In this paper, the steady-state response regimes of nonlinear energy harvesters with a resistor-inductor resonant circuit are theoretically investigated. The complexification averaging(CA) method is used to theoretica...In this paper, the steady-state response regimes of nonlinear energy harvesters with a resistor-inductor resonant circuit are theoretically investigated. The complexification averaging(CA) method is used to theoretically analyze the energy harvesting performance and reduce the motion equations into a set of first-order differential equations. The amplitudes and phases of both the response displacement and the output voltage are derived, and the corresponding stability conditions are determined. The response regimes are studied with the variation of nonlinear stiffness coefficients and coupling parameters, which are verified by the time domain analysis. The frequency island phenomenon is found and analyzed. Additionally, the backbone curve for deducing the extreme vibration frequency and amplitude is derived. Simultaneously, the analytical expressions of the switching points(critical amplitude and frequency) to identify the hardening and softening properties are established. Accordingly, a criterion is given to determine the occurrence of the jump phenomenon, and its effectiveness is verified. Overall, this paper presents an in-depth theoretical analysis of nonlinear energy harvesters with a resistor-inductor resonant circuit. It presents the theoretical framework and guidance for more extensive evaluations and understanding the theoretical analysis of nonlinear energy harvesters with external circuits.展开更多
For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Ki...For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Killing forms of a real Lie triple system To, the complexification T of To, and the realification of T.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11702201 and 11802237)the Young Talent Fund of University Association for Science and Technology in Shaanxi,China(Grant No.20200503)+2 种基金the 111 Project(Grant No.BP0719007)the China Postdoctoral Science Foundation(Grant No.2018M641012)the Natural Science Foundation of Shaanxi Province(Grant No.2018JQ1055)。
文摘In this paper, the steady-state response regimes of nonlinear energy harvesters with a resistor-inductor resonant circuit are theoretically investigated. The complexification averaging(CA) method is used to theoretically analyze the energy harvesting performance and reduce the motion equations into a set of first-order differential equations. The amplitudes and phases of both the response displacement and the output voltage are derived, and the corresponding stability conditions are determined. The response regimes are studied with the variation of nonlinear stiffness coefficients and coupling parameters, which are verified by the time domain analysis. The frequency island phenomenon is found and analyzed. Additionally, the backbone curve for deducing the extreme vibration frequency and amplitude is derived. Simultaneously, the analytical expressions of the switching points(critical amplitude and frequency) to identify the hardening and softening properties are established. Accordingly, a criterion is given to determine the occurrence of the jump phenomenon, and its effectiveness is verified. Overall, this paper presents an in-depth theoretical analysis of nonlinear energy harvesters with a resistor-inductor resonant circuit. It presents the theoretical framework and guidance for more extensive evaluations and understanding the theoretical analysis of nonlinear energy harvesters with external circuits.
基金the Natural Science Foundation of Hebei Province (Nos.A200500008A2007000138)
文摘For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Killing forms of a real Lie triple system To, the complexification T of To, and the realification of T.
