An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams

Several displacement-based theories are assessed by analyzing the free vibration and the buckling behaviors of laminated beams with arbitrary layouts as well as soft-core sandwich beams. The equations governing the dynamic response of laminated structures are derived by using Hamilton’s principle. However, equations of equilibrium for buckling problems are given by employing the principle of virtual displacements. Moreover, using Navier’s technique and solving the eigenvalue equations, analytical solutions based on the global–local higher-order theory used in this paper are first presented in present study. At the same time, the effect of the order number of higher-order shear deformation as well as interlaminar continuity of transverse shear stress on the global response of both laminated beams and soft-core sandwiches has been also studied. Numerical results show that by increasing the order number of in-plane and transverse displacement components, the global higher-order theories can reasonably predict the natural frequencies and the critical loads of laminated beams with arbitrary layouts and soft-core sandwich beams whereas these global higher-order theories are still less accurate compared to the global–local higher-order theory and the zig-zag theory used herein.