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AN asymptotic method FOR ANALYZING THE STRESS IN A FUNCTIONALLY GRADIENT MATERIAL LAYER ON A SURFACE OF A STRUCTURAL COMPONENT

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Acta Mechanica Solida Sinica 1997年第1期10卷 36-47页

作者： Shen, LX Yu, SW TSING HUA UNIV DEPT ENGN MECHBEIJING 100084PEOPLES R CHINA

A simple and effective method for analyzing the stress distribution in a Functionally Gradient Material(FGM) layer on the su;face of a structural component is proposed in this paper. Generally, the FGM layer is very thin compared with the characteristic length of the structural component, and the nonhomogeneity exists only in the thin layer. Based on these features, by choosing a small parameter I which characterizes the stiffness of the layer relative to the component, and expanding the stresses and displacements on the two sides of the interface according to the parameter lambda, then asymptotically using the continuity conditions of the stresses and displacements on the interface, a decoupling computing process of the coupling control equations of the layer and the structural component is realized. Finally, two examples are given to illustrate the application of the method proposed.

关键词： gradient material layer stress state asymptotic method

A class of asymptotic solution for the time delay wind field model of an ocean

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Chinese Physics B 2014年第4期23卷 83-90页

作者：周先春石兰芳莫嘉琪 College of Electronic and Information Engineering Nanjing University of Information Science and Technology (NUIST) Jiangsu Technology and Engineering Center for Meteorological Sensor Network Nanjing University of Information Science and Technology (NUIST) Jiangsu Key Laboratory of Meteorological Observation and Information Processing Nanjing University of Information Science and Technology (NUIST) College of Mathematics and Statistics Nanjing University of Information Science and Technology (NUIST)

A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-la... 详细信息

关键词： two-layers barotropic time delay model asymptotic method

Subharmonic resonance of single-degree-of-freedom piecewise-smooth nonlinear oscillator

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Acta Mechanica Sinica 2020年第5期36卷 1109-1118,I0003页

作者： Jiangchuan Niu Wenjing Zhang Yongjun Shen Shaopu Yang State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures Shijiazhuang Tiedao UniversityShijiazhuang 050043China School of Mechanical Engineering Shijiazhuang Tiedao UniversityShijiazhuang 050043China

Take the single degree of freedom nonlinear oscillator with clearance under harmonic excitation as an example,the 1/3 subharmonic resonance of piecewise-smooth nonlinear oscillator is *** approximate analytical solution of 1/3 subharmonic resonance of the single-degree-of-freedom piecewise-smooth nonlinear oscillator is *** changing the solving process of Krylov-Bogoliubov-Mitropolsky(KBM)asymptotic method for subharmonic resonance of smooth nonlinear system,the classical KBM method is extended to piecewise-smooth nonlinear *** existence conditions of 1/3 subharmonic resonance steady-state solution are achieved,and the stability of the subharmonic resonance steady-statesolution is also *** is found that the clearance affects the amplitude-frequency response of subharmonic resonance in the form of equivalent negative *** a demonstration example,the accuracy of approximate analytical solution is verified by numerical solution,and they have good *** on the approximate analytical solution,the infuences of clearance on the critical frequency and amplitude-frequency response of 1/3 subharmonic resonance are analyzed in *** analysis results show that the KBM method is an effective analytical method for solving the subharmonic resonance of piecewise-smooth nonlinear *** it provides an effective reference for the study of subharmonicr esonance of other piecewise-smooth systems.

关键词： Subharmonic resonance Piecewise-smooth system Approximate analytical solution asymptotic method

THE GROWTH OF DIFFERENCE EQUATIONS AND DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2021年第6期41卷 1911-1920页

作者： Zongxuan CHEN Ranran ZHANG Shuangting LAN Chuangxin CHEN School of Mathematical Sciences South China Normal UniversityGuangzhou510631China Department of Mathematics Guangdong University of EducationGuangzhou510303China School of Mathematics and Systems Sciences Guangdong Polytechnic Normal UniversityGuangzhou510665China College of Computational Sciences Zhongkai University of Agriculture and EngineeringGuangzhou510225China

In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential *** delete the condition(1.6)of Theorems E and F,ye... 详细信息

关键词： asymptotic method difference equations differential equations

asymptotic Calculation of the Wave Trough Exceedance Probabilities in A Nonlinear Sea

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China Ocean Engineering 2018年第2期32卷 189-195页

作者： WANG Ying-guang State Key Laboratory of Ocean Engineering Shanghai Jiao Tong UniversityShanghai 200240China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration(CISSE) Shanghai 200240China School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China

This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method. This is a new approach for the calculation of the wave trough exceedance probabilities, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The proposed asymptotic method has been applied to calculate the wave trough depth exceedance probabilities of a sea state with the surface elevation data measured at the coast of Yura in the Japan Sea. It is demonstrated that the proposed new method can offer better predictions than the theoretical Rayleigh wave trough depth distribution model. The calculated results by using the proposed new method have been further compared with those obtained by using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al.’s wave trough depth distribution model, and its accuracy has been once again substantiated. The research findings obtained from this study demonstrate that the proposed asymptotic method can be readily utilized in the process of designing various kinds of ocean engineering structures.

