Nonlinear vibration analysis of functionally graded material tubes with conveying fluid resting on elastic foundation by a new tubular beam model

In this paper, nonlinear free vibration analysis of shear deformable functionally graded material (FGM) tubes conveying fluid with immovable support conditions resting on a Pasternak-type foundation is presented. Based on Hamilton's principle, the equations of motion and boundary conditions are obtained by using a new high-order shear deformation tubular beam model with von Karman nonlinearity and the exact expression of curvature, in which contributions of fluid velocity to the kinetic energy and body forces are also considered. The differential quadrature method (DQM) is employed to determine the nonlinear frequencies and amplitude-frequency responses of fluid-conveying FGM tubes with different boundary conditions. A detailed parametric study is conducted to analyze the influences of different types of boundary conditions, geometric and physical properties. The numerical results reveal that the geometrical and physical properties, including elastic foundation, boundary conditions and flow velocity in the fluid-conveying pipes are crucial factors on their dynamical behavior.