An Analytical Method for Free Vibration Analysis of Laminated Composite Beams

A new laminated composite beam theory different from the traditional first-order shear deformation beam theories is carried out to analyze the laminated composite beams. In the bam theory used, the normal stress in lateral direction of the beam, assumed to be zero and the governing equations of motion are derived using Hamilton's principle. System of ordinary differential equations of free vibration analysis is solved using an analytical method. Combinations of simply supported, clamped and free boundary conditions are considered. By use of the proposed solution some comparisons are made among the different beam theories. Also, the effects of boundary conditions, fiber orientation and shear deformation and slenderness ratio on natural frequencies and mode shapes are investigated.