×
Home Current Archive Editorial board
News Contact
Original scientific paper

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

By
Miloš Jočković ,
Miloš Jočković
Contact Miloš Jočković

Faculty of Civil Engineering, University of Belgrade, Belgrade, Serbia

Marija Nefovska-Danilović ,
Marija Nefovska-Danilović

Faculty of Civil Engineering, University of Belgrade, Belgrade, Serbia

Aleksandar Borković
Aleksandar Borković

Institute for Applied Mechanics, Graz University of Technology, Graz, Austria

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

Adam, C., Hughes, T. J. R., Bouabdallah, S., Zarroug, M., & Maitournam, H. (2015). Selective and reduced numerical integrations for NURBS – based isogeometric analysis“. Comput. Methods Appl. Mech. Eng, 284, 732-761,.
Borković, A., Kovačević, S., Radenković, G., Milovanović, S., & Guzijan-Dilber, M. (2018). Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli–Euler beam". Computer Methods in Applied Mechanics and Engineering, 334, 238-267,.
Borković, A., Kovačević, S., Radenković, G., Milovanović, S., & Majstorović, D. (2019). Rotation-free isogeometric dynamic analysis of an arbitrarily curved plane Bernoulli–Euler beam“. Engineering Structures, 181, 192-215,.
Borković, A., Marussig, B., & Radenković, G. (2022a). Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam“. Computer Methods in Applied Mechanics and Engineering, 390, 114447,.
Borković, A., Marussig, B., & Radenković, G. (2022b). Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli–Euler beam“. Thin-Walled Structures, 170, 108539,.
Hughes, T. J. R., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement“. Comput. Methods Appl. Mech. Eng, 194(39–41), 4135-4195,.
MathWorks, M. A. T. L. A. B. (2013).
P, M. (1976). Do Carmo, Differential Geometry of Curves and Surfaces.
Piegl, L., & Tiller, W. (1997). The Nurbs Book.
Radenković, G. (2017). Finite rotation and finite deformation isogeometric structural analysis (in Serbian.
Radenković, G., & Borković, A. (2018). Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam“. Computer Methods in Applied Mechanics and Engineering, 341, 360-396,.
Stokes, G. G. (2009). Discussion of a Differential Equation relating to the Breaking of Railway Bridges. In Mathematical and Physical Papers (Vol. 2, pp. 178-220,).
Yang, Y. B., Wu, C.-M., & Yau, J.-D. (2001). Dynamic Response of a Horizontally Curved Beam Subjected To Vertical and Horizontal Moving Loads“. Journal of Sound and Vibration, 242(3), 519-537,.
(2019). Free vibration analysis of spatial Bernoulli–Euler and Rayleigh curved beams using isogeometric approach“. Appl. Math. Model, 71, 152-172,.
(2020). Isogeometric – based dynamic analysis of Bernoulli – Euler curved beam subjected to moving load“. Proc. STEPGRAD XIV, 63–70.

Citation

Article metrics

Google scholar: See link

The statements, opinions and data contained in the journal are solely those of the individual authors and contributors and not of the publisher and the editor(s). We stay neutral with regard to jurisdictional claims in published maps and institutional affiliations.