Large amplitude axisymmetric vibration of a circular plate having a circumferential crack

Here, the large amplitude axisymmetric vibration of a circular plate having a circumferential crack is studied considering the simply supported and clamped boundary conditions. Exact modal functions are generated by satisfying the boundary conditions and constraints along the crack. The inplane or membrane forces resulting from the large deflection are derived from the Berger's formulation. Next, the Galerkin's method is used to transform the differential equation into the Duffing equation with cubic nonlinearities. The amplitude and phase curves are generated using the Method of multiple scales. Natural frequency variations of axisymmetric modes are studied for a change in crack depth and crack position, considering both boundary conditions. Some natural frequencies are also compared with the finite element results and they are found to be in good agreement. For clamped boundary conditions, the natural frequency of a cracked plate is shown to approach that of an uncracked plate for a particular crack position independent of different crack depths. The amplitude and phase curves are shown for different crack parameters. Finally, the phase plane plot variations are presented for different crack depths, positions and boundary conditions.