Free Vibration Analysis of Elastic Bars using Isogeometric Approach

  • Received : 2011.05.17
  • Published : 2011.09.30


A study on the free vibration analysis of elastic bar is described in this paper. In order to determine the natural frequencies of bars, a bar element is developed by using isogeometric formulation. The B-spline is introduced to represent the geometry of bar and the same geometric definition is also used to define its unknown displacement field in isogeometric formulation. Therefore, the stiffness and mass matrices are derived by the order-free B-spline basis function. The efficiency and accuracy of the present isogeometric bar elementis demonstrated by using several numerical tests. From numerical results, it is found to be that the present isogeometric element produces very accurate natural frequencies of bars. Finally, the present isogeometric solutions are provided as future reference solutions.


Isogeometric Analysis;Elastic bar;Free Vibration;NURBS;Knot Vector;Control Point


  1. Cottrell, J.A., Bazilevs, Y. and Hughes, T.J.R. (2009) Isogeometric Analysis: Towards Integration of CAD and FEA.Wiley.
  2. De Boor, C. (1978)A Practical Guide to Splines. Springer
  3. Hughes, T.J.R. (2000)The Finite Element Method: Linear Static and Dynamic Finite ElementAnalysis. Dover Publications.
  4. Hughes,T. J.R . Cott rel l , J. A . and Ba z i le vs, Y. (2005) Isogeometricanalysis: CAD,finiteelements,NURBS,exact geometry andmesh refinement.Comput. Methods Appl. Mech. Eng., vol. 194, no. 39-41, pp. 4135-4195.
  5. Hughes, T.J.R. and Evans J.A. (2010) Isogeometric analysis.ICES Report 10-18, The Institute of Computational Engineering and Science, University of Texas Austin
  6. Rogers,D. (2001) An Introduction to NURBS: With Historical Perspective.Academic Press, London, UK.

Cited by

  1. Isogeometric Analysis of Laminated Plates under Free Vibration vol.16, pp.3, 2014,
  2. Topology Optimization for Plane Structures using Isogeometric Approach vol.32, pp.2, 2016,