关键词： wave trough depth second order nonlinear wave model asymptotic method measured data

Influences of Marangoni effect on solidification of curved interfaces with constant curvature

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Applied Mathematics and Mechanics(English Edition) 2008年第2期29卷 145-151页

作者：胡国辉周哲玮 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering Shanghai 200072P.R.China

The asymptotic method and phase field simulation are applied to study the influences of variation of the surface tension with temperature on the movements of solid-liquid interfaces in the solidification process of spherical and cylindrical nuclei, respectively. Results indicate that Marangoni effect will increase the critical nucleation radius, slow up the movement of interface. The tip speed of dendrite decreases linearly with Marangoni number for melt without convection. The results of phase field simulation are qualitatively in accord with that of asymptotic method.

关键词： solidification phase field simulation Marangoni effect asymptotic method wcrystal growth

Estimation of Nonlinear Roll Damping by Analytical Approximation of Experimental Free-Decay Amplitudes

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Journal of Ocean University of China 2019年第4期18卷 812-822页

作者： SUN Jinwei SHAO Meng College of Engineering Ocean University of China Qingdao 266100 China Key Laboratory of Ocean Engineering of Shandong Province Ocean University of China Qingdao 266100 China Institute of Oceanographic Instrumentation Qilu University of Technology (Shandong Academy of Sciences) Qingdao 266001 China Shandong Provincial Key Laboratory of Ocean Environmental Monitoring Technology Qingdao 266001 China National Engineering and Technological Research Center of Marine Monitoring Equipment Qingdao 266001 China

Damping is critical for the roll motion response of a ship in waves. A common method for the assessment of damping in a ship’s rolling motion is to perform a free-decay experiment in calm water. In this paper, we propose an approach for estimating nonlinear damping that involves a linear exponential analytical approximation of the experimental roll free-decay amplitudes, fol- lowed by parametric identification based on the asymptotic method. The restoring moment can be strongly nonlinear. To validate this method, we first analyzed numerically simulated roll free-decay data using rolling equations with two alternative parametric forms: linear-plus-quadratic and linear-plus-cubic damping. By doing so, we obtained accurate estimates of nonlinear damping coefficients, even for large initial roll amplitudes. Then, we applied the proposed method to real free-decay data obtained from a scale model of a bulk barrier, and found the simulated results to be in good agreement with the experimental data. Using only free-decay peak data, the proposed method can be used to estimate nonlinear roll-damping coefficients for conditions with a strongly nonlinear restoring moment and large initial roll amplitudes.

关键词： nonlinear roll damping parametric identification nonlinear restoring moment asymptotic method linear exponential approximation

asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation

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Chinese Annals of Mathematics,Series B 2023年第1期44卷 81-98页

作者： Qian YANG Mingkang NI College of Science University of Shanghai for Science and TechnologyShanghai 200093China School of Mathematical Sciences East China Normal UniversityShanghai 200062China Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Shanghai 200241China

A singularly perturbed boundary value problem for a piecewise-smooth nonlinear stationary equation of reaction-diffusion-advection type is studied.A new class of problems in the case when the discontinuous curve which separates the domain is monotone with respect to the time variable is *** existence of a smooth solution with an internal layer appearing in the neighborhood of some point on the discontinuous curve is *** efficient algorithm for constructing the point itself and an asymptotic representation of arbitrary-order accuracy to the solution is *** sufficiently small parameter values,the existence theorem is proved by the technique of matching asymptotic *** example is given to show the effectiveness of their method.

关键词： Reaction-Diffusion-Advection equation Internal layer asymptotic method Piecewise-Smooth dynamical system

asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation

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Science China Mathematics 2022年第2期65卷 291-308页

作者： Qian Yang Mingkang Ni School of Mathematical Sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Shanghai 200241China

A piecewise-smooth second-order singularly perturbed differential equation whose right-hand side is a nonlinear function with a discontinuity on some curve is investigated. This is a new class of problems in the case where the degenerate equation has a multiple root on the left-hand side of the curve which separates the domain and an isolated root on the right-hand side of that curve. The asymptotics of a solution with an internal layer near a point on the discontinuous curve and the transition point is constructed. The method to construct the internal layer function is proposed. The behavior of the solution in the internal layer consisting of four zones essentially differs from the case of isolated roots. For sufficiently small parameter values, the existence of a smooth solution with an internal layer from the multiple root of the degenerate equation to the isolated root in the neighborhood of a point on the discontinuous curve is proved. The method can be shown to be effective in the given example.

关键词： reaction-diffusion equation multizonal internal layer asymptotic method piecewise-smooth dynamical system