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Reseach Article

Free Vibration of Curved beams with Hierarchical Finite Element Method

by Ramon Macedo Correa, Marcos Arndt, Roberto Dalledone Machado
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 178 - Number 14
Year of Publication: 2019
Authors: Ramon Macedo Correa, Marcos Arndt, Roberto Dalledone Machado
10.5120/ijca2019918916

Ramon Macedo Correa, Marcos Arndt, Roberto Dalledone Machado . Free Vibration of Curved beams with Hierarchical Finite Element Method. International Journal of Computer Applications. 178, 14 ( May 2019), 1-6. DOI=10.5120/ijca2019918916

@article{ 10.5120/ijca2019918916,
author = { Ramon Macedo Correa, Marcos Arndt, Roberto Dalledone Machado },
title = { Free Vibration of Curved beams with Hierarchical Finite Element Method },
journal = { International Journal of Computer Applications },
issue_date = { May 2019 },
volume = { 178 },
number = { 14 },
month = { May },
year = { 2019 },
issn = { 0975-8887 },
pages = { 1-6 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume178/number14/30595-2019918916/ },
doi = { 10.5120/ijca2019918916 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:50:20.556211+05:30
%A Ramon Macedo Correa
%A Marcos Arndt
%A Roberto Dalledone Machado
%T Free Vibration of Curved beams with Hierarchical Finite Element Method
%J International Journal of Computer Applications
%@ 0975-8887
%V 178
%N 14
%P 1-6
%D 2019
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper the use of Hierarchical Finite Element Method (HFEM) in free vibration of curved beams is explored. The traditional Finite Element Method has been applied in dynamic structural problems over the years, but when searching for higher vibration frequencies a great computational effort is necessary. In this context, two hierarchical finite element approaches are proposed in order to achieve more accurate results than simple FEM mesh refinement, called h refinement. The proposed HFEM uses the Lobatto and Bardell polynomials to p refinement. The results are compared with references found in literature.

References
  1. N. M. Auciello and M. A. De Rosa. Free vibrations of circular arches: a review. Journal of Sound and Vibration, 4(176):433–458, 1994.
  2. N. S. Bardell. An engineering application of the h-p version of the finite element method to the static analysis of a euler-bernoulli beam. Computers & Structures, 59(2):195–211, 1996.
  3. S. D. Campion and J. L. Jarvis. An investigation of the implementation of the p-version finite element method. Finite Elements in Analysis and Design, 23:1–21, 1996.
  4. A. K. Chopra. Dynamics of Structures: Theory and Applications to Earthquake Engineering. Prentice Hall, New Jersey, 3 edition, 1995.
  5. D. J. Dawe. Numerical studies using circular arch finite elements. Computers and Structures, 4:729–740, 1974.
  6. A. Krishnan and Y. J. Suresh. A simple cubic linear element for static and free vibration analyses of curved beams. Computers and Structures, 68:473–489, 1998.
  7. A. W. Leissa and M. S. Qatu. Vibrations of Continuous Systems. McGraw-Hill, 2011.
  8. A. Y. T. Leung and B. Zhu. Fourier p-elements for curved beam vibrations. Thin-Walled Structures, 42:39–57, 2004.
  9. M. Petyt and C. C. Fleischer. Free vibration of a curved beam. Journal of Sound and Vibration, 18(1):1–30, 1971.
  10. R. Raveendranath, G. Singh, and B. Pradhan. A two-noded locking-free shear flexible curved beam element. International Journal for Numerical Methods in Engineering, 44:265–280, 1999.
  11. R. Raveendranath, G. Singh, and B. Pradhan. Free vibration of arches using a curved beam element based on a coupled polynomial displacement. Computers and Structures, 78:583–590, 2000.
  12. R. Raveendranath, G. Singh, and G. V. Rao. A three-noded shear-flexible curved beam element based on coupled displacement field interpolations. Journal for Numerical Methods in Engineering, 51:85–101, 2001.
  13. R. E. Rossi and P. A. A. Laura. Dynamic stiffening of an arch clamped at one end and free at the other. Journal of Sound and Vibration, 160:190–192, 1993.
  14. P. Sol´in, K. Segeth, and I. Dolezel. Higher-Order Finite Element Methods. CRC Press, 2004.
  15. S. Timoshenko. Vibration Problems in engineering. Van Nostrand, New York, 1955.
  16. F. Yang, R. Sedaghati, and E. Esmailzadeh. Free in-plane vibration of general curved beams using finite element method. Journal of Sound and Vibration, 318:850–867, 2008.
Index Terms

Computer Science
Information Sciences

Keywords

Hierarchical Finite Element Method Finite Element Method curved beams free vibration