Please wait a minute...
Shopping Cart Email List Chinese
Advanced Search Fig/Tab
Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

Postal Subscription Code 80-975

2018 Impact Factor: 0.989

Featured Articles  |  Most Downloaded  |  Most Reading
Online Submission Subscribe to Our RSS Content Feed
Front Mech Eng    2011, Vol. 6 Issue (4) : 409-418    https://doi.org/10.1007/s11465-011-0245-8
RESEARCH ARTICLE
Dynamic analysis of composite beam subjected to harmonic moving load based on the third-order shear deformation theory
Mohammad Javad REZVANIL1(), Mohammad Hossein KARGARNOVIN2, Davood YOUNESIAN3
1. Department of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran; 2. School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran; 3. Railway Engineering Department, Iran University of Science and Technology, Tehran, Iran
 Download: PDF(554 KB)   HTML
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

The response of an infinite Timoshenko beam subjected to a harmonic moving load based on the third-order shear deformation theory (TSDT) is studied. The beam is made of laminated composite, and located on a Pasternak viscoelastic foundation. By using the principle of total minimum potential energy, the governing partial differential equations of motion are obtained. The solution is directed to compute the deflection and bending moment distribution along the length of the beam. Also, the effects of two types of composite materials, stiffness and shear layer viscosity coefficients of foundation, velocity and frequency of the moving load over the beam response are studied. In order to demonstrate the accuracy of the present method, the results TSDT are compared with the previously obtained results based on first-order shear deformation theory, with which good agreements are observed.
Keywords timoshenko composite beam      pasternak viscoelastic foundation      third-order shear deformation theory (TSDT)      harmonic moving load     
Corresponding Author(s): REZVANIL Mohammad Javad,Email:m.rezvani@semnaniau.ac.ir   
Issue Date: 05 December 2011
 Cite this article:   
Mohammad Javad REZVANIL,Mohammad Hossein KARGARNOVIN,Davood YOUNESIAN. Dynamic analysis of composite beam subjected to harmonic moving load based on the third-order shear deformation theory[J]. Front Mech Eng, 2011, 6(4): 409-418.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-011-0245-8
https://academic.hep.com.cn/fme/EN/Y2011/V6/I4/409
Fig.1  Deformation of a transverse normal according to the FSDT and TSDT
Fig.2  Pasternak viscoelastic foundation with viscous shear layers
Number of layers/NWidth of layers b/cmAngle of layers θ/(o)Total thickness of the beam h/cm
45(0/90/90/0)10
Tab.1  Geometrical data for the composite layers beam
T300/5208Glass-epoxy
ρ1540 kg/m32000 kg/m3
E1132 GPa53.7 GPa
E210.8 GPa17.9 GPa
G125.65 GPa8.96 GPa
G133.38 GPa8.96 GPa
G233.38 GPa3.44 GPa
v120.240.25
v230.590.34
v130.590.25
Tab.2  Mechanical properties of composite materials
Rocking stiffness k?/(MN)Rocking damping η?/(N·s)Normal stiffness k/MPaNormal damping η/(kN·s·m-2)Shear viscosity μ/(kN·s)Load magnitude F/kNLoad velocity v/(m·s-1)Load frequency ω/Hz
13.8552069138100144.640200
Tab.3  The properties of the foundation
Fig.3  Deflection of T300/5208 composite beam, according to TSDT for different stiffness coefficients
Fig.4  Phase angle of the deflection
Fig.5  Deflection of T300/5208 composite beam, according to TSDT for different viscosity coefficients
Fig.6  Deflection of T300/5208 composite beam, according to TSDT for different load velocity
Fig.7  Deflection of T300/5208 composite beam, according to TSDT for different load frequency
