Free Vibration Analysis of Simply Supported Power Law Functionally Graded Beam Using Finite Element Method

Abstract

This paper studies the free vibration of simply supported functionally graded beam with material graduation transversally through the thickness using the power-law model. Two finite element models are proposed to calculate the first five frequency parameters of a simply supported FG beam. These models are shell and solid models and they are employed using the ANSYS APDL version 17.2. The two models have been verified with the previously published works and found a good agreement with them. Numerical results are presented in graphical forms to study the effects of the power-law index (i.e. material distribution), length-to-thickness ratio, and modulus ratio on the first five frequency parameter of the FG beam. The above mention effects play very important role on the free vibration of the beam. Index of power-law is a parameter that primarily has an effect on the FG beam frequency parameter. It was found that increasing the index of the power-law lead to frequency parameter increases when the modules ratio less than one and drops as an index of the power-law increase when the modules ratio is more than one, when the module ratio is equal to one (i.e., pure material), in this case, index of power-law has no effect. If the modulus ratio (E ratio) increases, the frequency parameter increases too, but with the change rate depending on the index of power-law and length to height ratio. Also, the frequency increase with increasing the length to height ratio at any power-law index.