Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

Application of the “Six-Step Teaching Method” in the Nursing Teaching of Obstetric Interns

Objective: The “six-step teaching method” is a teaching method, which is summarized based on practical experience. This study aimed to explore the effect of “six-step teaching method” in clinical teaching of obstetrics. Methods: A quasi-experimental study design was used, 30 nursing students who entered obstetrics practice from March 2022 to July 2022 were selected as the control group according to the order of time, and traditional teaching methods were adopted. From August to December 2022, 30 interns were selected as the experimental group, and the “six-step teaching method” was adopted. After 8 weeks of clinical practice, the assessment results and teaching effect satisfaction of the two groups were compared. Results: The scores of obstetrical specialty in the experimental group were higher than those in the control group, and the difference was statistically significant (P < 0.05);The evaluation of teaching methods, teaching quality, classroom atmosphere and individual observation ability, clinical thinking ability and nurse-patient communication ability of the experimental group were higher than those of the control group, and the differences were statistically significant (P Conclusion: “six-step teaching method” can effectively master the professional knowledge of obstetrics, stimulate the clinical thinking ability of interns, and improve the teaching effect and satisfaction. .

Temperature-dependent photoluminescence on organic inorganic metal halide perovskite CH3NH3Pb I3-xClx prepared on ZnO/FTO substrates using a two-step method

Temperature-dependent photoluminescence characteristics of organic-inorganic halide perovskite CH3NH3Pb I3-xClx films prepared using a two-step method on ZnO/FTO substrates were investigated. Surface morphology and absorption characteristics of the films were also studied. Scanning electron microscopy revealed large crystals and substrate coverage. The orthorhombic-to-tetragonal phase transition temperature was-140 K. The films＇ exciton binding energy was 77.6 ± 10.9 meV and the energy of optical phonons was 38.8 ± 2.5 meV. These results suggest that perovskite CH3NH3Pb I（3-x）Clx films have excellent optoelectronic characteristics which further suggests their potential usage in perovskitebased optoelectronic devices.

Applying the Dynamic Two-Step Method to Forecast Remaining Oil Distribution of Lower Series ,Xiaermen Oilfield

The distribution of remaining oil is often described qualitatively. The remaining oil distributed in the whole reservoir is calculated according to the characteristics of the space distribution of the saturation of remaining oil. Logging data are required to accomplish this. However, many such projects cannot be completed. Since the old study of remaining oil distribution could not be quantified efficiently, the ＂dynamic two-step method＂ is presented. Firstly, the water cut of every flow unit in one well at one time is calculated according to the comprehensive water cut of a single well at one time. Secondly, the remaining oil saturation of the flow unit of the well at one time is calculated based on the water cut of the flow unit at a given time. The results show that ＂dynamic two-step method＂ has characteristics of simplicity and convenience, and is especially suitable for the study of remaining oil distribution at high water-cut stage. The distribution of remaining oil presented banding and potato form, remaining oil was relatively concentrated in faultage neighborhood and imperfect well netting position, and the net thickness of the place was great. This proposal can provide an effective way to forecast remaining oil distribution and enhance oil recovery, especially applied at the high water-cut stage.

组合两步分解和ARIMA-LSTM的短期风速预测研究

为提高风速序列预测精度,提出一种基于两步分解的短期风速组合预测模型,首先使用鲁棒经验模态分解(REMD)将风速数据分解为不同频率的子序列,然后将REMD分解得到的高频模态分量使用小波包分解(WPD)进行第二步分解,降低风速序列不稳定性,提高其可预测性。其次对分解得到的高频子序列建立长短期记忆神经网络(LSTM)预测模型,低频子序列建立差分自回归移动平均模型(ARIMA)预测模型。最后叠加子序列预测结果得到风速预测结果。通过两组不同风速数据集的实验对该模型的性能进行科学评估,模型预测结果的平均绝对误差分别为0.3026、0.1255;均方根误差分别为0.498、0.1607。与其他几种对比预测模型相比,验证该模型具有一定的优越性。

