An analytical approach for the free vibration analysis of generally laminated composite beams with shear effect and rotary inertia

In this paper, the free vibration analysis of generally laminated composite beam (LCB) based on Timoshenko beam theory are presented using the method of Lagrange multipliers where in the free vibration problem is posed as a constrained variational problem. The effect of material couplings (bending–tension, bending–twist, and tension–twist couplings) with the effects of shear deformation, rotary inertia and Poissonʹs effect are taken into account. Analytical expression for the natural frequencies and mode shapes are presented. The calculated natural frequencies are verified against some available results in the literature and very good agreement is observed. Furthermore, the effects of some parameters such as slenderness ratio, the rotary inertia, the shear deformation, material anisotropy, ply configuration and boundary conditions on the natural frequency and mode shape are examined.