Free Vibration Analysis of Thin-Walled Box Beam of Crane Considering Distortion

被引：0
|
作者：
Tan M. [1 ]
Cheng W. [1 ]
Li H. [1 ]
Zang F. [1 ]
机构：
[1] School of Mechatronics Engineering, Southwest Jiaotong University, Chengdu
来源：
Xinan Jiaotong Daxue Xuebao/Journal of Southwest Jiaotong University | 2022年 / 57卷 / 05期
关键词：
bending; distortion; free vibration; thin-walled box beam; torsion;
D O I：
10.3969/j.issn.0258-2724.20200613
中图分类号：
学科分类号：
摘要：
In order to improve the calculation accuracy of the natural frequency of thin-walled box beams, the dynamic characteristics of thin-walled box beams are analyzed using the generalized coordinate principle. Firstly, the free vibration differential equations of five highly coupled modes (i.e., extension, bending, torsion, warping and distortion) are obtained by the virtual work principle and considering the influence of the distortion deformation. Secondly, considering the influence of the rotational inertial motion term, the kinematics model under the simply supported boundary condition is established. The fourth order algebraic equation of free vibration of the thin-walled box beam and the exact solution of the natural frequency are obtained. Finally, a numerical example is provided to compare the exact solution of natural frequency considering distortion with the results of Prokić theory and finite element analysis, so that the effectiveness and accuracy of present method are verified. The results show that when taking the distortion effect into consideration, the natural frequency of free vibration of the thin-walled box beam can be more accurately reflected in high-order modes. Comparison of natural frequencies at four orders of the free vibration indicates that when the length of the box girder is 3 m, the relative error of the present theory was reduced to 0.38% from Prokić’s 0.42%; when the length of the box girder is 4 and 5 m, the relative error can be further reduced to 0.30% and 0.40%, respectively. © 2022 Science Press. All rights reserved.
引用
收藏
页码：1040 / 1046
页数：6
相关论文
共 22 条
  • [1] GERE J M, LIN Y K., Coupled vibrations of thin-walled beams of open cross section[J], Journal of Applied Mechanics, 25, 3, pp. 373-378, (1958)
  • [2] DOKUMACI E., An exact solution for coupled bending and torsion vibrations of uniform beams having single cross-sectional symmetry[J], Journal of Sound and Vibration, 119, 3, pp. 443-449, (1987)
  • [3] FRIBERG P O., Coupled vibrations of beams−an exact dynamic element stiffness matrix[J], International Journal for Numerical Methods in Engineering, 19, 4, pp. 479-493, (1983)
  • [4] OHGA M, TAKAO H, HARA T., Natural frequencies and mode shapes of thin-walled members[J], Computers & Structures, 55, 6, pp. 971-978, (1995)
  • [5] ADAM C., Forced vibrations of elastic bending-torsion coupled beams[J], Journal of Sound and Vibration, 221, 2, pp. 273-287, (1999)
  • [6] ARPACI A, BOZDAG E., On free vibration analysis of thin-walled beams with nonsymmetrical open cross-sections[J], Computers & Structures, 80, 7, pp. 691-695, (2002)
  • [7] TANAKA M, BERCIN A N., Free vibration solution for uniform beams of nonsymmetrical cross section using Mathematica[J], Computers & Structures, 71, 1, pp. 1-8, (1999)
  • [8] JRAD W, MOHRI F, ROBIN G, Et al., Analytical and finite element solutions of free and forced vibration of unrestrained and braced thin-walled beams[J], Journal of Vibration and Control, 26, 5, pp. 255-276, (2020)
  • [9] GOKDAG H, KOPMAZ O., Coupled bending and torsional vibration of a beam with in-span and tip attachments[J], Journal of Sound and Vibration, 287, 3, pp. 591-610, (2005)
  • [10] RAFEZY B, HOWSON W P., Exact dynamic stiffness matrix for a thin-walled beam of doubly asymmetric cross-section filled with shear sensitive material, International Journal for Numerical Methods in Engineering, 69, 13, pp. 2758-2779, (2007)
123