A two-dimensional Duffing oscillator which can produce stochastic resonance (SR) is studied in this paper. We introduce its SR mechanism and present a generalized parameter-adjusted SR (GPASR) model of this oscillator for the necessity of parameter adjustments. The Kramers rate is chosen as the theoretical basis to establish a judgmental function for judging the occurrence of SR in this model; and to analyze and summarize the parameter-adjusted rules under unmatched signal amplitude, frequency, and/or noise-intensity. Furthermore, we propose the weak-signal detection approach based on this GPASR model. Finally, we employ two practical examples to demonstrate the feasibility of the proposed approach in practical engineering application.

Pink noise, which is similar to realistic ambient noise, is normally used to simulate ambience where a piezoelectric energy harvesting system (PEHS) is set up. However, pink noise with standard spectral representation can only be used to simulate excitations assumed to possess constant intensity, whereas realistic ambient noise normally appears with a random spectrum and varying intensity in terms of different locations and time. The output performance of conventional bistable magnetic repulsive energy harvesters is significantly affected by the ambience intensity. Considering this fact, a model bistable dual-piezoelectric-cantilever energy harvester (DPEH) is developed in this study to achieve optimal broadband energy harvesting under a varying-intensity realistic circumstance. We utilized various realistic ambient conditions as excitations to obtain the DPEH energy harvesting performance for theoretical and applied study. The elastically supported PEHS has been proven to be more adaptive to realistic ambience with significant or medium intensity variation, but is less qualified for realistic ambience with constant intensity compared with the rigidly supported PEHS (RPEHS). Fortunately, the dual-piezoelectric-cantilever energy harvesting system is superior to the RPEHS under all circumstances because the dual-piezoelectric cantilevers are efficiently utilized for electromechanical energy conversion to realize optimal energy harvesting.

Nonlinear mono-stable and multi-stable piezoelectric energy harvesters have attracted a lot of attention owing to their broadband frequency spectra and excellent energy harvesting performance. Herein, two types of nonlinear mono-stable, bi-stable, tri-stable, and quad-stable piezoelectric energy harvesters using cantilever structure and magnetic interaction are compared and analyzed. Based on the magnetizing current method, the magnetic force equations are obtained. Calculation results demonstrate that the stability of these harvesters is dependent on the equivalent linear elastic force and the vertical magnetic force. The equilibrium point occurs when the equivalent linear elastic force equals to the vertical magnetic force. The relationship between the number of stable equilibrium points E _S and the number of the intersections of the two force curves N _I is that E _S= (N _I + 1)/2. Experiments are carried out to verify the equivalent linear elastic force, vertical magnetic force, and the number of stable equilibrium points of the fabricated prototypes. The experimental results are consistent with the calculated results, which verifies the correctness of the stability mechanism. Moreover, it is found that the stability mechanism is also applicable to the harvesters with more stable equilibrium points, such as penta-stable and hexa-stable harvesters. This work reveals the stability mechanism of nonlinear mono-stable and multi-stable energy harvesters using cantilever structure and magnetic interaction, and provides technical methods for the design of multi-stable energy harvesters.