Vibration and Bending of a Cracked Plate - Aggarwala, B.D.; Ariel, P.D. (Engineering Transactions, 1981)
The vibration and bending of a square plate with four cracks emanating from the centre of the plate or the midpoints of the edges is considered. Dual series equations which result from the mixed boundary conditions along the lines of the cracks are derived. By isolating the singular part of the solution, the problem is reduced to a Fredholm integral equation which is solved numerically. For the vibrating plate the frequencies of the first two symmetric modes are obtained and the displacement and the strain energy are determined for the case of bending of the plate. Also in both cases, stress intensity factors are calculated.