Free Vibration of Laminated Composites Beams Using Strain Gradient Notation Finite Element Models

This works presents free vibration analysis of laminated composite beam problems using Timoshenko beam finite elements formulated in strain gradient notation. The formulation in physically interpretable notation identifies precisely the one parasitic shear term present in the in-plane, two-node, six-degree-of-freedom Timoshenko beam element. The spurious term can be eliminated a-priori of implementation and analysis. An assessment of the deleterious effects of parasitic shear in the computation of natural frequencies and mode shapes of laminated composite beams is performed via convergence studies. Beams with different boundary conditions and lamination schemes are analyzed. Results from models containing parasitic shear and from models corrected for it are compared. It is seen that parasitic shear affects significantly the convergence characteristics of the model as it retards convergence. It is also observed that parasitic shear affects the shapes of vibration modes. After elimination of parasitic shear, convergence of natural frequencies is attained quite rapidly. Such result is most pronounced when computing the fundamental frequency. Further, convergent results are compared to results presented in the literature for accuracy assessment, and very good agreement is found.

Keywords:
Free vibration; Laminated composites; Timoshenko beam; Finite element method; Strain gradient notation; Parasitic shear