The dynamic response of shear deformable functionally graded (FG) pipes conveying nd internal fluid is studied to determine the effects of temperature gradient, and to determine the effect of two cases of temperature distributions on their natural frequencies. Assuming that the material properties of the FG pipes obey a power-law distribution and are temperature-dependent, a differential governing equation is obtained using the extended Hamilton’s principle. A wavelet-based element of FG pipes considering shear deformations is developed and used to obtain ordinary differential equations for the system considered.
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The project was supported by the National Science Foundation of China (Grant No.51305350) and the Basic Research Foundation of NWPU (No.3102014JCQ01045)
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Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 54, No. 5, pp. 925-940, September-October, 2018.
Appendices
Appendix A.
Mass, Damping, and Stiffness Matrices of Finite Element
where ()· and ()′ denote ∂()/∂t and ∂()/∂ξ , respectively.
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Cao, J.H., Liu, Y.S. Comparison of Natural Frequencies of Fluid-Conveying Functionally Graded Thin-Walled Pipes in Two Cases of Temperature Distributions. Mech Compos Mater 54, 635–646 (2018). https://doi.org/10.1007/s11029-018-9771-3
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DOI: https://doi.org/10.1007/s11029-018-9771-3