This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), whe...This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), where the fractional derivative corresponds to a force applied to the solid (e.g. an impact force), and the second derivative corresponds to acceleration of the solid’s centre of mass, and therefore to the inertial force. Consequently, the equilibrium satisfies the principle of the force equilibrium. Further-more, the paper provides a new definition of under- and overdamping that is not exclusively disjunctive, i.e. not either under- or over-damped as in a linear Voigt model, but rather exhibits damping phases co-existing consecutively as time progresses, separated not by critical damping, but rather by a transition phase. The three damping phases of a power-law viscoelastic solid—underdamping, transition and overdamping—are characterized by: underdamping—centre of mass oscillation about zero line;transition—centre of mass reciprocation without crossing the zero line;overdamping—power decay. The innovation of this new definition is critical for designing non-linear visco-elastic power-law dampers and fine-tuning the ratio of under- and overdamping, considering that three phases—underdamping, transition, and overdamping—co-exist consecutively if 0 < η < 0.401;two phases—transition and overdamping—co-exist consecutively if 0.401 < η < 0.578;and one phase— overdamping—exists exclusively if 0.578 < η < 1.展开更多
在微带线基本理论的基础上,采用非均匀传输微带线研究设计了新型Wilkinson功分器有。运用阻抗匹配、奇偶模分析的方法,对基于非均匀传输微带线的Wilkinson功分器进行理论分析,并通过ADS2008（Advanced Design System 2008）软件的设计...在微带线基本理论的基础上,采用非均匀传输微带线研究设计了新型Wilkinson功分器有。运用阻抗匹配、奇偶模分析的方法,对基于非均匀传输微带线的Wilkinson功分器进行理论分析,并通过ADS2008（Advanced Design System 2008）软件的设计、仿真和优化得到了相关数据参数,设计制作了一款3.1-10.6 GHz范围内的非均匀传输微带线Wilkinson功分器,从而成功地实现了小型化、低功耗Wilkinson功分器。展开更多
文摘This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), where the fractional derivative corresponds to a force applied to the solid (e.g. an impact force), and the second derivative corresponds to acceleration of the solid’s centre of mass, and therefore to the inertial force. Consequently, the equilibrium satisfies the principle of the force equilibrium. Further-more, the paper provides a new definition of under- and overdamping that is not exclusively disjunctive, i.e. not either under- or over-damped as in a linear Voigt model, but rather exhibits damping phases co-existing consecutively as time progresses, separated not by critical damping, but rather by a transition phase. The three damping phases of a power-law viscoelastic solid—underdamping, transition and overdamping—are characterized by: underdamping—centre of mass oscillation about zero line;transition—centre of mass reciprocation without crossing the zero line;overdamping—power decay. The innovation of this new definition is critical for designing non-linear visco-elastic power-law dampers and fine-tuning the ratio of under- and overdamping, considering that three phases—underdamping, transition, and overdamping—co-exist consecutively if 0 < η < 0.401;two phases—transition and overdamping—co-exist consecutively if 0.401 < η < 0.578;and one phase— overdamping—exists exclusively if 0.578 < η < 1.
文摘在微带线基本理论的基础上,采用非均匀传输微带线研究设计了新型Wilkinson功分器有。运用阻抗匹配、奇偶模分析的方法,对基于非均匀传输微带线的Wilkinson功分器进行理论分析,并通过ADS2008（Advanced Design System 2008）软件的设计、仿真和优化得到了相关数据参数,设计制作了一款3.1-10.6 GHz范围内的非均匀传输微带线Wilkinson功分器,从而成功地实现了小型化、低功耗Wilkinson功分器。
