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The series solution to the metric of stationary vacuum with axisymmetry

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Chinese Physics B 2010年第3期19卷 90-100页

作者：辜英求 School of Mathematical Science Fudan University

The multipole moment method not only conduces to the understanding of the deformation of the space-time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.

关键词： stationary metric multipole moments asymptotically fiat series solution

A series solution for surface motion amplification due to underground twin tunnels:incident SV waves

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Earthquake Engineering and Engineering Vibration 2003年第2期2卷 289-298页

作者：梁建文张浩 Vincent W Lee Department of Civil Engineering Tianjin UniversityTianjin 300072China Professor Department of Civil Engineering Tianjin UniversityTianjin 300072China Graduate Student Department of Civil Engineering University of Southern CaliforniaLos AngelesCA 90089-2531USA Professor

A series solution of displacement response of the ground surface in the presence of underground twin tunnels subjected to excitation of incident plane SV waves is derived by using Fourier-Bessel series expansion *** numerical parametric study shows that underground twin tunnels significantly amplify the nearby surface ground *** is suggested that the effect of subways on ground motion should be considered when the subways are planned and designed.

关键词： underground twin tunnels surface motion plane SV wave scattering series solution

THE FLOW PRODUCED IN PARTICLE-SUSPENSION BY AN INFINITE ROTATING DISK:series solution

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Journal of Hydrodynamics 1992年第1期4卷 8-15页

作者： Din Xue-dong Shanghai University of Technology,Shanghai Institute of Applied Mathematics & Mechanics,Shanghai 200072,P.R.ChinaXu Xue-zi Zhejiang University,Hangzhou 310027,P.R.China

To the flow produced in particle-suspension by a rotating disk of infinite extent, the asymptotic behavior at infinity is analyzed.A corresponding series solution is *** is shown that this approach yields widely valid solutions of high accuracy for all the cases in which that suction or weak injection at the disk surface *** the cases that strong injection or par- ticle-free band exists,the series method fails.

关键词： rotating disk particle-suspension series solution suction injection

The series solution for a Class of Nonstationary Biological Population Systems and Their Stability

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生物数学学报 1997年第1期12卷 27-33页

作者： Wang Dingjiang(Pingdingshan Teachers College,Pingdingshan,Henan 467000) 平顶山师范高等专科学校河南平顶山 467000

This paper discusses the nonstationary population dynamics,and gives the series solution for the *** existence,uniqueness and stability of the solution are *** using the concept of critical proliferation rate,we obtai... 详细信息

关键词： Population system series solution proliferation rate stability

Longitudinal vibrations of arbitrary non-uniform rods

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Acta Mechanica Solida Sinica 2015年第2期28卷 187-199页

作者： Shuqi Guo Shaopu Yang Department of Engineering Mechanics Shijiazhuang Tiedao University School of Mechanical Engineering Shijiazhuang Tiedao University

Free and steady-state forced longitudinal vibrations of non-uniform rods are investi- gated by an iteration method, which results in a series solution. The series obtained are convergent and linearly independent. Its convergence is verified by convergence tests, its linear independence confirmed by the nonzero value of the corresponding Wronski determinant. Then, the solution obtained is an exact one reducible to a classical solution for the case of uniform rods. In order to verify the method, two examples are presented as an application of the proposed method. The results obtained are equivalent to the method in literature. In contrast to the proposed method ca- pable of dealing with arbitrary non-uniform rods in principle, the method in literature is confined to work on special cases.

关键词： longitudinal vibration arbitrary non-uniform rod series solution convergence

Transverse vibrations of arbitrary non-uniform beams

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Applied Mathematics and Mechanics(English Edition) 2014年第5期35卷 607-620页

作者：郭树起杨绍普 Department of Engineering Mechanics Shijiazhuang Tiedao University School of Mechanical Engineering Shijiazhuang Tiedao University

Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent in a convergence test and by the non-zero value of the corresponding Wronski determinant, respectively. The obtained solution is rigorous, which can be reduced to a classical solution for uniform beams. The proposed method can deal with arbitrary non-uniform Euler-Bernoulli beams in principle, but the methods in terms of special functions or elementary functions can only work in some special cases.

关键词： transverse vibration non-uniform beam series solution convergence

Approximate solutions of Primary Resonance for Forced Duffing Equation by Means of the Homotopy Analysis Method

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Chinese Journal of Mechanical Engineering 2011年第3期24卷 501-506页

作者： YUAN Peixin LI Yongqiang School of Mechanical Engineering ＆ Automation Northeastern University Shenyang 110004 China School of Science Northeastern University Shenyang 110004 China

Nonlinear dynamic equation is a common engineering *** is not precise analytical solution for most of nonlinear differential *** nonlinear differential equations should be solved by using approximate *** 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 *** 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 *** HAM provides a great freedom to choose base functions of solution series,so that a nonlinear problem may be approximated more *** 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 ***,HAM not only may solve the weakly non-linear problems but also may be suitable for the strong non-linear *** 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.

关键词： homotopy analysis method(HAM) series solution forced Duffing equation numerical solution

Peristaltic transport of pseudoplastic fluid in a curved channel with wall properties and slip conditions

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International Journal of Biomathematics 2014年第2期7卷 63-78页

作者： S. Hina T. Hayat M. Mustafa A. Alsaedi Department of Mathematical Sciences Fatima Jinnah Women University Rawalpindi 56000 Pakistan Department of Mathematics Quaid-I-Azam University45320 Islamabad 44000 Pakistan Department of Mathematics Faculty of Science King Abdulaziz University P. O. Box 80257 Jeddah 21589 Saudi Arabia National University of Sciences and Technology (NUST) Sector H-12 Islamabad Pakistan

Effects of wall properties and slip condition on the peristaltic flow of an incompressible pseudoplastic fluid in a curved channel are studied. series solution of the governing problem is obtained after applying long wavelength and low Reynolds number approximations. The results are validated with the numerical solutions through the built-in routine for solving nonlinear boundary value problems via software Mathematica. The variations of different parameters on axial velocity are carefully analyzed. Behaviors of embedding parameters on the dimensionless stream function are also discussed. It is noted that the axial velocity and size of trapped bolus increases with an increase in slip parameter. It is also observed that the profiles of axial velocity are not symmetric about the central line of the curved channel which is different from the case of planar channel.

关键词： Shear-thinning fluid compliant wall nonlinear boundary-value problem series solution curved channel peristalsis.

Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method

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Applied Mathematics and Mechanics(English Edition) 2010年第10期31卷 1293-1304页

作者：原培新李永强 Mechanical Engineering and Automation School Northeastern University(Shenyang) College of Science Northeastern University(Shenyang)

A homotopy analysis method（HAM）is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic *** validity of the HAM is independent of the existence of small parameters in the considered *** HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary *** 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.

关键词： homotopy analysis method primary resonance series solution strong nonlinearity multi-degree-of-freedom