Dynamic stiffness analysis of laminated composite beams using trigonometric shear deformation theory

The exact dynamic stiffness matrix of a uniform laminated composite beam based on trigonometric shear deformation theory is developed in this paper. A refined laminated beam constitutive equation is derived that takes into account the breadth direction strains. The dynamic stiffness matrix is formulated directly in an exact sense by solving the governing differential equations of motion that describe the deformations of laminated beams according to the trigonometric shear deformation theory, which includes the sinusoidal variation of the axial displacement over the cross-section. The derived dynamic stiffness matrix is then used in conjunction with the Wittrick–Williams algorithm to compute the natural frequencies and mode shapes of the composite beams. The results obtained from the present theory are compared with those available in the literature wherever possible.