Lagrange equations of nonholonomic systems with fractional derivatives

This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton's principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d'Alembert–Lagrange principle with fractional derivatives is presented,and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results.     

液晶苯酚酯相变内耗峰与振动频率的相关性

采用低频内耗方法，在强迫振动模式下研究了液晶苯酚酯材料相变过程内耗峰与振动频率之间的相关性.由一个简单的粘弹性的Maxwell模型出发，推导了在强迫振动模式下内耗峰的峰高与频率的关系式.从理论上得出了内耗峰高与振动频率之间的非线性关系.实验数据拟合的结果很好地符合这一关系式.这表明内耗峰随频率的变化规律是由振动系统本身的特征决定. 关键词：     

试样的内耗值与振动系统内耗值的比较

推导了四个力学模型和它们对应振动系统的内耗表达式，并给出了试样内耗值与振动系统内耗值的关系.发现对于不同的力学模型，或者说不同力学性质的材料，试样的内耗值与振动系统的内耗值有不同的关系. 关键词：     

低频内耗测量时标准滞弹性固体的内耗行为

用三参量力学模型的恒应力和恒应变弛豫时间描述了标准滞弹性固体的内耗行为.在低频内耗测量时,振动系统的惯量不可避免地影响测量的内耗值,当材料的内耗较大和测量频率与振动系统的共振频率可以比较时,惯量对内耗测量的影响较大,这时惯量的影响不可忽略. 关键词：     

基于应力分析的电镀保护光纤布喇格光栅传感性能分析(英文)

为保护光纤光栅,提出了一种镀层和光纤光栅结合良好的无粗化过程的化学镀和电镀保护方法.基于应力分析法,得到镀镍光纤光栅的温度灵敏度公式,采用ANSYS有限元软件分析了电镀后光纤光栅应力随温度变化关系,并进行了实验证实.结果表明:光纤光栅电镀后温度灵敏度理论和实验值分别为20.6951pm/℃、22.076pm/℃.理论分析和实验、仿真结果基本一致.相比裸光纤光栅,温度灵敏度增加到原来的2.2倍.该方法不仅可以获得厚度理想的保护层,还可以提高光纤光栅的温度灵敏度.     

铂微电极位点上氧化铝纳米孔的制备

金属微电极表面的纳米级处理可以大大提高电极的性能。本文基于微加工及电化学技术在铂微电极位点上制备了一致性良好的氧化铝纳米结构。通过对基片铂层表面等离子体处理,使铝膜与铂层之间粘附力明显增强。利用二次阳极氧化法,在铂微电极位点上制备出纳米孔。结果表明,30V是该条件下比较理想的氧化电压。同时,通过对氧化过程中电流的监测,发现当铝膜完全氧化后电流大幅上升,可将此现象作为终止阳极氧化的标志。这种微电极位点处的氧化铝模板可进一步用于不同材料纳米微电极的制备。     

Reductions and conserved quantities for discrete compound KdV–Burgers equations

We present two methods to reduce the discrete compound KdV–Burgers equation, which are reductions of the independent and dependent variables: the translational invariant method has been applied in order to reduce the independent variables; and a discrete spectral matrix has been introduced to reduce the number of dependent variables. Based on the invariance of a discrete compound KdV--Burgers equation under infinitesimal transformation with respect to its dependent and independent variables, we present the determining equations of transformation Lie groups for the KdV--Burgers equation and use the characteristic equations to obtain new forms of invariants.