Na_(2)O-CaO-SiO_(2)平板玻璃减反射功能化研究

随着光伏产业的高速发展,与之配套使用的减反射玻璃重新进入了研究者们的视野。本文采用湿化学二步刻蚀法制备了具有减反射性能的Na_(2)O-CaO-SiO_(2)平板玻璃,采用分光光度计、扫描电子显微镜、原子力显微镜和X射线能谱仪等测试样品的透过率、表面形貌和断面膜层厚度、表面化学成分、耐酸性和硬度,研究了反应温度和反应时间、玻璃膜层结构与透过率的关系。通过使用弱碱性的混合盐溶液对Na_(2)O-CaO-SiO_(2)玻璃表面进行化学刻蚀,使玻璃表面Si—O键断裂,在玻璃表面形成纳米膜层结构,当膜层厚度达到一定厚度时,一定波长的光在玻璃表面发生相消干涉,透过率最高可达到97.8%,刻蚀前后玻璃成分基本无变化,铅笔硬度达到3H。

Influence of two-step cooling method on magnetic properties of Fe_(82)Mo_7B_(10)Cu_1 nanocrystalline alloy

Soft magnetic properties of Fe82Mo7B10Cu1 nanocrystalline alloy were studied as a function of cooling condition. The results show that higher permeability and relaxation frequency can be obtained by the two-step cooling method, and the pinning field of the sample obtained by this method is smaller than that of the furnace-cooled and water-quenched samples. This phenomenon was interpreted in terms of internal stress and the magnetic ordering of the residual amorphous phase. The two-step cooling treatment is an effective way to improve the soft magnetic properties of Fe82Mo7B10Cu1 nanocrystalline alloy.

A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence

An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditions and their convergence are studied. The two-step continuity Runge-Kutta methods possess good numerical stability properties and higher stage-order, and keep the explicit process of computing the Runge-Kutta stages. The numerical experiments show that the TSCRK methods are efficient.

Noether＇s theorem and one-step corrections method for holonomic system

In this paper, a new computational method for improving the accuracy of numerically computed solutions is introduced. The computational method is based on the one-step method and conserved quantities of holonomic systems are considered as kinematical constraints in this method.

2-取代苯并恶唑衍生物的合成及其在药物合成中的应用

2-取代苯并恶唑是一类重要的杂环骨架,其在药物合成中受到广泛关注与运用。本文以廉价易得的邻氨基苯酚和芳香醛为原料,通过一锅两步法优化第一步与第二步反应条件,确定第一步二氧六环为溶剂,室温空气气氛反应5h;第二步2,3-二氯-5,6-二氰基苯醌为氧化剂,室温空气气氛反应1h,氧化环化合成一系列2-取代苯并恶唑衍生物,同时将该方法运用于药物Tafamidis的合成中。目标化合物结构经^(1)H-NMR、^(13)C-NMR和HRMS确证。该方法条件温和、操作简便、底物普适性广以及具有一定的实用性,为2-取代苯并恶唑化合物合成提供了一种新的思路。

On“The Five-Step Method”in Teaching Junior English for China

Junior English for China’ is based on the ’Five-Step’ teachingmethod: Revision, Presentation, Drilling, Practice, Consolidation. Each step has itsown particular methodology and requires the teacher to adopt a certain role. Thispaper is a discussion of the "Five-Step Method".

