Free Vibration Analysis of a Functionally Graded Material Coated Aluminum Beam

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Free Vibration Analysis of a Functionally Graded Material Coated Aluminum Beam

Erdurcan, Ersoy Fatih / Cunedioğlu, Yusuf

This paper presents a theoretical investigation on the free vibration of a symmetric beam consisting of an aluminum core coated with functionally graded material. The elastic modulus and density are varied throughout the thickness of the coating material with both a polynomial and an exponential function, whereas a classical lamination theory is applied to determine the effective elastic modulus and density. To model the gradually changing mechanical properties in a truthful way, the coating is represented by 25 layers of material, whereas each layer itself is homogeneous and isotropic. To obtain a numerical solution, the Timoshenko finite element model beam theory (which also takes first-order shear deformation effects into account) is used. For this purpose, a finite element code is written in MATLAB and the natural frequencies of the beam are found. A detailed parametric study is conducted to show the influences of the core thickness to beam height ratio ( $h / H$ ), the beam span to height ratio ( $L / H$ ), the exponential function and power law index $n$ , and multiple boundary conditions on the natural beam frequencies. It was observed that the studied parameters had a significant effect on the natural frequencies.