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

TAN Minyao; CHENG Wenming; LI Hangfei; ZANG Fulian

doi:10.3969/j.issn.0258-2724.20200613

Volume 57 Issue 5

Oct. 2022

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Journal of Southwest Jiaotong University > 2022 > 57(5): 1040-1046.

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TAN Minyao, CHENG Wenming, LI Hangfei, ZANG Fulian. Free Vibration Analysis of Thin-Walled Box Beam of Crane Considering Distortion[J]. Journal of Southwest Jiaotong University, 2022, 57(5): 1040-1046. doi: 10.3969/j.issn.0258-2724.20200613

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

doi: 10.3969/j.issn.0258-2724.20200613

School of Mechatronics Engineering, Southwest Jiaotong University, Chengdu 610031, China

Received Date: 09 Sep 2020
Rev Recd Date: 30 Oct 2020

Available Online: 09 Aug 2022

Publish Date: 04 Nov 2020

Abstract

Abstract

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.
- bending,
- torsion,
- distortion,
- thin-walled box beam,
- free vibration

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References

[1]	GERE J M, LIN Y K. Coupled vibrations of thin-walled beams of open cross section[J]. Journal of Applied Mechanics, 1958, 25(3): 373-378. doi: 10.1115/1.4011830
[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, 1987, 119(3): 443-449. doi: 10.1016/0022-460X(87)90408-1
[3]	FRIBERG P O. Coupled vibrations of beams−an exact dynamic element stiffness matrix[J]. International Journal for Numerical Methods in Engineering, 1983, 19(4): 479-493. doi: 10.1002/nme.1620190403
[4]	OHGA M, TAKAO H, HARA T. Natural frequencies and mode shapes of thin-walled members[J]. Computers & Structures, 1995, 55(6): 971-978.
[5]	ADAM C. Forced vibrations of elastic bending-torsion coupled beams[J]. Journal of Sound and Vibration, 1999, 221(2): 273-287. doi: 10.1006/jsvi.1998.2005
[6]	ARPACI A, BOZDAG E. On free vibration analysis of thin-walled beams with nonsymmetrical open cross-sections[J]. Computers & Structures, 2002, 80(7/8): 691-695.
[7]	TANAKA M, BERCIN A N. Free vibration solution for uniform beams of nonsymmetrical cross section using Mathematica[J]. Computers & Structures, 1999, 71(1): 1-8.
[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, 2020, 26(5/6): 255-276.
[9]	GÖKDAĞ H, KOPMAZ O. Coupled bending and torsional vibration of a beam with in-span and tip attachments[J]. Journal of Sound and Vibration, 2005, 287(3): 591-610. doi: 10.1016/j.jsv.2004.11.019
[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[J]. International Journal for Numerical Methods in Engineering, 2007, 69(13): 2758-2779. doi: 10.1002/nme.1864
[11]	李海超,庞福振,李玉慧,等. 复杂边界条件圆柱壳自由振动特性分析[J]. 振动工程学报,2020,33(1): 56-63. LI Haichao, PANG Fuzhen, LI Yuhui, et al. Free vibration characteristics analysis of circular cylindrical shell under complex boundary conditions[J]. Journal of Vibration Engineering, 2020, 33(1): 56-63.
[12]	蒲育,周凤玺. 基于一种广义梁理论的弹性地基FGM简支梁自由振动解析解[J]. 应用力学学报,2020,37(2): 840-845,946. PU Yu, ZHOU Fengxi. Exact solutions for free vibration of FGM simply supported beams on elastic foundation based on a generalized beam theory[J]. Chinese Journal of Applied Mechanics, 2020, 37(2): 840-845,946.
[13]	OVESY H R, KHANEH MASJEDI P. Investigation of the effects of constitutive equations on the free vibration behavior of single-celled thin-walled composite beams[J]. Mechanics of Advanced Materials and Structures, 2014, 21(10): 836-852. doi: 10.1080/15376494.2012.725266
[14]	VO T P, THAI H T. Vibration and buckling of composite beams using refined shear deformation theory[J]. International Journal of Mechanical Sciences, 2012, 62(1): 67-76. doi: 10.1016/j.ijmecsci.2012.06.001
[15]	FILIPPI M, PAGANI A, PETROLO M, et al. Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials[J]. Composite Structures, 2015, 132: 1248-1259. doi: 10.1016/j.compstruct.2015.07.014
[16]	WANG S, ZHANG C. Structure mechanical modeling of thin-walled closed-section composite beams, part 2: multi-cell cross section[J]. Composite Structures, 2014, 113: 56-62. doi: 10.1016/j.compstruct.2014.03.002
[17]	KIM Y Y, KIM J H. Thin-walled closed box beam element for static and dynamic analysis[J]. International Journal for Numerical Methods in Engineering, 1999, 45(4): 473-490. doi: 10.1002/(SICI)1097-0207(19990610)45:4<473::AID-NME603>3.0.CO;2-B
[18]	KAYA M O, OZGUMUS O O. Flexural-torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM[J]. Journal of Sound and Vibration, 2007, 306(3/4/5): 495-506.
[19]	KIM N I. Dynamic stiffness matrix of composite box beams[J]. Steel and Composite Structures, 2009, 9(5): 473-497. doi: 10.12989/scs.2009.9.5.473
[20]	PROKIĆ A, LUKIĆ D. Dynamic analysis of thin-walled closed-section beams[J]. Journal of Sound and Vibration, 2007, 302(4/5): 962-980.
[21]	DANCILA D S, ARMANIOS E A, LENTZ W K. Free vibration of thin-walled closed-section composite beams with optimum and near-optimum coupling[J]. Journal of Thermoplastic Composite Materials, 1999, 12(1): 2-12. doi: 10.1177/089270579901200101
[22]	TAN M Y, CHENG W M. Non-linear lateral buckling analysis of unequal thickness thin-walled box beam under an eccentric load[J]. Thin-Walled Structures, 2019, 139: 77-90. doi: 10.1016/j.tws.2019.02.028

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