Free vibration analysis of stepped beams by using Adomian decomposition method

被引：65

作者：

Mao, Qibo ^{[1
]}

Pietrzko, Stanislaw ^{[1
]}

机构：

[1] Empa, Swiss Fed Labs Mat Testing & Res, CH-8600 Dubendorf, Switzerland

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 07期

关键词：

Adomian decomposition method; Vibration analysis; Stepped beam; Natural frequency; Mode shape; EULER-BERNOULLI BEAM; CROSS-SECTION; FREQUENCIES; SUPPORTS;

D O I：

10.1016/j.amc.2010.09.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Adomian decomposition method (ADM) is employed in this paper to investigate the free vibrations of a stepped Euler-Bernoulli beam consisting of two uniform sections. Each section is considered a substructure which can be modeled using ADM. By using boundary condition and continuity condition equations, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions, step ratios and step locations are presented. Comparing the results using ADM to those given in the literature, excellent agreement is achieved. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：3429 / 3441

页数：13

共 15 条

[1]

Adomian G., 1994, Fundamental Theories of Physics

[2] A numerical solution of the vibration equation using modified decomposition method [J].

Das, S. .

JOURNAL OF SOUND AND VIBRATION, 2009, 320 (03) :576-583

[3] An exact solution for variable coefficients fourth-order wave equation using the Adomian method [J].

Haddadpour, Hassan .

MATHEMATICAL AND COMPUTER MODELLING, 2006, 44 (11-12) :1144-1152

[4] Free vibration of non-uniform Euler-Bernoulli beams with general elastically end constraints using Adomian modified decomposition method [J].

Hsu, Jung-Chang ;

Lai, Hsin-Yi ;

Chen, C. K. .

JOURNAL OF SOUND AND VIBRATION, 2008, 318 (4-5) :965-981

[5] FREE-VIBRATION OF STEPPED BEAMS - HIGHER MODE FREQUENCIES AND EFFECTS OF STEPS ON FREQUENCY [J].

JANG, SK ;

BERT, CW .

JOURNAL OF SOUND AND VIBRATION, 1989, 132 (01) :164-168

[6] FREE-VIBRATION OF STEPPED BEAMS - EXACT AND NUMERICAL-SOLUTIONS [J].

JANG, SK ;

BERT, CW .

JOURNAL OF SOUND AND VIBRATION, 1989, 130 (02) :342-346

[7] An innovative eigenvalue problem solver for free vibration of Euler-Bernoulli beam by using the Adomian decomposition method [J].

Lai, Hsin-Yi ;

Hsu, Jung-Chang ;

Chen, Cha'o-Luang .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (12) :3204-3220

[8] Dynamic analysis of flexible slider-crank mechanisms with non-linear finite element method [J].

Chen, JS ;

Huang, CL .

JOURNAL OF SOUND AND VIBRATION, 2001, 246 (03) :389-402

[9] Design of shaped piezoelectric modal sensor for beam with arbitrary boundary conditions by using Adomian decomposition method [J].

Mao, Qibo ;

Pietrzko, Stanislaw .

JOURNAL OF SOUND AND VIBRATION, 2010, 329 (11) :2068-2082

[10] Orthogonality condition for a multi-span beam, and its application to transient vibration of a two-span beam [J].

Mikata, Yozo .

JOURNAL OF SOUND AND VIBRATION, 2008, 314 (3-5) :851-866

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