Nonlinear forced vibration in a subcritical regime of a porous functionally graded pipe conveying fluid with a retaining clip

doi:10.1007/s10483-025-3206-9

Abstract

Abstract:

This study examines the nonlinear behaviors of a clamped-clamped porous pipe made of a functionally graded material (FGM) that conveys fluids and is equipped with a retaining clip, focusing on primary resonance and subcritical dynamics. The nonlinear governing equations for the FGM pipe are derived by the extended Hamilton's principle, and subsequently discretized through the application of the Galerkin method. The direct method of multi-scales is then used to solve the derived equations. A thorough analysis of various parameters, including the clip stiffness, the power-law index, the porosity, and the clip location, is conducted to gain a comprehensive understanding of the system's nonlinear dynamics. Through the analysis of the first natural frequency, the study highlights the influence of the flow velocity and the clip stiffness, while the comparisons with metallic pipes emphasize the role of FGM composition. The examination of the forced response curves reveals saddle-node bifurcations and their dependence on parameters such as the detuning parameter and the power-law index, offering valuable insights into the system's nonlinear resonant behavior. Furthermore, the frequency-response curves illustrate the hardening nonlinearities influenced by factors such as the porosity and the clip stiffness, revealing nuanced effects on the system response and resonance characteristics. This comprehensive analysis enhances the understanding of nonlinear behaviors in FGM porous pipes with a retaining clip, providing key insights for practical engineering applications in system design and optimization.

Key words: functionally graded material (FGM) pipe conveying fluid, retaining clip, porosity, primary resonance, subcritical regime

2010 MSC Number:

O175.2

M. GHOLAMI, M. EFTEKHARI. Nonlinear forced vibration in a subcritical regime of a porous functionally graded pipe conveying fluid with a retaining clip. Applied Mathematics and Mechanics (English Edition), 2025, 46(1): 101-122.

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Figures/Tables 19

Fig. 1

Table 1

Material properties of the FGM pipe"

Item	Description	Value
$L$ /m	Pipe length	1
$D o$ /mm	Outer diameter	8
$D i$ /mm	Inner diameter	6.4
$E c$ /GPa	Young's modulus of ceramic	348.43
$E m$ /GPa	Young's modulus of metal	201.04
$ρ c$ / $(kg ⋅ m − 3)$	Ceramic density	2 370
$ρ m$ / $(kg ⋅ m − 3)$	Metal density	8 166
$ρ f$ / $(kg ⋅ m − 3)$	Fluid density	872
$p$ /MPa	Fluid pressure	28

Table 1

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