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Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions
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作者 Xiaoyang SU Tong HU +3 位作者 Wei ZHANG Houjun KANG Yunyue CONG Quan YUAN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第6期983-1000,共18页
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 th... 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. 展开更多
关键词 transfer matrix method(TMM) free vibration forced vibration functionally graded material(FGM) stepped beam
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Numerical Solution of the Rotating Shallow Water Flows with Topography Using the Fractional Steps Method
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作者 Hossam S. Hassan Khaled T. Ramadan Sarwat N. Hanna 《Applied Mathematics》 2010年第2期104-117,共14页
The two-dimensional nonlinear shallow water equations in the presence of Coriolis force and bottom topography are solved numerically using the fractional steps method. The fractional steps method consists of splitting... The two-dimensional nonlinear shallow water equations in the presence of Coriolis force and bottom topography are solved numerically using the fractional steps method. The fractional steps method consists of splitting the multi-dimensional matrix inversion problem into an equivalent one dimensional problem which is successively integrated in every direction along the characteristics using the Riemann invariant associated with the cubic spline interpolation. The height and the velocity field of the shallow water equations over irregular bottom are discretized on a fixed Eulerian grid and time-stepped using the fractional steps method. Effects of the Coriolis force and the bottom topography for particular initial flows on the velocity components and the free surface elevation have been studied and the results are plotted. 展开更多
关键词 Shallow Water Equations Fractional steps method RIEMANN INVARIANTS Bottom TOPOGRAPHY Cubic SPLINE Interpolation
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Application of the “Six-Step Teaching Method” in the Nursing Teaching of Obstetric Interns
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作者 Rui Liu Kun Yuan Yuanyuan Li 《Open Journal of Nursing》 2023年第9期615-623,共9页
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 ... 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. . 展开更多
关键词 “Six-step Teaching method Obstetrics Intern Nursing Education
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Synthesis of Vanadium Nitride by a One Step Method 被引量:6
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作者 Sansan YU Nianxin FU +1 位作者 Feng GAO Zhitong SUI 《Journal of Materials Science & Technology》 SCIE EI CAS CSCD 2007年第1期43-46,共4页
Vanadium nitrides were prepared via one step method of carbothermal reduction and nitridation of vanadium trioxide. Thermalgravimetric analysis (TGA) and X-ray diffraction were used to determine the reaction paths o... Vanadium nitrides were prepared via one step method of carbothermal reduction and nitridation of vanadium trioxide. Thermalgravimetric analysis (TGA) and X-ray diffraction were used to determine the reaction paths of vanadium carbide, namely the following sequential reaction: V2O3→V8C7 in higher temperature stage, the rule of vanadium nitride synthesized was established, and defined conditions of temperature for the production of the carbides and nitrides were determined. Vanadium oxycarbide may consist in the front process of carbothermal reduction of vanadium trioxide. In one step method for vanadium nitride by carbothermal reduction and nitridation of vanadium trioxide, the nitridation process is simultaneous with the carbothermal reduction. A one-step mechanism of the carbothermal reduction with simultaneous nitridation leaded to a lower terminal temperature in nitridation process for vanadium nitride produced, compared with that of carbothermal reduction process without nitridation. The grain size and shape of vanadium nitride were uniform, and had the shape of a cube. The one step method combined vacuum carborization and nitridation (namely two step method) into one process. It simplified the technological process and decreased the costs. 展开更多
关键词 Vanadium nitride Vanadium trioxide Carbothermal reduction NITRIDATION One step method
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Modified precise time step integration method of structural dynamic analysis 被引量:6
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作者 汪梦甫 周锡元 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2005年第2期287-293,共7页
The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficu... The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method (e.g., an algorithm with an arbitrary order of accuracy) is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm. 展开更多
关键词 structural dynamics time step integration method Gaussian quadrature method
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Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method 被引量:4
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作者 DeYao Zhang WenYong Pan +3 位作者 DingHui Yang LingYun Qiu XingPeng Dong WeiJuan Meng 《Earth and Planetary Physics》 CSCD 2021年第2期149-157,共9页
The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the tim... The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the time-domain.This study applies the NAD method to solving three-dimensional(3D)acoustic wave equations in the frequency-domain.This forward modeling approach is then used as the“engine”for implementing 3D frequency-domain full waveform inversion(FWI).In the numerical modeling experiments,synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods.Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods.The inversion results show that the NAD method is more suitable than traditional methods,in terms of computational cost and stability,for 3D frequency-domain FWI,and represents an effective approach for inversion of subsurface model structures. 展开更多
关键词 THREE-DIMENSION frequency-domain NAD method forward modeling full waveform inversion
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A New Infeasible Interior-point Method for Linear Complementarity Problem Based on Full Newton Step 被引量:1
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作者 龚小玉 胡振鹏 王先甲 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第4期624-632,共9页
This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists... This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists of a feasibility step and several centrality steps. At last,we prove that the algorithm has O(nlog n/ε) polynomial complexity,which coincides with the best known one for the infeasible interior-point algorithm at present. 展开更多
关键词 complementarity problem infeasible interior-point methods full-Newton step polynomial complexity
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Gradient Step Method to Predict the Ozone Solubility in Water 被引量:1
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作者 Marco Aurelio Cremasco Vanessa Trevizan Mochi 《Journal of Environmental Science and Engineering(A)》 2012年第2期256-260,共5页
In this work it presents a strategy to obtain the ozone solubility in water by gradient step method. In this methodology, the ozone in mixture with oxygen is bubbling in a reactor with distilled water at 21℃ and pH 7... In this work it presents a strategy to obtain the ozone solubility in water by gradient step method. In this methodology, the ozone in mixture with oxygen is bubbling in a reactor with distilled water at 21℃ and pH 7. The ozone concentration on gas phase is continually increased after the saturation is reached. The method proposed is faster than conventional method (isocratic method). The solubility from the gradient method is compared with that values obtained from correlations founded in the literature. 展开更多
关键词 OZONE SOLUBILITY gradient step method isocratic method.
