Calculating the fundamental frequency of power law functionally graded beam using ANSYS software

In this work free vibration of simply supported, clamped-clamped and clamped-free functionally graded (FG) beam with material graduation transversally through the thickness, using the power-law model, were investigated. The beam's functionally graded material (FGM) consists of aluminium (Al2O3) and steel (used in a typical case). Pure steel is the beam's bottom surface, whereas pure aluminium is the beam's top surface throughout the thickness change condition. Two finite element models were proposing to calculate the first non-dimensional frequency parameters of FG beam. These models are shell and solid, and they were employed using the ANSYS APDL version 17.2. The two models have been verifying with the previously published works, and a good agreement was founding. Numerical results were presented in graphical forms to study the effects of the power-law index (i.e. material distribution), length-to-thickness ratio, modulus ratio and types of support for the first non-dimensional frequency parameter of the FG beam. The above mention effects play a significant role in the free vibration of the beam. Power-law index (k) is one of the parameters affecting mainly on the frequency parameter of FG beam. The frequency parameter increase with increasing the power-law index when the modulus ratio less than one and decease with increasing the power-law index when the modulus ratio more than one, when the modulus ratio equal one ( i.e. pure material ), there is no effect of the power-law index in this case. When the modulus ratio (E ratio) increases, the frequency parameter increases too, but with the change rate depending on the length-to-thickness ratio (L/h) and power-law index(K). Also, the frequency increase with increasing the length to thickness ratio at any power-law index.