On the homotopy analysis method for non-linear vibration of beams

被引：102
|
作者：
Pirbodaghi, T. [1 ]
Ahmadian, M. T. [1 ]
Fesanghary, M. [2 ]
机构：
[1] Sharif Univ Technol, Ctr Excellence Design Robot & Automat, Sch Mech Engn, Tehran 113659567, Iran
[2] Amirkabir Univ Technol Tehran Polytech, Dept Mech Engn, Tehran 158754413, Iran
来源：
MECHANICS RESEARCH COMMUNICATIONS | 2009年 / 36卷 / 02期
关键词：
Non-linear vibration; Euler-Bernoulli beam; Homotopy analysis method; AMPLITUDE FREE-VIBRATIONS; FORMULATION;
D O I：
10.1016/j.mechrescom.2008.08.001
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
In this study, the homotopy analysis method (HAM) is used to investigate non-linear vibration behaviour of Euler-Bernoulli beams subjected to axial loads. Analytical expressions for geometrically non-linear vibration of beams are provided. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. Comparison between HAM results and those available in literature demonstrates the accuracy of this method. This study shows that a first-order approximation of the HAM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes. (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码：143 / 148
页数：6
相关论文
共 50 条
  • [31] Non-linear vibration of variable speed rotating viscoelastic beams
    Younesian, Davood
    Esmailzadeh, Ebrahim
    NONLINEAR DYNAMICS, 2010, 60 (1-2) : 193 - 205
  • [32] New Homotopy Perturbation Method to Solve Non-Linear Problems
    Rabbani, M.
    JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2013, 7 (04): : 272 - 275
  • [33] A new homotopy method for solving non-linear complementarity problems
    Xu, Qing
    Dang, Chuangyin
    OPTIMIZATION, 2008, 57 (05) : 681 - 689
  • [34] Modified homotopy method to solve non-linear integral equations
    Rabbani, Mohsen
    INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2015, 6 (02): : 133 - 136
  • [35] The scalar homotopy method for solving non-linear obstacle problem
    Fan, Chia-Ming
    Liu, Chein-Shan
    Yeih, Weichung
    Chan, Hsin-Fang
    Computers, Materials and Continua, 2010, 15 (01): : 67 - 86
  • [36] A constraint shifting homotopy method for general non-linear programming
    Yang, Li
    Yu, Bo
    Xu, Qing
    OPTIMIZATION, 2014, 63 (04) : 585 - 600
  • [37] The Scalar Homotopy Method for Solving Non-Linear Obstacle Problem
    Fan, Chia-Ming
    Liu, Chein-Shan
    Yeih, Weichung
    Chan, Hsin-Fang
    CMC-COMPUTERS MATERIALS & CONTINUA, 2010, 15 (01): : 67 - 86
  • [38] Non-linear Forced Vibration Analysis of Piezoelectric Functionally Graded Beams in Thermal Environment
    El Khouddar, Y.
    Adri, A.
    Outassafte, O.
    Rifai, S.
    Benamar, R.
    INTERNATIONAL JOURNAL OF ENGINEERING, 2021, 34 (11): : 2387 - 2396
  • [39] Non-linear forced vibration analysis of piezoelectric functionally graded beams in thermal environment
    El Khouddar Y.E.
    Adri A.
    Outassafte O.
    Rifai S.
    Benamar R.
    International Journal of Engineering, Transactions B: Applications, 2021, 34 (11):
  • [40] On the DQ analysis of geometrically non-linear vibration of immovably simply-supported beams
    Chen, W
    Zhong, TX
    Liang, SP
    JOURNAL OF SOUND AND VIBRATION, 1997, 206 (05) : 745 - 748
12345