Shahrood University of Technology Journal of Solid and Fluid Mechanics 2251-9475 9 4 2019 12 22 Vibration analysis of pipe conveying fluid, made of functionally graded material in thickness direction Vibration analysis of pipe conveying fluid, made of functionally graded material in thickness direction 107 116 1709 10.22044/jsfm.2020.8281.2884 FA M. Saeidiha shahrood university of technology A. Karami Mohammadi Assoc. prof., Mech. Eng. Dept., Shahrood Univ.,Shahrood, Iran. Journal Article 2019 04 15 The pipes conveying fluid are capable of displaying complex dynamical behaviors. In this paper, the dynamic behavior of a simply supported fluid-conveying pipe made of functionally graded material in thickness direction, is analysed. The Young Modulus are assumed to be graded along the thickness direction according to a simple power law and equations of motion of the Euler–Bernoulli beam are derived. The partial differential equation is discretized to ordinary differential equations by the Galerkin method. The natural frequencies are obtained for different dimensionless parameters and compared with a homogenious pipe conveying fluid, and the effect of gradually changed material has been studied. Dimensionless critical flow velocities which couse instability are obtained for particular mass parameter and different distribution of Young Modulus. The results show that by increasing Young Modulus from inner to outer surface of pipe, the natural frequencies of system increase and instability is occurred in higher critical velocities The pipes conveying fluid are capable of displaying complex dynamical behaviors. In this paper, the dynamic behavior of a simply supported fluid-conveying pipe made of functionally graded material in thickness direction, is analysed. The Young Modulus are assumed to be graded along the thickness direction according to a simple power law and equations of motion of the Euler–Bernoulli beam are derived. The partial differential equation is discretized to ordinary differential equations by the Galerkin method. The natural frequencies are obtained for different dimensionless parameters and compared with a homogenious pipe conveying fluid, and the effect of gradually changed material has been studied. Dimensionless critical flow velocities which couse instability are obtained for particular mass parameter and different distribution of Young Modulus. The results show that by increasing Young Modulus from inner to outer surface of pipe, the natural frequencies of system increase and instability is occurred in higher critical velocities https://jsfm.shahroodut.ac.ir/article_1709_1c7b70a88f3e8dcf9f2881dbbc844cc4.pdf