FREE VIBRATION ANALYSIS OF A LAMINATED SHALLOW CURVED BEAM BASED ON TRIGONOMETRIC SHEAR DEFORMATION THEORY

Free vibration analysis of cross-ply laminated shallow curved beams is carried out by using the dynamic stiffness method. Hamilton's principle is adopted to derive the governing equations of motion for laminated shallow curved beams based on the trigonometric shear deformation theory in which the sinusoidal function is used in the displacement field in terms of the thickness coordinate to represent the shear deformation. The dynamic stiffness matrix is formulated directly from the exact solutions of the homogeneous governing differential equations. The application of the dynamic stiffness matrix is demonstrated by investigating the natural frequencies and mode shapes of the laminated shallow curved beams with various boundary conditions. The effects of stacking sequence, material orthotropy ratio, length to thickness ratio, and curvature ratio on the free vibration characteristics of the laminated shallow curved beams are studied. Compared to some available solutions in the literature, the numerical results validate the correctness and accuracy of the proposed formulation.