非线性能量汇(nonlinear energy sink,NES)具有减振频带宽、减振效果好等诸多优点.但是NES没有线性刚度的特征导致其难以驱动大重量的NES振子,从而难以应用于对大型工程结构的减振.因此,将NES以高效和便捷的方式应用于工程减振,仍然是...非线性能量汇(nonlinear energy sink,NES)具有减振频带宽、减振效果好等诸多优点.但是NES没有线性刚度的特征导致其难以驱动大重量的NES振子,从而难以应用于对大型工程结构的减振.因此,将NES以高效和便捷的方式应用于工程减振,仍然是有待研究的问题.将NES以胞元的形式装配于振动的主结构中,通过多个NES胞元的共同作用,是一种有前景的减振策略.文章在偏心转子激励下,探究了多个NES胞元对远大于单个NES自身重量的振动结构的减振效果,分析了多个NES胞元耦合主结构组成的系统的整体响应特征.建立了NES胞元减振系统的运动微分方程,采用复化平均法(complexification-averaging,CxA)导出系统的慢不变流形及稳态响应满足的近似解析表达式,通过慢变流形的扰动运动微分方程对稳态解进行稳定性分析,再利用伪弧长法获得系统响应的近似解,分析了NES胞元的减振规律及系统响应规律,最后利用龙格-库塔(Runge-Kutta,R-K)法进行数值验证.结果表明,通过多个NES胞元共同作用,能够有效控制较大重量的主系统振动,而且减振效率随NES胞元个数和重量的增加而显著提高,共振区的响应状态随着胞元个数的增加从稳定状态、强调制状态、稳定状态依次变化.因此,本研究有助于推动NES的工程应用.展开更多
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
文摘非线性能量汇(nonlinear energy sink,NES)具有减振频带宽、减振效果好等诸多优点.但是NES没有线性刚度的特征导致其难以驱动大重量的NES振子,从而难以应用于对大型工程结构的减振.因此,将NES以高效和便捷的方式应用于工程减振,仍然是有待研究的问题.将NES以胞元的形式装配于振动的主结构中,通过多个NES胞元的共同作用,是一种有前景的减振策略.文章在偏心转子激励下,探究了多个NES胞元对远大于单个NES自身重量的振动结构的减振效果,分析了多个NES胞元耦合主结构组成的系统的整体响应特征.建立了NES胞元减振系统的运动微分方程,采用复化平均法(complexification-averaging,CxA)导出系统的慢不变流形及稳态响应满足的近似解析表达式,通过慢变流形的扰动运动微分方程对稳态解进行稳定性分析,再利用伪弧长法获得系统响应的近似解,分析了NES胞元的减振规律及系统响应规律,最后利用龙格-库塔(Runge-Kutta,R-K)法进行数值验证.结果表明,通过多个NES胞元共同作用,能够有效控制较大重量的主系统振动,而且减振效率随NES胞元个数和重量的增加而显著提高,共振区的响应状态随着胞元个数的增加从稳定状态、强调制状态、稳定状态依次变化.因此,本研究有助于推动NES的工程应用.
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.
