Experimental and analytical investigation of free vibration of a crack FG beam reinforced with alumina nano particles

The crack defect is the main problem that occurs in any structure so the effect of crack dimensions on the free vibration of the functionally graded beam (FGB) is studied theoretically and experimentally. This crack is designed as a notch on the top surface of FGB, which is designed based on Euler and Timoshenko beam theories. In this work, FGB consists of five layers in the thickness direction according to the power law model with different percentages of nano Al2O3 and epoxy. Eighteen tensile samples were prepared using a mixture of epoxy Quickmast 105 and nano alumina (Al2O3) at volume fractions of 0%, 1%, 2%, 3%, 4%, and 5%. The experiment aimed to determine the nano alumina volume fraction at which the elastic modulus begins to decrease. Then, this beam is prepared from epoxy and alumina Al2O3 nano with different percentages by hand lay-up method to measure the natural frequency. The effect of nano percentage, power index value, and crack dimensions is studied extensively. The results revealed that at a 5% volume fraction of nano alumina (Al2O3), the elastic modulus increased by 107.12% compared to the pure epoxy sample, while the tensile strength decreased by 16.41% compared to the sample with a 4% volume fraction of nano alumina. Additionally, at a 4% volume fraction, the tensile strength showed an 86.41% increase compared to the pure epoxy sample. Furthermore, when the crack depth ratio and crack position ratio are both 0.5, the natural frequency decreases by 23.30% compared to the intact beam designed with five index values. Finally, the theoretical and experimental results show good agreement, with a maximum difference of 5%.