Applied Mathematics and Mechanics (English Edition) ›› 2024, Vol. 45 ›› Issue (2): 239-260.doi: https://doi.org/10.1007/s10483-024-3083-6
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Jie JING1, Xiaoye MAO1,2,*(
), Hu DING1,2, Liqun CHEN1,2
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RSSReceived:2023-10-07
Online:2024-02-01
Published:2024-01-27
Contact:
Xiaoye MAO
E-mail:xmao3@shu.edu.cn
Supported by:2010 MSC Number:
Jie JING, Xiaoye MAO, Hu DING, Liqun CHEN. Parametric resonance of axially functionally graded pipes conveying pulsating fluid. Applied Mathematics and Mechanics (English Edition), 2024, 45(2): 239-260.
Fig. 1
Model of the AFG pipe conveying fluid (color online)"
Table 1
Comparison of values before and after buckling (Γ0-sup = 1.1Γ0-cr)"
 |
Fig. 2
Parametric resonance boundaries in the subcritical region: (a) pulsating flow velocity boundaries; (b) damping boundaries (color online)"
Fig. 3
Total responses of parametric resonance at the midpoint of the subcritical pipe: (a) time history via the DQEM; (b) numerical and analytical solutions (color online)"
Fig. 4
(a) Pulsating flow velocity boundary under different αE. Total responses of the pipe under different pulsating flow velocities at (b) αE=0.8, (c) αE=1.0, and (d)αE=1.2 (color online)"
Fig. 5
Responses of the subcritical pipe at 0.25L and 0.75L under (a) αE=0.4, 0.8 and (b) αE=1.2, 1.6 (color online)"
Fig. 6
Relative deviations of the non-trivial response at 0.25L and 0.75L of the subcritical pipe: (a) stable solution; (b) unstable solution (color online)"
Fig. 7
Parametric resonance boundaries in the supercritical region: (a) pulsating flow velocity boundaries; (b) damping boundaries (color online)"
Fig. 8
Time history of the supercritical pipe via the DQEM (color online)"
Fig. 9
Analyses of (a) the solution of the midpoint at the T0 scale, (b) the natural frequency component of the midpoint at the T1 scale, (c) the external excitation frequency component of the midpoint at the T1 scale, (d) the zero-shift component of the midpoint at the T1 scale, and (e) the synthesis of the T0 and T1 scale solutions (color online)"
Fig. 10
(a) Pulsating flow velocity boundaries at different αE. Total responses at (b) αE=0.8, (c)αE=1.2, and (d) αE=1.4 (color online)"
Fig. 11
Responses of the supercritical pipe at 0.25L and 0.75L under (a) αE=0.4, 0.8 and (b) αE=1.2, 1.4 (color online)"
Fig. 12
Relative deviations of the parametric response at 0.25L and 0.75L of the supercritical pipe: (a) stable solution; (b) unstable solution (color online)"
Table 2
Comparison of parametric vibration in the subcritical and supercritical regions (Γ0-sup = 1.1Γ0-cr)"
 |
Fig. 13
Pulsating flow velocity boundaries of the pipe at (a)αE=0.4 and (c) αE=1.4. (b) Relationship between the gradient parameter and the pulsating flow velocity boundaries (color online)"
Fig. 14
Damping boundaries of the pipe at (a) αE=0.4 and (c) αE=1.4. (b) Relationship between the gradient parameter and the damping boundaries (color online)"
Fig. 15
Parametric responses at (a) αE=0.4, (b)αE=0.8, (c)αE=1.2, and (d) αE=1.4 before and after buckling (color online)"
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