Dynamic analysis of helicoidal bars with non-circular cross-sections via mixed FEM


Eratlı N. , Yılmaz M. , Darılmaz K. , Omurtag M. H.

STRUCTURAL ENGINEERING AND MECHANICS, vol.57, no.2, pp.221-238, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.12989/sem.2016.57.2.221
  • Title of Journal : STRUCTURAL ENGINEERING AND MECHANICS
  • Page Numbers: pp.221-238
  • Keywords: mixed finite element, non-cylindrical helix, non-circular cross-sections, Poisson's equation, torsional moment of inertia, NONCYLINDRICAL HELICAL SPRINGS, FREE-VIBRATION ANALYSIS, FINITE-ELEMENT SOLUTION, TRANSFER-MATRIX METHOD, NATURAL FREQUENCIES, ARBITRARY SHAPE, COIL SPRINGS, TORSIONAL RIGIDITY, NONUNIFORM TORSION, CURVED BEAMS

Abstract

One of the objectives of this study is to implement the direct calculation of the torsional moment of inertia for non-circular cross-sections, which is based on the St. Venant torsion formulation and the finite element method. Recently the proposed method provides a unique calculation of the torsional rigidity of simply and multiply connected cross-sections. Next, free vibration analyses of cylindrical and non cylindrical helices with non-circular cross-sections are solved by a curved two-nodded mixed finite element based on the Timoshenko beam theory. Some thin-thick closed or open sections are handled and the natural frequencies of cylindrical and non-cylindrical helices are compared with the literature and the commercial finite element program SAP2000.