Nonlinear free vibration of laminated composite Euler-Bernoulli beams based on finite strain using generalized differential quadrature method

In this research, free vibration of laminated composite Euler-Bernoulli beams has been studied using finite strain assumptions. Governing equations of motion and boundary conditions have been obtained using the Green-Lagrange strain tensor and employing Hamilton's principle. The generalized differential quadrature method has been engaged to solve the equation of motion. Frequencies of the beam have been computed for carbon/epoxy material with various lay-ups subjected to different boundary conditions. The effects of fiber orientation change and lay-ups sequences of angle-ply composite beams on the frequency of the beam have been investigated. Also, dimensionless frequencies for different ratios of length to thickness of the beam subjected to different boundary conditions have been obtained.