Vibration analysis of edge-cracked beam on elastic foundation with axial loading using the differential quadrature method

The eigenvalue problems of clamped-free and hinged-hinged Bernoulli-Euler beams on elastic foundation with a single edge crack, axial loading and excitation force were numerically formulated using the differential quadrature method (DQM). Appropriate boundary conditions accompanied the DQM to transform the partial differential equation of a Bernoulli-Euler beam with a single edge crack into a discrete eigenvalue problem. The DQM results for the natural frequencies of cracked beams agree well with other literature values. The sampling point number effect, the location of the crack effect and the depth of the crack effect on the accuracy variation of calculated natural frequencies are presented by using two elements in this work. The effects of axial loading, foundation stiffness, opening crack and closing crack are also studied.