Exact solutions for stability and free vibration of thin-walled Timoshenko laminated beams under variable forces

In this paper, an efficient thin-walled Timoshenko laminated beam subjected to variable forces is developed for the coupled stability and free vibration analyses. First, the analytical technique is employed to present the thin-walled laminated beam theory considering the transverse shear and the restrained warping induced shear deformation and the rotary inertia based on the orthogonal Cartesian coordinate system. The displacement field of thin-walled cross section is introduced based on the inclusion of second-order terms of finite rotation and the potential energy corresponding to the semitangential moments and the kinetic energy with rotary inertia effects are derived. The equations of motion are derived from the Hamilton’s principle, and the explicit expressions for displacement parameters are presented based on generalized power series expansions of displacement components. Finally, the exact (i.e., with arbitrary precision) static and dynamic stiffness matrices are determined using the force-displacement relations. Numerical examples are carried out focusing attention in the validation of the present theory with respect to other available results.