Analytic Approach to Free Vibration and Buckling Analysis of Functionally Graded Beams with Edge Cracks using four Engineering Beam Theories

Similarly, the three first natural frequencies of the composite beam due to the crack as functions of the angle of fibers (α) and volume fraction of fiber are

The last location of the second crack ( ⁄ = 0.8) is very nearer to the unconstrained end, hence at this location even though crack depth increases, the value of characteristics

Starting from the derivation of the governing differential equations of motion in free vibration, the dynamic stiffness matrix of a functionally graded Timoshenko beam has been

Adda Bedia, A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets,

The comparison of the fundamental frequency parameter of the uniform cross-section FG- CNTRC beam obtained in the present work with that of Lin and Xiang [11] is given in Table 3 for