Transient Response of Laminated Composite Curved Beams with General Boundary Conditions under Moving Force

Document Type : Research Article

Authors

Department of Mechanical Engineering, University of Mazandaran, Babolsar, Iran.

Abstract

Vibrational analysis of beams has been an important subject for many years. Despite the wide applications of curved beams, especially laminated composite curved beams, less attention has been paid to this subject. In this study, the transient response of the laminated composite curved beam due to a moving force with constant velocity for different boundary conditions has been obtained. By employing Hamilton’s principle, the equations of motion along with the corresponding boundary conditions of the beam are determined. The finite element method is employed to solve these equations. Using the eigenvalue technique, the vibrational characteristics of the beam are calculated. Results for the free and forced vibration of the beam have been compared against available data in the literature and the three-dimensional model in ANSYS. The effects of different parameters such as the geometry of the beam, fibers orientation, and boundary conditions on the transient response of the beam have been investigated. It has been shown that beam with cross-ply layups has lower values of transient deflection compared to the angle-ply layups. Also, the anti-symmetric cross-ply beam has more deflection with respect to the symmetric one.

Keywords

Main Subjects


  1. Report of the Commissioners Appointed to Inquire Into the Application of Iron to Railway Structures, William Clowes and sons, (1) (1849).
  2. Y. Dugush , M. Eisenberger, Vibrations of non-uniform continuous beams under moving loads, Journal of Sound and vibration, 254(5) (2002) 911-926.
  3. G. Stokes, Discussion of a differential equation relating to the breaking of railway bridges, Printed at the Pitt Press by John W. Parker, (1849)
  4. S.Timoshenko, On the transverse vibrations of bars of uniform cross-section, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 43(253) (1922) 125-131.
  5. Y.B. Yang, J.D. Yau, Y.S Wu, Vehicle-bridge interaction dynamics: with applications to high-speed railways, World Scientific, ( 2004).
  6. B. Gören Kiral, Z. Kiral, B. Okutan Baba, Dynamic behavior of laminated composite beams subjected to a moving load, Journal of Applied Sciences, 4(2) (2004) 271-276.
  7. V. Kahya, Dynamic analysis of laminated composite beams under moving loads using finite element method, Nuclear engineering and design, 243 (2012) 41-48.
  8. M.H. Kargarnovin , R.A. Jafari-Talookolaei, M.T. Ahmadian, Vibration analysis of delaminated Timoshenko beams under the motion of a constant amplitude point force traveling with uniform velocity, International Journal of Mechanical Sciences, 70 (2013) 39-49.
  9. M.H. Kadivar, S.R. Mohebpour, Finite element dynamic analysis of unsymmetric composite laminated beams with shear effect and rotary inertia under the action of moving loads, Finite elements in Analysis and Design, 29(3-4) (1998) 259-273.
  10. R.A. Jafari-Talookolaei, M.H. Kargarnovin, M.T. Ahmadian, Dynamic response of a delaminated composite beam with general lay-ups based on the first-order shear deformation theory, Composites Part B: Engineering, 55 (2013) 65-78.
  11. V. Kahya, A. Mosallam, Dynamic analysis of composite sandwich beams under moving mass, Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 14(1)(2011).
  12. H. Zibdeh, M. Abu-Hilal, Stochastic vibration of laminated composite coated beam traversed by a random moving load, Engineering structures, 25(3) (2003) 397-404.
  13. J. Genin, E.C. Ting, Z. Vafa, Curved bridge response to a moving vehicle, Journal of Sound and Vibration, 81(4) (1982) 469-475.
  14. Y.B. Yang, C.M. Wu, J.D. Yau, Dynamic response of a horizontally curved beam subjected to vertical and horizontal moving loads, Journal of Sound and vibration, 242(3) (2001) 519-537.
  15. J.S. Wu, L.K. Chiang, Out-of-plane responses of a circular curved Timoshenko beam due to a moving load, International Journal of Solids and Structures, 40(26) (2003) 7425-7448.
  16. S.H. Li, J.Y. Ren, Analytical study on dynamic responses of a curved beam subjected to three-directional moving loads, Applied Mathematical Modelling, 58 (2018) 365-387.
  17. M. Arefi, A.M. Zenkour,  Transient sinusoidal shear deformation formulation of a size-dependent three-layer piezo-magnetic curved nanobeam, Acta Mechanica, 228(10) (2017) 3657-3674.
  18. M. Arefi, E. Mohammad-Rezaei Bidgoli, R. Dimitri, M. Bacciocchi, F. Tornabene, Nonlocal bending analysis of curved nanobeams reinforced by graphene nanoplatelets, Composites Part B: Engineering, 166 (2019)1-12.
  19. M. Hajianmaleki, M.S. Qatu, Static and vibration analyses of thick, generally laminated deep curved beams with different boundary conditions, Composites Part B: Engineering, 43(4) (2012) 1767-1775.
  20. T. Ye, G. Jin, X. Ye, X. Wang, A series solution for the vibrations of composite laminated deep curved beams with general boundaries, Composite Structures, 127 (2015) 450-465.
  21. R.A. Jafari-Talookolaei, M. Abedi, M. Hajianmaleki, Vibration characteristics of generally laminated composite curved beams with single through-the-width delamination, Composite Structures, 138 (2016) 172-183.
  22. X.X. Qin, H.P. Chen, S.J. Wang, Analytical Solution of Composite Curved I-Beam considering Tangential Slip under Uniform Distributed Load, Mathematical Problems in Engineering,2021 (2021)4094753.
  23. J. Luo, S. Zhu, W. Zhai, Formulation of curved beam vibrations and its extended application to train-track spatial interactions, Mechanical Systems and Signal Processing, 165 (2022)108393.
  24. D. Shao, S. Hu, Q.Wang, F. Pang, A unified analysis for the transient response of composite laminated curved beam with arbitrary lamination schemes and general boundary restraints, Composite Structures, 154 (2016) 507-526.
  25. H. Kurtaran, Geometrically nonlinear transient analysis of thick deep composite curved beams with generalized differential quadrature method, Composite Structures, 128 (2015) 241-250.
  26. J. Zhao, Z. Gao, H. Li, J. Guan, Q. Han, Q. Wang, A unified modeling method for dynamic analysis of CFRC-PGPC circular arche with general boundary conditions in hygrothermal environment, Composite Structures, 255 (2021) 112884.
  27. H. Sarparast, A. Ebrahimi-Mamaghani. Vibrations of laminated deep curved beams under moving loads, Composite Structures, 226 (2019) 111262.