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A Review on Sources,Extractions and Analysis Methods of a Sustainable Biomaterial:Tannins
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作者 Antonio Pizzi Marie-Pierre Laborie Zeki Candan 《Journal of Renewable Materials》 EI CAS 2024年第3期397-425,共29页
Condensed and hydrolysable tannins are non-toxic natural polyphenols that are a commercial commodity industrialized for tanning hides to obtain leather and for a growing number of other industrial applications mainly ... Condensed and hydrolysable tannins are non-toxic natural polyphenols that are a commercial commodity industrialized for tanning hides to obtain leather and for a growing number of other industrial applications mainly to substitute petroleum-based products.They are a definite class of sustainable materials of the forestry industry.They have been in operation for hundreds of years to manufacture leather and now for a growing number of applications in a variety of other industries,such as wood adhesives,metal coating,pharmaceutical/medical applications and several others.This review presents the main sources,either already or potentially commercial of this forestry by-materials,their industrial and laboratory extraction systems,their systems of analysis with their advantages and drawbacks,be these methods so simple to even appear primitive but nonetheless of proven effectiveness,or very modern and instrumental.It constitutes a basic but essential summary of what is necessary to know of these sustainable materials.In doing so,the review highlights some of the main challenges that remain to be addressed to deliver the quality and economics of tannin supply necessary to fulfill the industrial production requirements for some materials-based uses. 展开更多
关键词 TANNINS FLAVONOIDS SOURCES extraction methods analysis methods
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A novel method for gamma spectrum analysis of low-level and intermediate-level radioactive waste 被引量:1
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作者 Hui Yang Xin-Yu Zhang +4 位作者 Wei-Guo Gu Bing Dong Xue-Zhi Jiang Wen-Tao Zhou De-Zhong Wang 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2023年第6期199-213,共15页
The uncertainty of nuclide libraries in the analysis of the gamma spectra of low-and intermediate-level radioactive waste(LILW)using existing methods produces unstable results.To address this problem,a novel spectral ... The uncertainty of nuclide libraries in the analysis of the gamma spectra of low-and intermediate-level radioactive waste(LILW)using existing methods produces unstable results.To address this problem,a novel spectral analysis method is proposed in this study.In this method,overlapping peaks are located using a continuous wavelet transform.An improved quadratic convolution method is proposed to calculate the widths of the peaks and establish a fourth-order filter model to estimate the Compton edge baseline with the overlapping peaks.Combined with the adaptive sensitive nonlinear iterative peak,this method can effectively subtracts the background.Finally,a function describing the peak shape as a filter is used to deconvolve the energy spectrum to achieve accurate qualitative and quantitative analyses of the nuclide without the aid of a nuclide library.Gamma spectrum acquisition experiments for standard point sources of Cs-137 and Eu-152,a segmented gamma scanning experiment for a 200 L standard drum,and a Monte Carlo simulation experiment for triple overlapping peaks using the closest energy of three typical LILW nuclides(Sb-125,Sb-124,and Cs-134)are conducted.The results of the experiments indicate that(1)the novel method and gamma vision(GV)with an accurate nuclide library have the same spectral analysis capability,and the peak area calculation error is less than 4%;(2)compared with the GV,the analysis results of the novel method are more stable;(3)the novel method can be applied to the activity measurement of LILW,and the error of the activity reconstruction at the equivalent radius is 2.4%;and(4)The proposed novel method can quantitatively analyze all nuclides in LILW without a nuclide library.This novel method can improve the accuracy and precision of LILW measurements,provide key technical support for the reasonable disposal of LILW,and ensure the safety of humans and the environment. 展开更多
关键词 HPGe detector Low-level and intermediate-level radioactive waste Gamma spectrum analysis method Deconvolution method Continuous wavelet transform
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Overview of Precious Metal Content Analysis Methods in Automotive Catalytic Converter 被引量:1
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作者 Xianpeng Yang Chengbao Xie +4 位作者 Ning Liu Xin Du Suqing Wang Huasheng Jiang Zhengang Zhang 《Journal of Materials Science and Chemical Engineering》 2023年第11期7-14,共8页
With the increasing awareness of environmental protection, people’s concern of pollution issues arising. Vehicles, as the most important means of transportation, its exhaust emission has received considerable attenti... With the increasing awareness of environmental protection, people’s concern of pollution issues arising. Vehicles, as the most important means of transportation, its exhaust emission has received considerable attention. The catalytic converter is able to purify harmful substances in exhaust gas. The absolute content of precious metals in the catalytic converter dominates the exhaust gas purification effect. Accurate detection of precious metal content is of great significance for controlling the cost of catalysts, ensuring catalytic performance and recovering precious metals from spent catalysts. We herein summarized several instruments for precious metals content exploration, such as X-ray fluorescence spectrometer (XRF), atomic absorption spectrometer (AAS), inductively coupled plasma emission spectrometer (ICP) and spectrophotometer. In this thesis, the feasibility of using various devices for characterizing precious metal content in catalytic converters is analyzed and their strengths or weaknesses are elaborated. 展开更多
关键词 Catalytic Converter Precious Metal Content analysis methods
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Quantitative Analysis of Seeing with Height and Time at Muztagh-Ata Site Based on ERA5 Database
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作者 Xiao-Qi Wu Cun-Ying Xiao +3 位作者 Ali Esamdin Jing Xu Ze-Wei Wang Luo Xiao 《Research in Astronomy and Astrophysics》 SCIE CAS CSCD 2024年第1期87-95,共9页
Seeing is an important index to evaluate the quality of an astronomical site.To estimate seeing at the Muztagh-Ata site with height and time quantitatively,the European Centre for Medium-Range Weather Forecasts reanal... Seeing is an important index to evaluate the quality of an astronomical site.To estimate seeing at the Muztagh-Ata site with height and time quantitatively,the European Centre for Medium-Range Weather Forecasts reanalysis database(ERA5)is used.Seeing calculated from ERA5 is compared consistently with the Differential Image Motion Monitor seeing at the height of 12 m.Results show that seeing decays exponentially with height at the Muztagh-Ata site.Seeing decays the fastest in fall in 2021 and most slowly with height in summer.The seeing condition is better in fall than in summer.The median value of seeing at 12 m is 0.89 arcsec,the maximum value is1.21 arcsec in August and the minimum is 0.66 arcsec in October.The median value of seeing at 12 m is 0.72arcsec in the nighttime and 1.08 arcsec in the daytime.Seeing is a combination of annual and about biannual variations with the same phase as temperature and wind speed indicating that seeing variation with time is influenced by temperature and wind speed.The Richardson number Ri is used to analyze the atmospheric stability and the variations of seeing are consistent with Ri between layers.These quantitative results can provide an important reference for a telescopic observation strategy. 展开更多
关键词 site testing atmospheric effects methods:data analysis telescopes EARTH
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Observation and Analysis of VLF Nocturnal Multimode Interference Phenomenon based on Waveguide Mode Theory
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作者 Sai Yang You-Tian Niu +5 位作者 Zhe Wang Xiu-Kun Zhao Bei Li Yu-Ling Ding Ge-Ge Zhao An-Qi Zhang 《Research in Astronomy and Astrophysics》 SCIE CAS CSCD 2024年第1期78-86,共9页
Very low frequency(VLF)signals are propagated between the ground-ionosphere.Multimode interference will cause the phase to show oscillatory changes with distance while propagating at night,leading to abnormalities in ... Very low frequency(VLF)signals are propagated between the ground-ionosphere.Multimode interference will cause the phase to show oscillatory changes with distance while propagating at night,leading to abnormalities in the received VLF signal.This study uses the VLF signal received in Qingdao City,Shandong Province,from the Russian Alpha navigation system to explore the multimode interference problem of VLF signal propagation.The characteristics of the effect of multimode interference phenomena on the phase are analyzed according to the variation of the phase of the VLF signal.However,the phase of VLF signals will also be affected by the X-ray and energetic particles that are released during the eruption of solar flares,therefore the two phenomena are studied in this work.It is concluded that the X-ray will not affect the phase of VLF signals at night,but the energetic particles will affect the phase change,and the influence of energetic particles should be excluded in the study of multimode interference phenomena.Using VLF signals for navigation positioning in degraded or unavailable GPS conditions is of great practical significance for VLF navigation systems as it can avoid the influence of multimode interference and improve positioning accuracy. 展开更多
关键词 WAVES methods:data analysis Sun:flares Sun:X-rays GAMMA-RAYS
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Comprehensive Analysis Method of Slope Stability Based on the Limit Equilibrium and Finite Element Methods and Its Application
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作者 Yajun Wang Yifeng Li Jinzhou Chen 《Open Journal of Civil Engineering》 2023年第4期555-571,共17页
To study the safety and stability of large slopes, taking the right side slope of the Yuxi’an tunnel of the Yuchu Expressway Bridge in Yunnan Province as an example, limit equilibrium and finite element analysis were... To study the safety and stability of large slopes, taking the right side slope of the Yuxi’an tunnel of the Yuchu Expressway Bridge in Yunnan Province as an example, limit equilibrium and finite element analysis were applied to engineering examples to calculate the stability coefficient of the slope before and after excavation in the natural state. After comparative analysis, it was concluded that the former had a clear mechanical model and concept, which could quickly provide stability results;the latter could accurately determine the sliding surface of the slope and simulate the stress state changes of the rock and soil mass. The stability coefficients calculated by the two methods were within the stable range, but their values were different. On this basis, combined with the calculation principles, advantages and disadvantages of the two methods, a comprehensive analysis method of slope stability based on the limit equilibrium and finite element methods was proposed, and the rationality of the stability coefficient calculated by this method was judged for a slope case. 展开更多
