ANALYTICAL SOLUTION FOR DYNAMIC ANALYSIS OF ASYMMETRIC LAMINATED COMPOSITE SHEAR-DEFORMABLE BEAMS
The exact analytical solutions towards investigating the dynamic analysis of extensional-flexural coupled vibration responses for asymmetric composite laminated rectangular beams under various harmonic axial and bending forces are presented.
Three governing coupled differential equations and related boundary conditions were derived from the variational form of Hamilton’s principle. The formulations are based on the first order shear-deformable beam theory, account for the effects of rotary inertia, Poisson’s ratio, and structural bending-extensional coupling coming from material anisotropy. The resulting coupled equations for asymmetric composite beams were exactly solved and closed-form solutions for extensional-flexural coupled response were obtained for different boundary conditions. Numerical examples were performed for antisymmetric cross-ply and angle-ply laminated composite beams in order to investigate the effects of transverse shear deformation, fibre orientation angle on coupled natural frequencies, quasi-static, and steady state dynamic responses.
Results for dynamic bending and axial displacements are discussed in detail and the validity and accuracy of the present solutions were verified against published exact and finite element solutions.