Comparison between free vibration of laminated composite beams based on finite strain and von Karman assumptions

Abstract

In this article, the effects of finite strain on nonlinear free vibration of symmetric laminated composite Euler-Bernoulli and Timoshenko beams have been studied and compared to von Karman assumption. Governing equations of motion and boundary conditions have been obtained by using the Green-Lagrange tensor and Hamilton’s principle. According to the finite strain assumption, none of the trans-formation terms eliminate in the Green-Lagrange strain tensor. Also, the equations have been solved by applying generalized differential quadrature method (GDQM). The natural frequencies of the Euler-Bernoulli and Timoshenko beams for different lay-ups have been compared to each other. Also, the ef-fects of fiber orientation change on the natural frequencies of two beams have been calculated. The re-sults demonstrate that the natural frequencies obtained by the finite strain assumption are more than the von Karman one for different lay-ups. Furthermore, difference between the finite strain and von Karman assumptions for laminated Timoshenko beams is more than the Euler-Bernoulli ones.