Nonlinear Frequency Analysis of FGM Pipes Based on the Homotopy Method北大核心CSCD

Based on the homotopy analysis method, the nonlinear vibration of porous functionally graded material (FGM) conveying pipes under generalized boundary conditions was studied. Based on the power-law distribution of the FGM and the Voigt model, the physical properties of the porous pipe material were described. Under the Euler-Bernoulli beam theory and the von Kármán nonlinear theory, and by means of Hamilton’s variational principle, the dynamic control equations and generalized boundary conditions for porous FGM conveying pipes were established. The homotopy analysis method was used to solve the nonlinear vibration characteristics of the porous FGM conveying pipe under generalized boundary conditions. The numerical results show that, the translation spring has little effect on the critical velocity of instability, while the rotation spring increases the critical velocity of instability, making the system more stable; in the nonlinear system, the viscoelastic coefficient does not change the critical velocity; the pipe length, the power-law exponent and the porosity all influence the nonlinear free vibration of the porous FGM conveying pipe. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

四例基于1, 4-双(3-/4-吡啶基)-2, 3-二氮杂-1, 3-丁二烯的配位聚合物的组装和性质:金属离子对结构的影响

通过水热合成法,合成了4例由混合配体构筑的的过渡金属配位聚合物:{[Zn(4-bpdb)(pnba)₂]·4H₂O}_n(1),[Cd(4-bpdb)(pnba)₂]_n(2),{[Cd₂(3-bpdb)₂(OAc)₄]·5H₂O}_n(3),和{[Co(3-bpdb)(pnba)₂(H₂O)₂]·2H₂O}_n(4)(4-bpdb=1,4-双(4-吡啶基)-2,3-二氮杂-1,3-丁二烯,3-bpdb=1,4-双(3-吡啶基)-2,3-二氮杂-1,3-丁二烯,Hpnba=对硝基苯甲酸,HOAc=乙酸),并且分别用X-射线单晶衍射、元素分析、红外光谱、热差分析、X-射线粉末衍射表征了这4个配合物。晶体结构分析表明,配合物1显示出一维锯齿形链状结构,金属锌(Ⅱ)离子具有稍微变形的四面体配位几何构型。而配合物2和3却展现出一维梯状双链结构,镉(Ⅱ)离子展现出五角双锥几何构型。而配合物4却拥有一维直线型链状结构,其中钴(Ⅱ)离子拥有八面体几何形状。上述结果说明,金属离子的几何构型可能对配合物的结构具有重要的影响。此外,还研究了配合物1~3的荧光性质。     

一种应用于水样中汞离子检测的新型罗丹明B衍生物荧光探针

合成了一种新的罗丹明B酰肼-肉桂酸硫脲(RBHT)荧光探针,利用红外光谱、元素分析、核磁共振等方法对探针结构进行了表征。该探针与Hg2+作用后产生较强荧光,由此建立了一种测定Hg2+的荧光分析新方法。Hg2+测定的线性范围为8.0×10-7～6.0×10-6 mol·L-1,检出限为7.0×10-8 mol·L-1。该方法具有操作简单、灵敏度高和选择性好等特点,可用于自来水、河水中痕量Hg2+的测定。     

Fabrication of pillar-array superhydrophobic silicon surface and thermodynamic analysis on the wetting state transition

Textured silicon （Si） substrates decorated with regular microscale square pillar arrays of nearly the same side length, height, but different intervals are fabricated by inductively coupled plasma, and then silanized by self-assembly octadecyl- trichlorosilane （OTS） film. The systematic water contact angle （CA） measurements and micro/nanoscale hierarchical rough structure models are used to analyze the wetting behaviors of original and silanized textured Si substrates each as a function of pillar interval-to-width ratio. On the original textured Si substrate with hydrophilic pillars, the water droplet possesses a larger apparent CAs （〉 90~） and contact angle hysteresis （CAH）, induced by the hierarchical roughness of microscale pil- lar arrays and nanoscale pit-like roughness. However, the silanized textured substrate shows superhydrophobicity induced by the low free energy OTS overcoat and the hierarchical roughness of microscale pillar arrays, and nanoscale island-like roughness. The largest apparent CA on the superhydrophobic surface is 169.8~. In addition, the wetting transition of a gently deposited water droplet is observed on the original textured substrate with pillar interval-to-width ratio increasing. Furthermore, the wetting state transition is analyzed by thermodynamic approach with the consideration of the CAH effect. The results indicate that the wetting state changed from a Cassie state to a pseudo-Wenzel during the transition.     

