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

The vibrational behavior of pre-twisted composite space rods under isotherm al conditions is theoretically investigated based on the Timoshenko beam th eory. The anisotropy of the rod material, the curvatures of the rod axis, a nd 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 Po isson effect is incorporated in the formulation of the beam resultant const itutive equations. To explain by example the present model, the out-of-plan e bending free vibration of a simply supported beam with three special orth otropic lay-ups is analyzed. The second out-of-plane bending free vibration example for a simply supported beam with a transversely isotropic unidirec tional 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 degr ees/-45 degrees/45 degrees) laminated beams with fixed-free ends. The last example is related to the fundamental natural frequencies of symmetric cros s-ply laminated beams with several boundary conditions. A quite good agreem ent is observed with the reported results. (C) 1999 Elsevier Science Ltd. A ll rights reserved.