Nonlinear modelling and dynamic analysis of cracked Timoshenko functionally graded beams based on neutral surface approach

The present work accounts Timoshenko beam theory followed by Ritz approximation and an iterative technique to deal nonlinear free vibration problems of cracked Functionally Graded Material (FGM) beams based on neutral surface location. Using neutral surface as a reference rather than the midsurface reduces the complexity of nonlinear problems. It is assumed that crack always remains open. Analysis is carried out for clamped-clamped and clamped-free boundary conditions. Nonlinear frequencies and mode shapes corresponding to first three mode of vibration are obtained for the first time for different crack parameters, amplitudes of vibration and material indexes. The accuracy of the present solution is verified by comparing some of the obtained results with existing solutions. It can be concluded that present results are not only accurate but the methodology is very simple and easy to perform.