https://doi.org/10.1140/epjp/s13360-022-03570-1
Regular Article
Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection
College of Mechanical and Vehicle Engineering, Chongqing University, 400044, Chongqing, China
Received:
30
August
2022
Accepted:
4
December
2022
Published online:
10
December
2022
In this paper, the nonlinear bifurcation buckling and primary resonance of functionally graded material (FGM) fluid-conveying pipes with initial geometric imperfections resting on elastic foundations under three different boundary conditions are investigated. Firstly, the Euler–Lagrange equation is employed to derive the nonlinear equations of motion. Then, the two-step perturbation method is applied to discrete nonlinear motion equations, and a series of perturbation equations are obtained. Subsequently, the primary resonance, buckling and post-buckling path of the FGM fluid-conveying pipes are predicted with the help of the Galerkin method and the modified Lindstedt–Poincare method. Finally, the effects of temperature changes, elastic foundations, fluid velocity, functionally graded index, and initial geometric imperfections on the bifurcation buckling and resonance behaviors are analyzed, and many meaningful conclusions are drawn.
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