Frequency Analysis of Cracked Porous Functionally Graded Beams on Elastic Foundation using Reddy Third Order Shear Deformation Theory

In this paper, Frequency analysis of cracked porous functionally graded beams which are resting on elastic foundation based on reddy third order shear deformation theory is studied. Mechanical property gradients defined in accordance with model of exponential law. Governing equations obtained with the aid of third order shear deformation theory and by considering elastic foundation effects within hamilton’s principle. Due to complicating closed form solution of equations, differential equations solved utilizing Generalized Differential Quadrature Method by considering various end conditions. In order to validate the results, comparisons are made with solutions which are available for other papers. This study shows that the difference between the results of this paper and the results of others is negligible. Finally the effects of geometrical parameters, exponential law indexes, crack location and depth, elastic foundation and porosity on natural frequencies of functionally graded beams are studied. The results of this paper and effects of these parameters can be used in the optimum design of functional graded beams and crack prediction, detection and monitoring techniques.