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Dynamic stiffness for thin-walled structures by power series

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第8期7卷 1351-1357页

作者： ZHU Bin LEUNG A.Y.T. Department of Civil Engineering Zhejiang University Hangzhou 310027 China Department of Building and Construction City University of Hong Kong Hong Kong China

The dynamic stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. With the obtained thin-walled beam dynamic stiffness matrices, the thin-walled frame dynamic stiffness matrix can also be formulated by satisfying the required displacements compatibility and forces equilib-rium, a method which is similar to the finite element method (FEM). Then the thin-walled structure natural frequencies can be found by equating the determinant of the system dynamic stiffness matrix to zero. By this way, just one element and several elements can exactly predict many modes of a thin-walled beam and a spatial thin-walled frame, respectively. Several cases are studied and the results are compared with the existing solutions of other methods. The natural frequencies and buckling loads of these thin-walled structures are computed.

关键词： Dynamic stiffness method Thin-wall structures power series Buckling

Solution of Duffing-Harmonic Oscillator by the power series Method

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Journal of Mechanics Engineering and Automation 2021年第6期11卷 165-170页

作者： Mazen I.Qaisi Mechanical Engineering Department University of JordanAmman 11942Jordan

This paper provides a power series solution to the Duffing-harmonic oscillator and compares the frequencies with those obtained by the harmonic balance *** capture the periodic motion of the oscillator,the power series expansion is used upon transforming the time variable into an“oscillating time”which reduces the governing equation to a form well-conditioned for a power series solution.A recurrence equation for the series coefficients is established in terms of the“oscillating time”frequency which is then determined by employing Rayleigh’s energy *** response of the oscillator is compared with a numerical solution and good agreement is demonstrated.

关键词： Nonlinear power series Duffing-harmonic oscillator

Numerical Solutions of a Generalized Nth Order Boundary Value Problems Using power series Approximation Method

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Applied Mathematics 2016年第11期7卷 1215-1224页

作者： Ignatius N. Njoseh Ebimene J. Mamadu Department of Mathematics and Computer Science Delta State University Abraka Nigeria Department of Mathematics University of Ilorin Ilorin Nigeria

In this paper, a new approach called power series Approximation Method (PSAM) is developed for the numerical solution of a generalized linear and non-linear higher order Boundary Value Problems (BVPs). The proposed method is efficient and effective on the experimentation on some selected thirteen-order, twelve-order and ten-order boundary value problems as compared with the analytic solutions and other existing methods such as the Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) available in the literature. A convergence analysis of PSAM is also provided.

关键词： power series Linear and Nonlinear Problems Boundary Value Problem (BVP) Numerical Simulation

Application of power series on Vibration Analyses

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Journal of Donghua University(English Edition) 2003年第1期20卷 86-89页

作者：沈永刚 Engineering Training Center Shanghai University of Engineering Science Shanghai 200336

power series is extensively used for engineering studies. To raise the synthesis efficiency and computation accuracy of vibration mode synthesis (MS), the choosing of power series as the component mode-function is studied in this paper, and emphasis is laid on its effect upon the system computation accuracy when using the mode synthesis method for a high speed compound rotating elastic system.

关键词： power series vibration analyses mode synthesis (MS) mode-function computation accuracy.

Algebraic Independence of Certain Values of Exponential Function

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Acta Mathematica Sinica,English series 2006年第2期22卷 571-576页

作者： Yao Chen ZHU Academy of Mathematics and Systems Science Chinese Academy of Sciences

The algebraic independence of e^θ1,…,e^θs is proved, where θ1,… ,θs are certain gap series or power series of algebraic numbers, or certain transcendental continued fractions with algebraic elements.