关键词 Slope Body Excavation Mechanical Model Sliding Surface Coefficient of Stability Calculation Principle Comprehensive analysis method
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PSRDP:A Parallel Processing Method for Pulsar Baseband Data
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作者 Ya-Zhou Zhang Hai-Long Zhang +7 位作者 Jie Wang Xin-Chen Ye Shuang-Qiang Wang Xu Du Han Wu Ting Zhang Shao-Cong Guo Meng Zhang 《Research in Astronomy and Astrophysics》 SCIE CAS CSCD 2024年第1期300-310,共11页
To address the problem of real-time processing of ultra-wide bandwidth pulsar baseband data,we designed and implemented a pulsar baseband data processing algorithm(PSRDP)based on GPU parallel computing technology.PSRD... To address the problem of real-time processing of ultra-wide bandwidth pulsar baseband data,we designed and implemented a pulsar baseband data processing algorithm(PSRDP)based on GPU parallel computing technology.PSRDP can perform operations such as baseband data unpacking,channel separation,coherent dedispersion,Stokes detection,phase and folding period prediction,and folding integration in GPU clusters.We tested the algorithm using the J0437-4715 pulsar baseband data generated by the CASPSR and Medusa backends of the Parkes,and the J0332+5434 pulsar baseband data generated by the self-developed backend of the Nan Shan Radio Telescope.We obtained the pulse profiles of each baseband data.Through experimental analysis,we have found that the pulse profiles generated by the PSRDP algorithm in this paper are essentially consistent with the processing results of Digital Signal Processing Software for Pulsar Astronomy(DSPSR),which verified the effectiveness of the PSRDP algorithm.Furthermore,using the same baseband data,we compared the processing speed of PSRDP with DSPSR,and the results showed that PSRDP was not slower than DSPSR in terms of speed.The theoretical and technical experience gained from the PSRDP algorithm research in this article lays a technical foundation for the real-time processing of QTT(Qi Tai radio Telescope)ultra-wide bandwidth pulsar baseband data. 展开更多
关键词 (stars:)pulsars:general methods:data analysis techniques:miscellaneous
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Species distribution of polymeric aluminium ferrum——timed complexation colorimetric analysis method of Al-Fe-Ferron 被引量:8
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作者 Hu, YY Tu, CQ Wu, HH 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2001年第4期418-421,共4页
The effects of the calorimetric buffer solutions were investigated while the two colorimetric reactions of AI-ferron complex and Fe-ferron complex occurred individually, and the effects of the testing wavelength and t... The effects of the calorimetric buffer solutions were investigated while the two colorimetric reactions of AI-ferron complex and Fe-ferron complex occurred individually, and the effects of the testing wavelength and the pH of the solutions were also investigated. A timed complexatian colorimetric analysis method of Al-Fe-ferron in view of the total concentration of {AI + Fe} was then established to determine the species distribution of polymeric Al-Fe. The testing wavelength was recommended at 362 net and the testing pH value was 5. With a comparison of the ratios of n(Al)/n(Fe), the standard adsorption curves of the polymeric Al-Fe solutions were derived from the experimental results. Furthermore, the solutions' composition were carious in both the molar n(Al)/n(Fe) ratios, i.e. 0/0, 5/5, 9/1 and 0/10, and the concentrations associated with the total ( Al + Fe which ranged from 10(-5) to 10(-4) mol/L.. 展开更多
关键词 polymeric aluminum-ferrum species distribution timed complexation colarimetric analysis method Al-Fe-ferron
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Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads 被引量:7
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作者 Zhiping Qiu Xiaojun Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第3期265-276,共12页
Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories o... Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model. 展开更多
关键词 Impulsive response Interval analysis method Convex model Uncertain-but-bounded impulse
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Slope stability analysis under seismic load by vector sum analysis method 被引量:15
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作者 Mingwei Guo Xiurun Ge Shuilin Wang 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE 2011年第3期282-288,共7页
The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method (DFEM). Combining with the DFEM, the vector sum analysis method (VSAM) is... The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method (DFEM). Combining with the DFEM, the vector sum analysis method (VSAM) is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load. 展开更多
关键词 slope stability vector sum analysis method (VSAM) seismic load dynamic finite element method (DFEM)
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Nonlinear oscillations with parametric excitation solved by homotopy analysis method 被引量:5
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作者 Jianmin Wen Zhengcai Cao 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2008年第3期325-329,共5页
