Free vibration of a beam subjected to large static deflection

被引:15
作者
Cornil, Marie-Blanche
Capolungo, Laurent
Qu, Jianmin [1 ]
Jairazbhoy, Vivek A.
机构
[1] Georgia Inst Technol, Sch Mech Engn, Atlanta, GA 30332 USA
[2] Visteon Corp, Adv Technol Dev, Dearborn, MI 48121 USA
关键词
D O I
10.1016/j.jsv.2007.02.016
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
Considered in this paper is the problem of free vibration of a beam that has undergone a large static deflection. The nonlinear equations of motion for the beam are derived first. The equations are then decomposed into a set of nonlinear differential equations for the static deflection and a set of linear differential equations for the vibrational motion of the beam. The coefficients of the vibration equations consist of the beam's static deflection. The nonlinear differential equations are solved analytically to obtain the static deflection. The vibration equations are solved by expanding the displacements in a power series. Coefficients of the power series are constructed analytically through a recursive relationship. The natural frequencies of the beam under large static bending are determined by solving a 3 x 3 eigenvalue problem. Substitution of the eigenvalues and eigenvectors into the power-series expansion of the displacements yields the corresponding modes of vibration. Several numerical examples are given to illustrate the solution procedure. (c) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码:723 / 740
页数:18
相关论文
共 18 条
  • [1] ON THE RELATIONSHIP BETWEEN VEERING OF EIGENVALUE LOCI AND PARAMETER SENSITIVITY OF EIGENFUNCTIONS
    CHEN, PT
    GINSBERG, JH
    [J]. JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, 1992, 114 (02): : 141 - 148
  • [2] IN-PLANE VIBRATION OF CONTINUOUS CURVED BEAMS
    CHEN, S
    [J]. NUCLEAR ENGINEERING AND DESIGN, 1973, 25 (03) : 413 - 431
  • [3] Chidamparam P., 1993, Applied MechanicsReview, V46, P467, DOI DOI 10.1115/1.3120374
  • [4] Crum MR, 1997, TRANSPORT J, V37, P5
  • [5] Freitag L, 2000, ELEC COMP C, P1259
  • [6] Development of flex stackable carriers
    Isaak, H
    Uka, P
    [J]. 50TH ELECTRONIC COMPONENTS & TECHNOLOGY CONFERENCE - 2000 PROCEEDINGS, 2000, : 378 - 384
  • [7] Kirchhoff G, 1859, J REINE ANGEW MATH, V56, P285, DOI DOI 10.1515/CRLL.1859.56.285
  • [8] Laura P. A. A., 1987, SHOCK VIBRATION DIGE, V19, P6
  • [9] LEE B, 1989, J SOUND VIBRATION, V6, P75
  • [10] FREE VIBRATION OF RECTANGULAR-PLATES
    LEISSA, AW
    [J]. JOURNAL OF SOUND AND VIBRATION, 1973, 31 (03) : 257 - 293