scholarly journals The equivalent loading method and the equivalent beam method

1949 ◽  
Vol 7 (2) ◽  
pp. 183-200 ◽  
Author(s):  
Pei-Ping Chen
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Bai-Lin Xiang ◽  
Lin Fu ◽  
Yongfei Li ◽  
Yuejin Liu

The metal-organic framework MOF-5 was synthesized by self-assembling of Zn(NO3)2·7H2O and H2BDC using DMF as solvent by the direct precipitation method and loaded with Fe2+ by the equivalent loading method at room temperature to prepare Fe(II)/MOF-5 catalyst and the microstructure, phases, and pore size of which was characterized by IR, XRD, SEM, TEM, and BET. It was found that Fe(II)/MOF-5 had high specific surface and porosity like MOF-5 and uniform pore distribution, and the pore size is 1.2 nm. In order to study the catalytic activity and reaction conditions of Fe(II)/MOF-5, it was used to catalyze the hydroxylation reaction of phenol with hydrogen peroxide. The results showed that the dihydroxybenzene yield of 53.2% and the catechol selectivity of 98.6% were obtained at the Fe2+ content of 3 wt.%, the mass ratio of Fe(II)/MOF-5 to phenol of 0.053, the reaction temperature of 80°C, and the reaction time of 2 h.


Author(s):  
Vladimir Yu. Kolosov ◽  
Anders R. Thölén

In this paper we give a short overview of two TEM applications utilizing the extinction bend contour technique (BC) giving the advantages and disadvantages; especially we consider two areas in which the BC technique remains unique. Special attention is given to an approach including computer simulations of TEM micrographs.BC patterns are often observed in TEM studies but are rarely exploited in a serious way. However, this type of diffraction contrast was one of the first to be used for analysis of imperfections in crystalline foils, but since then only some groups have utilized the BC technique. The most extensive studies were performed by Steeds, Eades and colleagues. They were the first to demonstrate the unique possibilities of the BC method and named it real space crystallography, which developed later into the somewhat similar but more powerful convergent beam method. Maybe, due to the difficulties in analysis, BCs have seldom been used in TEM, and then mainly to visualize different imperfections and transformations.


2017 ◽  
Vol 137 (6) ◽  
pp. 826-833
Author(s):  
Takaho Sekiguchi ◽  
Hiromu Odanaka ◽  
Yoshinobu Okano ◽  
Satoshi Ogino

Author(s):  
Chengcheng Liu ◽  
Koichi Suematsu ◽  
Akihito Uchiyama ◽  
Ken Watanabe ◽  
Yanbao Guo ◽  
...  

2021 ◽  
pp. 107754632110276
Author(s):  
Jun-Jie Li ◽  
Shuo-Feng Chiu ◽  
Sheng D Chao

We have developed a general method, dubbed the split beam method, to solve Euler–Bernoulli equations for cantilever beams under multiple loading conditions. This kind of problem is, in general, a difficult inhomogeneous eigenvalue problem. The new idea is to split the original beam into two (or more) effective beams, each of which corresponds to one specific load and bears its own Young’s modulus. The mode shape of the original beam can be obtained by linearly superposing those of the effective beams. We apply the split beam method to simulating mechanical responses of an atomic force microscope probe in the “dynamical” operation mode, under which there are a stabilizing force at the positioner and a point-contact force at the tip. Compared with traditional analytical or numerical methods, the split beam method uses only a few number of basis functions from each effective beam, so a very fast convergence rate is observed in solving both the resonance frequencies and the mode shapes at the same time. Moreover, by examining the superposition coefficients, the split beam method provides a physical insight into the relative contribution of an individual load on the beam.


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