Governing equations of initially twisted elastic space rods made of laminated composite materials

Yildirim V.

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, vol.37, no.8, pp.1007-1035, 1999 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 8
  • Publication Date: 1999
  • Doi Number: 10.1016/s0020-7225(98)00106-2
  • Page Numbers: pp.1007-1035


The vibrational behavior of pre-twisted composite space rods under isothermal conditions is theoretically investigated based on the Timoshenko beam theory. The anisotropy of the rod material, the curvatures of the rod axis, and the effects of the rotary inertia, the shear and axial deformations are considered in the formulation. The governing equations concerning laminated rods with N anisotropic layers are presented in the canonical form. The Poisson effect is incorporated in the formulation of the beam resultant constitutive equations. To explain by example the present model, the out-of-plane bending free vibration of a simply supported beam with three special orthotropic lay-ups is analyzed. The second out-of-plane bending free vibration example for a simply supported beam with a transversely isotropic unidirectional layer is solved to compare the present frequencies with the existing numerical results. The third example is studied to demonstrate the Poisson effect for the out-of-plane bending free vibration of (45 degrees/-45 degrees/-45 degrees/45 degrees) laminated beams with fixed-free ends. The last example is related to the fundamental natural frequencies of symmetric cross-ply laminated beams with several boundary conditions. A quite good agreement is observed with the reported results. (C) 1999 Elsevier Science Ltd. All rights reserved.