An analytical technique, namely the homotopy analysis method (HAM), is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small phys... An analytical technique, namely the homotopy analysis method (HAM), is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small physical parameters at all, and thus valid for both weakly and strongly nonlinear problems. In addition, HAM is different from all other analytic techniques in providing a simple way to adjust and control convergence region of the series solution by means of an auxiliary parameter h. In the present paper, a periodic analytic approximations for nonlinear oscillations with parametric excitation are obtained by using HAM, and the results are validated by numerical simulations. 展开更多
关键词 Nonlinear oscillation Parametric excitation Series solutions Homotopy analysis method
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Improving convergence of incremental harmonic balance method using homotopy analysis method 被引量:3
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作者 Yanmao Chen Jike Liu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第5期707-712,共6页
We have deduced incremental harmonic balance an iteration scheme in the (IHB) method using the harmonic balance plus the Newton-Raphson method. Since the convergence of the iteration is dependent upon the initial va... We have deduced incremental harmonic balance an iteration scheme in the (IHB) method using the harmonic balance plus the Newton-Raphson method. Since the convergence of the iteration is dependent upon the initial values in the iteration, the convergent region is greatly restricted for some cases. In this contribution, in order to enlarge the convergent region of the IHB method, we constructed the zeroth-order deformation equation using the homotopy analysis method, in which the IHB method is employed to solve the deformation equation with an embedding parameter as the active increment. Taking the Duffing and the van der Pol equations as examples, we obtained the highly accurate solutions. Importantly, the presented approach renders a convenient way to control and adjust the convergence. 展开更多
关键词 Incremental harmonic balance method Homotopy analysis method Initial value CONVERGENCE
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Utilizing comprehensive decision analysis methods to determine an optimal planting pattern and nitrogen application for winter oilseed rape 被引量:2
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作者 DU Ya-dan CUI Bing-jing +3 位作者 ZHANG Qian SUN Jun WANG Zhen NIU Wen-quan 《Journal of Integrative Agriculture》 SCIE CAS CSCD 2020年第9期2229-2238,共10页
Oilseed rape is one of the most important oil crops globally.Attaining the appropriate cultivation method(planting pattern and nitrogen level)is necessary to achieve high yield,quality and resource utilization efficie... Oilseed rape is one of the most important oil crops globally.Attaining the appropriate cultivation method(planting pattern and nitrogen level)is necessary to achieve high yield,quality and resource utilization efficiency.However,the optimal method for oilseed rape varies across countries and regions.The objective of the present study was to determine an appropriate cultivation method,including planting pattern and nitrogen application,for winter oilseed rape in northwestern China.Two planting patterns:ridge film mulching and furrow planting(RFMF)and flat planting(FP),and six nitrogen(N)amounts:0(N0),60(N60),120(N120),180(N180),240(N240),and 300(N300)kg N ha–1 were applied across three growing seasons(2014–2017).Three comprehensive decision analysis methods:principal component analysis,grey correlation degree analysis and the combined entropy weight and dynamic technique for order preference by similarity to ideal solution method were used to evaluate the growth and physiological indicators,nutrient uptake,yield,quality,evapotranspiration,and water use efficiency of winter oilseed rape.Planting pattern,nitrogen amount and their interaction significantly affected the indicators aforementioned.The RFMF pattern significantly increased all indicators over the FP pattern.Application of N also markedly increased all the indicators except for seed oil content,but the yield,oil production and water use efficiency were decreased when N fertilizer exceeded 180 kg N ha–1 under FP and 240 kg N ha–1 under RFFM.The evaluation results of the three comprehensive decision analysis methods indicated that RFMF planting pattern with 240 kg N ha–1 is an appropriate cultivation method for winter oilseed rape in northwestern China.These findings are of vital significance to maximize yield,optimize quality and improve resource use efficiencies of winter oilseed rape. 展开更多
关键词 appropriate cultivation method comprehensive decision analysis method northwestern China winter oilseed rape
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New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology 被引量:4
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作者 M.M.Khader Sunil Kumar S.Abbasbandy 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第11期135-139,共5页
We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on t... We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method (HAM). This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained. 展开更多
关键词 discretized mKdV lattice equation nonlinear differential-difference equations Laplace transform homotopy analysis transform method
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Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method 被引量:1
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作者 原培新 李永强 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第10期1293-1304,共12页
