Free and Forced Vibration of Laminated Composite Beams

A new higher-order zig-zag theory is proposed for the free and forced vibration analysis of laminated composite and sandwich beams with different thickness at each ply. In-plane displacements in the proposed model nonlinearly distribute through the thickness and exhibit an abrupt discontinuity of slope at interfaces, which coincide with three-dimensional analysis. Differing from previous approaches, the transverse shear stress satisfies the continuity condition at interface by integrating the three-dimensional equilibrium equations, whereas the higher-order derivatives of displacement parameters have been eliminated using the three-field Hu-Washizu (HW) mixed variational principle. Moreover, the accurate transverse shear stresses are introduced in the equations of motion by using Hamilton’s principle, which actively impact the accurate prediction of natural frequencies of the laminated composite beams with arbitrary layouts. The performance of the proposed model is tested with different examples. It is observed that the present model gives most accurate results with respect to two-dimensional elasticity solutions for the free and forced vibration analysis compared with the existing higher-order models recently reported in the literature.