Linear Dynamic Analysis of a Spatially Curved Bernoulli-Euler Beam Subjected to a Moving Load

Authors

  • Miloš Jočković University of Belgrade, Faculty of Civil Engineering, Serbia, mjockovic@grf.bg.ac.rs, https://orcid.org/0000-0002-2409-9450
  • Marija Nefovska-Danilović University of Belgrade, Faculty of Civil Engineering, Serbia, marija@grf.bg.ac.rs, https://orcid.org/0000-0002-2613-1952
  • Aleksandar Borković Graz University of Technology, Institute for Applied Mechanics, Austria, aborkovic@tugraz.at, https://orcid.org/0000-0002-4091-3379

DOI:

https://doi.org/10.7251/AGGPLUS/2210048J

Keywords:

isogeometric approach, Bernoulli-Euler curved beam, moving load

Abstract

This paper considers the dynamic analysis of a spatially curved Bernoulli-Euler beam subjected to a moving load. The isogeometric approach is used for the spatial discretization of the weak form of the equation of motion. Both the reference geometry and the solution space are represented using the same NURBS basis functions that guarantee an accurate description of the beam centerline. The time integration is done by the explicit technique. The presented formulation is validated by the comparison with the existing results from the literature for the curved beam subjected to a constant load moving with a constant velocity. In addition, the influence of the moving load velocity on the dynamic response of a spatially curved beam has been investigated.

References

G. G. Stokes, “Discussion of a Differential Equation relating to the Breaking of Railway Bridges” in Mathematical and Physical Papers, vol. 2, Cambridge: Cambridge University Press, pp. 178–220, 2009.

T. J. R. Hughes, J. A. Cottrell, Y. Bazilevs, „Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement“, Comput. Methods Appl. Mech. Eng. 194 (39–41), pp. 4135–4195, 2005.

M. Jočković, G. Radenković, M. Nefovska – Danilović, M. Baitsch, “Free vibration analysis of spatial Bernoulli–Euler and Rayleigh curved beams using isogeometric approach“, Appl. Math. Model. 71, pp. 152–172, 2019.

L. Piegl, W. Tiller, The Nurbs Book, Springer, 1997.

A. Borković, S. Kovačević, G. Radenković, S. Milovanović, M. Guzijan-Dilber, "Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli–Euler beam", Computer Methods in Applied Mechanics and Engineering, 334, pp. 238-267, 2018.

A. Borković, S. Kovačević, G. Radenković, S. Milovanović, D. Majstorović, “Rotation-free isogeometric dynamic analysis of an arbitrarily curved plane Bernoulli–Euler beam“, Engineering Structures, 181, pp. 192-215, 2019.

M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976.

G. Radenković, Finite rotation and finite deformation isogeometric structural analysis (in Serbian), University of Belgrade, Faculty of Architecture, 2017.

G. Radenković, A. Borković, “Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam“, Computer Methods in Applied Mechanics and Engineering, 341, pp. 360-396, 2018.

M. Jočković, M. Nefovska – Danilović, “Isogeometric – based dynamic analysis of Bernoulli – Euler curved beam subjected to moving load“, in Proc. STEPGRAD XIV, 2020, pp. 63-70.

C. Adam, T. J. R. Hughes, S. Bouabdallah, M. Zarroug, H. Maitournam, “Selective and reduced numerical integrations for NURBS – based isogeometric analysis“, Comput. Methods Appl. Mech. Eng. 284, pp. 732 – 761, 2015.

MathWorks, MATLAB 2013, 2013. https://www.mathworks.com/products/matlab.html

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, pp. 519–537, 2001.

A. Borković, B. Marussig, G. Radenković, “Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam“, Computer Methods in Applied Mechanics and Engineering, 390, 114447, 2022.

A. Borković, B. Marussig, G. Radenković, “Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli–Euler beam“, Thin-Walled Structures, 170, 108539, 2022.

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Published

2022-12-09

How to Cite

[1]
M. Jočković, M. Nefovska-Danilović, and A. Borković, “Linear Dynamic Analysis of a Spatially Curved Bernoulli-Euler Beam Subjected to a Moving Load”, AGG+, vol. 10, no. 01, pp. 048-061, Dec. 2022.