Thermomechanical vibration analysis of a functionally graded shell with flowing fluid.

*(English)*Zbl 1151.74364Summary: This paper reports the results of an investigation into the vibration of functionally graded cylindrical shells with flowing fluid, embedded in an elastic medium, under mechanical and thermal loads. By considering rotary inertia, the first-order shear deformation theory (FSDT) and the fluid velocity potential, the dynamic equation of functionally graded cylindrical shells with flowing fluid is derived. Here, heat conduction equation along the thickness of the shell is applied to determine the temperature distribution and material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The equations of eigenvalue problem are obtained by using a modal expansion method. In numerical examples, effects of material composition, thermal loading, static axial loading, flow velocity, medium stiffness and shell geometry parameters on the free vibration characteristics are described. The new features in this paper are helpful for the application and the design of functionally graded cylindrical shells containing fluid flow.

##### MSC:

74H45 | Vibrations in dynamical problems in solid mechanics |

74K25 | Shells |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

74E05 | Inhomogeneity in solid mechanics |

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\textit{G. G. Sheng} and \textit{X. Wang}, Eur. J. Mech., A, Solids 27, No. 6, 1075--1087 (2008; Zbl 1151.74364)

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