Abstract
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).