过渡金属负载Silicalite-1分子筛的制备及其催化糠醛加氢性能研究

糠醛是一种重要的生物质平台分子,研发具有高活性和稳定性的糠醛加氢催化剂是当前的研究焦点,但贵金属催化剂的高成本问题使得其难以满足大规模工业生产的需求。利用一步水热法成功地合成了过渡金属负载Silicalite-1分子筛催化剂,并探讨了引入不同类型的过渡金属(如Ni、Co、Cu和Fe)对Silicalite-1分子筛结构产生的影响。研究结果表明:低金属负载量并不会对分子筛结构的形成产生影响,同时金属物种在分子筛载体的表面也能均匀分布。在糠醛的加氢转化过程中,Ni基催化剂S-Ni2展现出优异的糠醛转化能力,糠醛的转化率高达96%,产物呋喃的选择性保持在71%左右。Cu基催化剂S-Cu1表现出优异的糠醇选择性,产物选择性接近100%,这一性能明显优于通过浸渍法制得的铜基催化剂(76%)。因此,与浸渍法相比,采用一步水热法可以获得具有高选择性的催化剂,且该方法简单易操作。本研究为寻找高效、稳定且经济的金属加氢催化剂开辟了新的方向,并促进了生物质资源的高值化应用。

The convergence ball and error analysis of the two-step Secant method

Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order,we obtain an estimate of the radius of the convergence ball for the two-step secant method.Moreover,we also provide an error estimate that matches the convergence order of the two-step secant method.At last,we give an application of the proposed theorem.

Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

Adaptive split-step Fourier method for simulating ultrashort laser pulse propagation in photonic crystal fibres

In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin （SUPG） method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid axe performed by the Galerkin method. The second-order semi- implicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are lineaxized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.

Applying a Step Approach Method in Solving the Multi-Frequency Radiation From a Complex Obstacle

In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integral Equation and derived in the time domain;thus,the time-harmonic Neumann boundary condition can be imposed.By the present method,the values of the initial conditions are set to zero,and the approach process is carried forward in a loop from the first time step to the last.At each time step,the radiated pressure on each element is updated.After several loops,the correct radiated pressures can be obtained.A sphere pulsating with a monopole frequency in an infinite acoustic domain is calculated first.This result is compared with the analytical solution,and both of them are in good agreement.Then,a complex-shaped radiator is taken as the studied case.The pulsating frequency of this case is multiple,and the waves propagate in half space.It is shown that the present method can treat multiple-frequency pulsation well,even when the radiator is a complex shape,and a robust convergence can be attained quickly.

三维纳米花NiCo-MOF非对称超级电容器储能特性

针对储能器件对高比容量、长寿命、高安全性、绿色环保电极材料的应用需求,利用一步溶剂热法制备三维纳米花镍钴双金属有机框架(NiCo-MOF)电极材料,并与活性炭(AC)一起组装了工作电压窗口可达1.45 V的高性能非对称超级电容器。通过调控优化金属前驱体摩尔比和水热时间制备得到NiCo-MOF电极材料。该NiCo-MOF电极材料在电流密度为1.0 A·g^(-1)下,比容量高达1839.23 F·g^(-1),这主要归因于由薄纳米片组成的纳米花NiCo-MOF提供了较大的比表面积和较多的电化学活性位点,极大地促进了电解质的浸入和氧化还原反应的发生。以NiCo-MOF为正极、AC为负极制备的非对称超级电容器在1.0 A·g^(-1)下,其比容量达到105.27 F·g^(-1),经过1000次循环后,比容量保持率为89.85%。结果表明,三维纳米花NiCoMOF电极材料在超级电容器等储能领域具有较好的应用前景。

Application of Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet

In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-conditions at infinity. For this reason the governing boundary-layer equations are solved by the Multi-step Differential Transform Method (MDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization, discretization, or perturbation. It is a semi analytical-numerical technique that formulizes Taylor series in a very different manner. By applying the MDTM the interval of convergence for the series solution is increased. The MDTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. It is predicted that the MDTM can be applied to a wide range of engineering applications.

Half-Step Continuous Block Method for the Solutions of Modeled Problems of Ordinary Differential Equations

In this paper, we developed a new continuous block method using the approach of collocation of the differential system and interpolation of the power series approximate solution. A constant step length within a half step interval of integration was adopted. We evaluated at grid and off grid points to get a continuous linear multistep method. The continuous linear multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent and zero stable hence convergent. The new method was tested on real life problems namely: SIR model, Growth model and Mixture Model. The results were found to compete favorably with the existing methods in terms of accuracy and error bound.