Free Vibration of Exponential Functionally Graded Beams with Single Delamination

Abstract

FGMs are regarded as one of the most promising candidates for future advanced composites in many engineering sectors, but they may suffer the problem of delamination. Delaminations in structures may significantly reduce the stiffness and strength of the structure and may 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. Kirchhoff-Love hypothesis, the ‘free mode’ and ‘constrained mode’ assumption in delamination vibration are adopted. The shifting of neutral axis due to asymmetrical distribution of material property (in thickness direction) is also taken into consideration. This is the first study on the influences of delamination (its length and location) on the vibration of exponential functionally graded beams. Results show that the natural frequency increases as the Young's modulus ratio increases, but such increase is smaller when the beam suffers a longer delamination. Furthermore, the effect of delamination length and longitudinal location on reducing natural frequency is aggravated when the material property (Young's modulus and density) changes less dramatically from the bottom to the top. The difference of natural frequency 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.