| Bistable piezoelectric cantilever generating system is a new type of independentpower supply unit, which can convert vibration power to electronic power under thepositive piezoelectric effect. As the bistable power generation sysems can appear largedeformation, mathematical model is required to establish to ensure to correspond tothe actual model. Piezoelectric vibrator’s motion is closely related with the ability ofpower generation, and the high-energy rail is needed in the bistable piezoelectricpower generation systems, so how to make the high-energy rail acquired in the lowand broad frequency and what influence of the system parameters is on this type ofmotion are one of the key research of this paper. Besides, in order to have a profoundunderstanding of the bistable piezoelectric power generation systems on whole andlocal dynamics and on the effect of parameters to the system, the complex dynamicsanalysis is studied in this paper, which is also one of the key research of this paper.Aiming at the above problems, Applying theoretical modeling, numericalsimulation and analytic method, this paper analyzes the response characteristics,power generation efficiency and other relevant parameters which can affectpiezoelectric cantilever power systems. The result and discussion have a guidingsignificance for design and application of bistable piezoelectric power generationsystems.The following aspects are discussed in this paper,(1)The first part is the literature review of piezoelectric cantilever system and thebrief summary of research concerned problems.(2) Given the non-linear influence on systems by the deformation of cantilever,Hamilton’s principle is applied to this paper to establish dynamics model of the largedeformation of the beam aiming at improving bistable cantilever piezoelectric vibrator,and the dimensionless equation of the system is acquired as well.(3)As the large movements has outstanding advantages in the bistablepiezoelectric power generation, the harmonic balance method is used to analyze theconditions of large movements happened in a wide and low frequency. Besides, theinfluence of different levels of incentive, geometric nonlinear correlation coefficient,the electromechanical coupling terms and the reaction of load resistance are analyzed.The result turns out that the amplitude response of bistable piezoelectric power generation system changes abruptly with soft characteristics. Multiple solutions andjumping phenomenon basically concentrate in low frequency band, and this featurecorresponds with the low frequency in the environment. Because of the addition ofgeometric nonlinearity, the number of system solutions increases from three to fiveattracting the high energy solutions from low-energy solution. Moreover, forelectromechanical coupling coefficient has a great influence on the approximateresonance peak, the electromechanical coupling properties could be mediated to adaptto the low broadband characteristics in the environment. Finally, the simulation resultverifies the influence on output power of the system by the optimal load.(4) Then Matlab is applied to the research to numerical simulation analysis ofthe electromechanical coupling equation modified by the dimensionless processing.The following parts talk about the influence on the system response exerted byincentive system, load impedance, sharp periodic motion, chaotic motion and thenonlinear deformation. It shows some of the dynamic characteristics of this model.Given sort of incentive, the system could get the largest output power produced by theoptimal impedance. In addition, of the same level of incentive, generation capacity ofthe large periodic motion performs better than the one of chaotic motions. Also,geometric nonlinearity could produce more dynamic behaviors in this system, bycontrolling the beam length within the expected scope of periodic motion, so thesystem can increase the capacity to generate power.To sum up, this paper analyzed the bistable piezoelectric power systemcomprehensively, considering the dynamic response characteristics of the geometricnonlinearity. This paper also explored the related parameters, which could influencethe generating capacity, and improves the understanding of bistable piezoelectricpower generation systems. The research could contribute to the design andoptimization of the structure of the bistable piezoelectric power generation systems. |