微/纳器件粗糙表面间弯月面力及黏着力计算

微/纳器件表面微观粗糙结构间由于液体介质而引起的弯月面力和黏着力是导致器件精度降低乃至失效的主要原因之一。通过建立微/纳米尺度上球面-平面接触的物理模型,基于Young-Laplace方程和Reynolds润滑理论,分析得到粗糙表面接触分离过程中弯月面力和黏着力的计算公式。在此基础上,计算得到接触表面分离过程中的弯月面形状变化规律,并分别讨论了固体表面分离距离、液滴初始弯月面高度、固体表面润湿性能和分离时间等因素对弯月面力和黏着力的影响。研究结果为微/纳米表面抗黏着机理提供了理论依据。     

固相萃取法对微量药物的选择性富集和直接测定

选用能够识别抗菌药物氧苄氨嘧啶（ＴＭＰ）的模权聚合物作固相萃取剂,从稀溶液中可选择性地富集ＴＭＰ,在生理浓度下,富集因数为３５．７,而非模板事物无富集能力。在洗脱过程中直接用于ＴＭＰ的测定,不需要随后的色谱分析手续。基于此,建立了一个样品富集和测定的新方法,方便简单可靠,用于尿样中低２的ＴＭＰ的测定,回收率达到９１．７％,结果满意。     

KBrO3-KBr紫外分光光度法测定痕量苯酚

研究了在盐酸介质中以 KBrO3-KBr 紫外分光光度法测定痕量苯酚的条件,在浓度为 0.6mol/L HCl,3×10-5mol/L KBrO3,5×10-4mol/L KBr,6×10-4mol/L KI 溶液中测定苯酚时,线性范围为 0.10～2.5mg/L,表观摩尔吸光系数为 1.89×104L·mol-1·cm-1,Sandell 指数为 4.98μg/cm2.本法已用于测定废水中苯酚.     

金属配位模板聚合物的分子识别特性的研究

以Ｃｏ（Ⅱ）和敌鼠配合物为模板,４－乙烯吡啶为功能基单体,乙二醇二甲基丙烯酸酯为交联剂,采用分子印迹技术,合成了具有类似于金属螯合抗体结合位点的金属配位模板聚合物。系统研究了金属离子对模板聚合物靠拢性结构敌鼠的调节作用。     

基于图注意力网络的三维网格分割算法

针对三维网格模型分割质量提升问题，提出了感知几何的图注意力网络。首先，定义了感知几何的图注意力系数，利用节点之间的边特征扩展由网络学习得到的注意力系数，引入与节点局部几何信息相关的注意力系数，更好地反映节点之间的相似性。然后，通过调整网络架构，将三维网格模型的几何特征与标签信息共同作为图注意力网络的输入，使标签信息参与网络训练和验证，并通过残差形式的线性连接实现网络的更稳定输出。大量实验结果表明，本文算法能够获得精确的分割边界，其在PSB数据集上的分割准确率较现有经典算法提升约2个百分点，也取得了更好的兰德指数。同时，通过消融实验验证了算法的合理性。     

极大外平面图（r,k）——扇的4染色

定义了一类极大外平面图：(r,k）--扇。证明了当G是以r个顶点的圈Qr为标定界环的(r,k）一扇，G'是以Qr为标定界环的任意极大外平面图时，G和G'有公共四染色；同时对△(G)=r-3的极大外平在图也得到相同的结论。从而证明了四色定理的等价命题在给定条件下成立。