Modeling the coupled bending-torsional vibrations of symmetric laminated composite beams

A shear-deformable beam theory is proposed to model the coupled bending and twisting vibration in a symmetric laminated beam with a rectangular cross section. The warping of the beam cross section and Poisson effect are considered in the formulation. The governing equations of motion for the symmetric laminated beams exhibiting bending-torsional coupling are derived by using the Hamilton's principle, and the dynamic stiffness matrix is formulated from the exact analytical solutions of the homogeneous governing differential equations. Numerical results of appropriately chosen symmetric laminated beams are presented and compared with the previously published numerical and experimental solutions whenever possible. The influences of Poisson effect, layup, and boundary condition on the natural frequencies of symmetric laminated beams are extensively investigated.