Vibration analysis with second-order effects of pultruded FRP frames using locking-free elements

Vibrations of pultruded (FRP) thin-walled beams and frames are analysed. A second-order approximation of the displacement field is adopted, accounting for shear strain effects due to both nonuniform bending and torsion. Geometric nonlinearities arising from concentrated or distributed external loads are considered. A simple two-node finite element model using polynomial interpolation is adopted. In particular, the interpolating polynomials follow from the solutions to the homogeneous Timoshenko-beam problem and to the warping-torsion problem for a beam with doubly-symmetrical cross-section. Such shape functions contain parameters which tend to zero when the influence of shear deformations becomes negligible, resulting in a locking-free formulation. The convergence properties of the adopted element in the presence of flexural–torsional vibrations are highlighted with reference to mono-symmetrical cross-section carbon-FRP profiles. Vibration frequencies and mode shapes of pultruded glass-FRP portal frames are extensively evaluated as a function of the applied loads and sudden exchanges of fundamental modes are pointed out. The influence of frame geometry, shear deformations, participating masses and geometrical effects due to distributed external loads is investigated.