Free vibration of FGM Timoshenko beams with through-width delamination

Free vibration of functionally graded beams with a through-width delamination is investigated. It is assumed that the material property is varied in the thickness direction as power law functions and a single through-width delamination is located parallel to the beam axis. The beam is subdivided into three regions and four elements. Governing equations of the beam segments are derived based on the Timoshenko beam theory and the assumption of ‘constrained mode’. By using the differential quadrature element method to solve the eigenvalue problem of ordinary differential equations governing the free vibration, numerical results for the natural frequencies of the beam are obtained. Natural frequencies of delaminated FGM beam with clamped ends are presented. Effects of parameters of the material gradients, the size and location of delamination on the natural frequency are examined in detail.