Static and Dynamic Stability Analysis of A Functionally Graded Timoshenko Beam

This article presents the evaluation of static and dynamic behavior of functionally graded ordinary (FGO) beam and functionally graded sandwich (FGSW) beam for pined–pined end condition. The variation of material properties along the thickness is assumed to follow exponential and power law. A finite element method is used assuming first order shear deformation theory for the analysis. The element chosen is different from the conventional elements as the shape functions of the element are obtained from the exact solution of the static part of governing differential equation derived according to Hamilton's principle. Moreover, the shape functions depend on length, cross-section and material properties which ensure better accuracy of the solution. The effect of power law index on critical buckling load and natural frequencies of FGO beam is investigated. The critical buckling load of FGO beam with steel-rich bottom increases with power law index whereas the trend reverses for beam with Al-rich bottom. The first three natural frequencies of FGO beam are found to decrease to a minimum value and then increase as the power law index increases from one. The dynamic stability of FGO beam with steel-rich bottom is found to be more than that of beam with Al-rich bottom. An FGSW beam with alumina as bottom skin, steel top skin, and mixture of alumina and steel as core is chosen for analysis. The critical buckling load of FGSW beam increases with the increase of core thickness for variation of material properties in core as per power law with index more than one, whereas it decreases with the increase of core thickness for variation of material properties in core as per exponential law. The first three natural frequencies of the FGSW beam increase with the increase of FGM core for both the types of property distributions. The dynamic stability of the FGSW beam is enhanced as the thickness of the FGM core is increased.