关键词： Algebraic independence Exponential function Gap series power series Continued fraction Algebraic number

DYNAMIC BUCKLING OF ELASTIC-PLASTIC COLUMN IMPACTED BY RIGID BODY

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Applied Mathematics and Mechanics(English Edition) 2006年第3期27卷 377-382页

作者：韩志军程国强马宏伟张善元 Institute of Applied Mechanics Taiyuan University of Technology Taiyuan 030024P. R. China

The dynamic buckling of an elastic-plastic column subjected to an axial impact by a rigid body was discussed by using the energy law. The traveling process of elastic-plastic waves under impact action was analyzed by characteristics method. The equation of lateral disturbance used to analyze the problem was developed by taking into account the effect of elastic-plastic stress wave. The power series solution of this problem has been the power series approach. The buckling criterion of this problem was proposed by analyzing the characteristics of the solution. The relationship among critical velocity and impact mass, critical buckling length, hardening modulus was given by using theoretical analysis and numerical computation.

关键词： dynamic buckling stress wave critical criteria power series

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

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Computer Modeling in Engineering & Sciences 2023年第6期135卷 2137-2153页

作者： Fairouz Tchier Hassan Khan Shahbaz Khan Poom Kumam Ioannis Dassios Mathematics Department King Saudi UniversityRiyadh145111Saudi Arabia Department of Mathematics Abdul Wali Khan UniversityMardan23200Pakistan Department of Mathematics Near East UniversityNicosia99138Turkey Theoretical and Computational Science(TaCS)Center Department of Mathematics Faculty of ScienceKing Mongkuts University of Technology Thonburi(KMUTT)Bangkok10140Thailand Department of Medical Research China Medical University HospitalChina Medical UniversityTaichung40402Taiwan AMPSAS University College DublinDublinA94 XF34Ireland

The nonlinearity inmany problems occurs because of the complexity of the given physical *** present paper investigates the non-linear fractional partial differential equations’solutions using the Caputo operator with Laplace residual power *** is found that the present technique has a direct and simple implementation to solve the targeted *** comparison of the obtained solutions has been done with actual solutions to the *** fractional-order solutions are presented and considered to be the focal point of this research *** results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each *** of the simple implementation,the present technique can be extended to solve other important fractional order problems.

关键词： Fractional calculus laplace transform laplace residual power series method fractional partial differential equation power series fractional power series

Numerical Simulation of Sound Field in Axisymmetric Jet ofIncompresible Fluid

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Communications in Nonlinear Science and Numerical Simulation 1997年第3期 10-14页

作者： ShiJun LIAO (Department of Naval Architecture & Ocean Engineering, Shanghai Jiao Tong Univ.,Shanghai 200030, P. R. China) E mail : sjliao@***

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关键词： power series non linear differential equations

A General Analytic Approximation Technique for the Modified Bessel Functions with Fractional Order Iv (x), Applied to I1/6(x) and I1/7(x)

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Advances in Pure Mathematics 2024年第9期14卷 768-777页

作者： Jorge Olivares Pablo Martín Maria T. Veliz Departamento de Matemticas Universidad de Antofagasta Antofagasta Chile Departamento de Fsica Universidad de Antofagasta Antofagasta Chile

A general technique to obtain simple analytic approximations for the first kind of modified Bessel functions. The general procedure is shown, and the parameter determination is explained through the applications to this particular case I1/6(x)and I1/7(x). In this way, it shows how to apply the technique to any particular orderν, in order to obtain an approximation valid for any positive value of the variable x. In the present method power series and asymptotic expansion are simultaneously used. The technique is an extension of the multipoint quasirational approximation method, MPQA. The main idea is to look for a bridge function between the power and asymptotic expansion of the I1/6(x), and similar procedure for I1/7(x). To perform this, rational functions are combined with hyperbolic ones and fractional powers. The number of parameters to be determined for each case is four. The maximum relative errors are 0.0049 for ν=1/6, and 0.0047 for ν=7. However, these relative errors decrease outside of the small region of the variables, wherein the maximum relative errors are reached. There is a clear advantage of this procedure compared with any other ones.

关键词： Bessel Functions power series Asymptotic Expansion MPQA Technique