system are relatively large [18]. The multi degrees of freedom method is relatively complex but more robust, and generally establishes double or more degrees of freedom in a composite form. The system, due to the coupling between multi modalities, reduces the individual response amplitude for each degree of freedom [19]. The nonlinear optimization methods mainly utilize various auxiliary structures to introduce nonlinear stiffness. One of the representative methods is the 'Stop Blocking Method' in Figure 1a, which introduces piecewise stiffness for the system [20; 21; 22]. This method broadens the band at the expense of decreasing the peak value, and requires that the vibration amplitude is greater than the stopper spacing, which does not work in a small vibration environment. Another representative method is the 'Multi-Stable Method', and the nonlinear stiffness is introduced by magnetic force to generate various steady states [23; 24]. Higher amplitude is generated across multiple potential wells. One common structure utilizes two axially opposite magnets to build the bistable system [25; 26], as shown in Figure 1b. The structure has a large operating frequency range and amplitude. However, more precise design and processing are required for the multi-stable method, and small amplitude or fast changing excitation is not suitable. Another nonlinear method, called the 'Vertical Magnetic Method', utilizes vertical auxiliary magnets. This method was proposed earlier by [PERSON] et al. [27; 28], as shown in Figure 1c. He set up two fixed auxiliary magnets, and adjusted the system resonance frequency between 22 and 32 Hz by adjusting the spacing. [PERSON] et al. [29; 30] studied the resonant response of a single fixed auxiliary magnet structure using a three-time scale method, and found that the structure has a certain effect of widening the frequency band. [PERSON] et al. [31] established a distributed reduced-order model based on the [PERSON] method, taking into account the angle between the magnets during motion. [PERSON] et al. [32] installed the auxiliary magnet on the other cantilever beam parallel, and published a letter which compared the structure with the fixed auxiliary magnet preliminarily. [PERSON] established a lumped parameter model for the nonlinear piezomagnetoelastic harvester. [PERSON] et al. [33] established a distributed parameter model, which was compared with [PERSON]'s lumped parameter model, but still mainly discussed the fixed magnet structure, and did not further analyze the structure of [PERSON]. [PERSON] et al. [34] applied the harmonic balance method with alternating frequency/time domain progress to predict steady-state responses of nonlinear piezoelectric mechanical systems, and [PERSON]'s  
Figure 1: Schematic diagram of common nonlinear optimization methods: (**a**) Stop Blocking Method; (**b**) Multi-Stable Method; (**c**) Vertical Magnetic Method. model was used as an example to verify the feasibility of the algorithm. The research to date has not analyzed the parameter optimization or properties of the structure. In this paper, the performance of a magnetic coupled piezoelectric energy harvester is analyzed in detail through experiments and simulations. For analysis and parameter optimization, a theoretical lumped parameter model is established. Compared with [PERSON]'s model [32], the model of this paper considers more details. Based on simulation and experiment, different parameter configurations are discussed. The parameters are optimized and the optimized results are tested experimentally. The results show that the magnetic coupled piezoelectric energy harvester can effectively improve the performance of the conventional harvester and has better practical potential.