Nonlinear vibration of edged cracked FGM beams using differential quadrature method

This paper investigated the nonlinear vibration of functionally graded beams containing an open edge crack based on Timoshenko beam theory. The cracked section is modeled by a massless elastic rotational spring. It is assumed that material properties follow exponential distributions through the beam thickness. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of beams with different boundary conditions. The effects of the material gradient, crack depth and boundary conditions on nonlinear free vibration characteristics of the cracked FGM beams are studied in detail