Dynamic response of antisymmetric cross-ply laminated composite beams with arbitrary boundary conditions

An analytical solution of the classical, first- and third-order laminate beam theories is developed to study the transient response of antisymmetric cross-ply laminated beams with generalized boundary conditions and for arbitrary loadings. A general modal approach, utilizing the state form of the equations of motion and their biorthogonal eigenfunctions, is presented to solve the equations of motion of beams with arbitrary boundary conditions. The results obtained using the higher-order theory of Reddy (HOBT) are compared with those obtained by Timoshenko shear deformation beam theory (FOBT) as well as the Bernoulli-Euler theory (CBT)

A remark on the state-space concept applied to bending, buckling and free vibration of composite laminates

The present study shows that the state-space concept used to generate exact solutions for various boundary conditions for bending, buckling and free vibration of composite laminates, can be modified easily and exactly and has no drawback when the laminate thickness is reduced. Numerical results for central deflections, axial stresses, transverse shear stresses, critical buckling loads and natural frequencies of cross-ply laminated plates are obtained using the classical, first- and third-order theories for large side to thickness ratios. Copyright (C) 1996 Elsevier Science Ltd

FREE-VIBRATION OF CROSS-PLY LAMINATED BEAMS WITH ARBITRARY BOUNDARY-CONDITIONS

Analytical solutions of refined beam theories are developed to study the free vibration behavior of cross-ply rectangular beams with arbitrary boundary conditions in conjunction with the state space approach. The study concludes that the disagreement between different shear deformation theories is much less than the disagreement between any of them and Euler-Bernoulli theory

Free and forced vibration of cross-ply laminated composite shallow arches

A model for the dynamic behavior of a laminated composite shallow arch is developed from shallow shell theory. Linear equations of motion are derived for thin, moderately thick and thick arches. Free vibration of the arch is explored and exact natural frequencies of the third-order, second-order, first-order and classical arch theories are determined for various boundary conditions. A generalized modal approach is presented to solve the dynamic response of cross-ply laminated arches with arbitrary boundary conditions and for arbitrary loadings. The Poisson effect and rotary inertia are incorporated in the formulation of the arch constitutive equation, in the analytical approaches and in the numerical results. (C) 1997 Elsevier Science Ltd

Buckling of cross-ply laminated beams with arbitrary boundary conditions

Analytical solutions of refined beam theories are developed to study the buckling behaviour of cross-ply rectangular beams with arbitrary boundary conditions. The state space concept in conjunction with Jordan canonical form will be used to solve exactly the governing equations of the buckling problems. The correlation between different shear deformation theories and the classical theory has been established. (C) 1997 Elsevier Science Ltd

An exact solution for the bending of thin and thick cross-ply laminated beams

The state-space concept in conjunction with the Jordan canonical form is presented to solve the governing equations for the bending of cross-ply laminated composite beams. The classical, first-order, second-order and third-order theories have been used in the analysis. Exact solutions have been developed for symmetric and antisymmetric cross-ply beams with arbitrary boundary conditions subjected to arbitrary loadings. Several sets of numerical results are presented to show the deflected curve of the beam, the effect of shear deformation, the number of layers and the orthotropicity ratio on the static response of composite beams. (C) 1997 Elsevier Science Ltd