Free vibration analysis of exponential functionally graded beams with a single delamination

Functionally graded materials (FGMs) are regarded as one of the most promising candidates for future advanced composites in many engineering sectors. However, FGMs is not immune to the occurrence of delamination, which can significantly reduce the stiffness and strength of the structures and affect their vibration characteristics. In the present study, an analytical solution is developed to study the free vibration of exponential functionally graded beams with a single delamination. Euler-Bernoulli hypothesis, the 'free mode' and 'constrained mode' assumptions in delamination vibration are adopted. The shifting of neutral axis, as a result of the asymmetrical distribution of material property (in thickness direction), is also taken into consideration. This is the first study investigating the effects of delamination (its length and location) on the vibration of exponential functionally graded beams. Results show that the natural frequencies increase as the Young's modulus ratio becomes bigger, but such increase is less significant when the beam suffers a longer delamination. Furthermore, the effects of delamination length and longitudinal location on reducing natural frequencies are aggravated when the material property (Young's modulus and density) changes less dramatically from the bottom to the top. The difference of natural frequencies between 'free mode' and 'constrained mode' becomes smaller with a decreasing Young's modulus ratio. The analytical results of this study can serve as the benchmark for FEM and other numerical solutions.