A homotopy analysis method(HAM)is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces.The validity of the HAM is independent of the existenc... A homotopy analysis method(HAM)is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces.The validity of the HAM is independent of the existence of small parameters in the considered equation.The HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter.Two examples are presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincar'e method and the incremental harmonic balance method. 展开更多
关键词 homotopy analysis method primary resonance series solution strong nonlinearity MULTI-DEGREE-OF-FREEDOM
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An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system 被引量:7
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作者 Peng Chen Jin-Yang Liu Jia-Zhen Hong 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2016年第2期326-334,共9页
In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are t... In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y. 展开更多
关键词 Multi-body dynamics Contact–impact analysis Lagrangian method Component mode synthesis
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MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method 被引量:1
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作者 S. Nadeem Anwar Hussain 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第12期1569-1578,共10页
The present paper investigates the magnetohydrodynamic(MHD) flow of a viscous fluid towards a nonlinear porous shrinking sheet.The governing equations are simplified by similarity transformations.The reduced problem... The present paper investigates the magnetohydrodynamic(MHD) flow of a viscous fluid towards a nonlinear porous shrinking sheet.The governing equations are simplified by similarity transformations.The reduced problem is then solved by the homotopy analysis method.The pertinent parameters appearing in the problem are discussed graphically and presented in tables.It is found that the shrinking solutions exist in the presence of MHD.It is also observed from the tables that the solutions for f(0) with different values of parameters are convergent. 展开更多
关键词 MHD flow stagnation flow shrinking sheet homotopy analysis method
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Approximate solution for the Klein Gordon-Schrdinger equation by the homotopy analysis method 被引量:1
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作者 王佳 李彪 叶望川 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第3期83-89,共7页
The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parame... The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution. 展开更多
关键词 Klein-Gordon-Schrodinger equation homotopy analysis method approximate solution
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Approximate Solutions of Primary Resonance for Forced Duffing Equation by Means of the Homotopy Analysis Method 被引量:1
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作者 YUAN Peixin LI Yongqiang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2011年第3期501-506,共6页
Nonlinear dynamic equation is a common engineering model.There is not precise analytical solution for most of nonlinear differential equations.These nonlinear differential equations should be solved by using approxima... Nonlinear dynamic equation is a common engineering model.There is not precise analytical solution for most of nonlinear differential equations.These nonlinear differential equations should be solved by using approximate methods.Classical perturbation methods such as LP method,KBM method,multi-scale method and the averaging method on weakly nonlinear vibration system is effective,while the strongly nonlinear system is difficult to apply.Approximate solutions of primary resonance for forced Duffing equation is investigated by means of homotopy analysis method (HAM).Different from other approximate computational method,the HAM is totally independent of small physical parameters,and thus is suitable for most nonlinear problems.The HAM provides a great freedom to choose base functions of solution series,so that a nonlinear problem may be approximated more effectively.The HAM provides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter and the auxiliary function.Therefore,HAM not only may solve the weakly non-linear problems but also may be suitable for the strong non-linear problem.Through the approximate solution of forced Duffing equation with cubic non-linearity,the HAM and fourth order Runge-Kutta method of numerical solution were compared,the results show that the HAM not only can solve the steady state solution,but also can calculate the unsteady state solution,and has the good computational accuracy. 展开更多
关键词 homotopy analysis method(HAM) series solution forced Duffing equation numerical solution
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Application of the homotopy analysis method for the Gross-Pitaevskii equation with a harmonic trap 被引量:1
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作者 石玉仁 刘丛波 +1 位作者 王光辉 周志刚 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第12期88-93,共6页
The Homotopy analysis method (HAM) is adopted to find the approximate analytical solutions of the Gross- Pitaevskii equation, a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapp... The Homotopy analysis method (HAM) is adopted to find the approximate analytical solutions of the Gross- Pitaevskii equation, a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapped in a harmonic potential. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they fit very well with each other when the atomic interaction is weak. 展开更多
关键词 Gross-Pitaevskii equation homotopy analysis method analytical solution
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