Fig.8  Bending moment of T300/5208 composite beam, according to TSDT for different stiffness coefficients
Fig.9  Phase angle of the bending moment
Fig.10  Bending moment of T300/5208 composite beam, according to TSDT for different viscosity coefficients
Fig.11  Bending moment of T300/5208 composite beam, according to TSDT for different load velocity
Fig.12  Bending moment of T300/5208 composite beam, according to TSDT for different load frequency
Fig.13  Deflection of beam, according to TSDT for two types of composite materials
Fig.14  Bending moment of beam, according to TSDT for two types of composite materials
Fig.15  Deflection of composite beam based on the FSDT and TSDT
Fig.16  Bending moment of composite beam based on the FSDT and TSDT
Fig.17  Stress of composite beam based on the FSDT and TSDT
1 Fryba L. Vibration of Solids and Structures Under Moving Loads. London: Thomas Telford, 1999
2 Heteny M. Beam on Elastic Foundation. New York: The University of Michigan Press, 1971
3 Achenbach J D, Sun C T. Moving load on a flexibly supported Timoshenko beam. International Journal of Solids and Structures , 1965, 1(4): 353-370
doi: 10.1016/0020-7683(65)90001-6
4 Torchanis A M, Chelliah R, Bielak J. Unified approach for beams on elastic foundations under moving loads. Journal of Geotechnical Engineering , 1987, 113(8): 879-895
doi: 10.1061/(ASCE)0733-9410(1987)113:8(879)
5 Kargarnovin M H, Younesian D. Dynamics of Timoshenko beams on Pasternak foundation under moving load. Mechanics Research Communications , 2004, 31(6): 713-723
doi: 10.1016/j.mechrescom.2004.05.002
6 Kargarnovin M H, Younesian D, Thompson D J, Jones C J C. Response of beams on nonlinear viscoelastic foundations to harmonic moving loads. Computers & Structures , 2005, 83(23-24): 1865-1877
doi: 10.1016/j.compstruc.2005.03.003
7 Rezvani M J, Karami K M. Dynamic analysis of a composite beam subjected to a moving load. Journal of Mechanical Engineering Science , 2009, 223: 1543-1554
8 Kant T, Marur S R, Rao G S. Analytical solution to the dynamic analysis of laminated beams using higher order refined theory. Composite Structures , 1997, 40(1): 1-9
doi: 10.1016/S0263-8223(97)00133-5
9 BannerjeeJ R, WilliamsF W. Exact dynamic stiffness matrix for composite Timoshenko beams with applications. Journal of Sound and Vibration , 1996, 194(4): 573-585
doi: 10.1006/jsvi.1996.0378
10 Teh K K, Huang C C. The effects of fibre orientation on free vibrations of composite beams. Journal of Sound and Vibration , 1980, 69(2): 327-337
doi: 10.1016/0022-460X(80)90616-1
11 Teoh L S, Huang C C. The vibration of beams of fibre reinforced material. Journal of Sound and Vibration , 1977, 51(4): 467-473
doi: 10.1016/S0022-460X(77)80044-8
12 Abramovich H, Livshits A. Free vibration of non-symmetric cross-ply laminated composite beams. Journal of Sound and Vibration , 1994, 176(5): 597-612
doi: 10.1006/jsvi.1994.1401
13 Simsek M S, Kocaturk T. Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load. Composite Structures , 2009, 90(4): 465-473
doi: 10.1016/j.compstruct.2009.04.024
14 Chen Y H, Huang Y H, Shih C T. Response of an infinite Timoshenko beam on a viscoelastic foundation to a harmonic moving load. Journal of Sound and Vibration , 2001, 241(5): 809-824
doi: 10.1006/jsvi.2000.3333
15 Seong M K, Yoon H Ch. Vibration and dynamic buckling of shear beam-columns on elastic foundation under moving harmonic loads. International Journal of Solids and Structures , 2006, 43(3-4): 393-412
doi: 10.1016/j.ijsolstr.2005.06.025
16 Reddy J N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis,2nd ed. Boca Raton: CRC Press, 2004
17 Wunsch A D. Complex Complex Variables with Applications. Massachusetts: Reading , 1994
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed