Finite strain analysis of nonlinear vibrations of symmetric laminated composite Timoshenko beams using generalized differential quadrature method

In this study, free vibrations of laminated composite Timoshenko beams undergoing finite strain have been studied. The Green-Lagrange strain tensor according to finite strain assumption has been used to obtain governing equations and boundary conditions of the beam. The generalized differential quadrature method has been employed for solving the governing equations and boundary conditions. Frequencies of the beam have been calculated for carbon/epoxy material subjected to different boundary conditions. The dimensionless frequencies of the beam for different lay-ups based on finite strain and von Karman assumptions have been obtained and compared to each other. Also, the effects of fiber orientation change and lay-ups sequence of angle-ply composite beams have been investigated on the lateral frequency of the beam.