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Noether's theorem and one-step corrections method for holonomic system 被引量:4
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作者 尚玫 陈向炜 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第12期2788-2791,共4页
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 syst... 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. 展开更多
关键词 conserved quantities one-step method holonomic system
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Acoustic viscoelastic modeling by frequency-domain boundary element method 被引量:1
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作者 Xizhu Guan Li-Yun Fu Weijia Sun 《Earthquake Science》 CSCD 2017年第2期97-105,共9页
Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element method... Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green's function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method. 展开更多
关键词 Viscoelastic media Viscoelastic boundary element method frequency-domain implementation Viscoelastic numerical modeling
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On“The Five-Step Method”in Teaching Junior English for China 被引量:1
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作者 黄金岩 《湖南工业大学学报(社会科学版)》 1997年第1期48-50,共3页
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 certa... 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". 展开更多
关键词 The Five-step method JUNIOR English for China REVISION PRESENTATION DRILLING Practice CONSOLIDATION
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Temperature-dependent photoluminescence on organic inorganic metal halide perovskite CH_3NH_3Pb I_(3-)Cl_ prepared on ZnO/FTO substrates using a two-step method 被引量:4
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作者 Shiwei Zhuang Deqian Xu +6 位作者 Jiaxin Xu Bin Wu Yuantao Zhang Xin Dong Guoxing Li Baolin Zhang Guotong Du 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第1期482-487,共6页
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 ab... 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. 展开更多
关键词 PEROVSKITE temperature-dependent photoluminescence two-step method ZNO
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Applying the Dynamic Two-Step Method to Forecast Remaining Oil Distribution of Lower Series ,Xiaermen Oilfield 被引量:2
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作者 周红 汤传意 李增辉 《Journal of China University of Geosciences》 SCIE CSCD 2006年第1期65-70,共6页
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 re... 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. 展开更多
关键词 dynamic two-step method flow unit quantitative forecast remaining oil
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INTERACTION OF A SOLITARY WAVE AND A FRONT STEP SIMULATED BY LEVEL SET METHOD
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作者 谢伟松 陶建华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第7期761-766,共6页
As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been invest... As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments. 展开更多
关键词 Level Set method distance function solitary wave front step
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Adaptive split-step Fourier method for simulating ultrashort laser pulse propagation in photonic crystal fibres 被引量:3
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作者 李曙光 邢光龙 +5 位作者 周桂耀 韩颖 侯蓝田 胡明列 栗岩锋 王清月 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第2期437-443,共7页
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 sol... 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. 展开更多
关键词 photonic crystal fibre ultrashort laser pulse propagation adaptive split-step Fourier method
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Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems 被引量:1
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作者 A. MALATIP N. WANSOPHARK P. DECHAUMPHAI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第1期99-116,共18页
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 str... 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. 展开更多
关键词 fluid-solid interaction finite element method fractional four-step method
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Finite Element Methods Applied to the Tubular Linear Stepping Motor
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作者 Walid El Fezzani Abdessattar Ben Amor 《Journal of Electromagnetic Analysis and Applications》 2013年第5期219-222,共4页
In this paper proposes a Finite Element Methods analyzing applied to the linear tubular stepping actuator. The linear displacement is modeled by means of a layer of finite elements placed in the air gap. The design of... In this paper proposes a Finite Element Methods analyzing applied to the linear tubular stepping actuator. The linear displacement is modeled by means of a layer of finite elements placed in the air gap. The design of the linear stepper motor for achieving a specific performance requires the choice of appropriate tooth geometry. The magnetic field of the actuator has been analyzed using the finite element method over a current-displacement variation. The magneto static field and electromagnetic force was introduced in order to predict before construction, the inductance values according to the displacement and the currents into the coils. The results were obtained for the magnetic flux density distribution and the electromagnetic force for different positions and current. 展开更多
关键词 FINITE Element methods Linear TUBULAR stepPING ACTUATOR MESH Repartition
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Application of Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet 被引量:6
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作者 M.M Rashidi Ali J. Chamkha M Keimanesh 《American Journal of Computational Mathematics》 2011年第2期119-128,共10页
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) solution... 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. 展开更多
关键词 Non-Newtonian Fluid STRETCHING Surface SHRINKING SHEET MULTI-step DIFFERENTIAL TRANSFORM method (MDTM)
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Applying a Step Approach Method in Solving the Multi-Frequency Radiation From a Complex Obstacle
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作者 Jui-Hsiang Kao 《Computer Modeling in Engineering & Sciences》 SCIE EI 2016年第7期59-73,共15页
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 Integra... 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. 展开更多
关键词 step approach method Time domain Radiated WAVES Multiple frequencies BOUNDARY integral equation NEUMANN BOUNDARY condition
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A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence 被引量:1
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作者 Leng Xin Liu Degui +1 位作者 Song Xiaoqiu Chen Lirong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第4期908-916,共9页
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 conditio... 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. 展开更多
关键词 CONVERGENCE singular delay differential equations two-step continuity Runge-Kutta methods.
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