Non-planar motions due to nonlinear interactions between unstable oscillatory modes in a cantilevered pipe conveying fluid

Yamashita, Kiyotaka; Kitaura, K.; Nishiyama, Naoto; Yabuno, Hiroshi

doi:10.1016/j.ymssp.2022.109183

Cited by 12 publications

(3 citation statements)

References 27 publications

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“…At this time, the complex frequencies corresponding to the second-and third-order modes had positive real parts, and these two modes were excited to perform interactions. Yamashita et al [62] considered the spatial vibration of a cantilevered fluid-conveying pipe with a concentrated mass attached to the free end and investigated the "in-plane and out-of-plane" interactions of its second-and thirdorder modes based on the results reported in Ref. [60].…”

Section: Introductionmentioning

confidence: 99%

“…[60]. The methods used in references [60][61][62] were all projection methods [63], and the coefficients of the reduced-order equations were all determined by numerical calculations. Zhang and Huang [64] adopted a mode analysis method to study the effect of Poisson, junction, and friction couplings on the stability of cantilevered fluid-conveying pipes.…”

Section: Introductionmentioning

confidence: 99%

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Periodic motion of macro- and/or micro-scale cantilevered fluid-conveying pipes with O(2) symmetry: a finite dimensional analysis

Guo

2024

Front. Phys.

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Introduction: In this study, the spatial bending vibration of macro- and/or micro-scale cantilevered fluid-conveying pipes is investigated through finite dimensional analysis.Methods: Firstly, the Galerkin method is employed to discretize the partial differential equations of motion of the system into a system of ordinary differential equations. Then, the projection method based on center manifold-normal form theory is adopted to derive the coefficient formula that determines the pipe’s nonlinear dynamic behaviors, i.e., the change rate of the real part of the critical eigenvalue with respect to the flow velocity and the nonlinear resonance term, thereby obtaining reduced-order equations. Compared to previous studies that relied on the numerical solution of ordinary differential equations to determine the existence and stability of periodic motion, this paper concludes the existence and stability of periodic motion by utilizing the coefficients of the Galerkin discretized equations and the reduced-order equations, significantly saving time in determining the dynamic properties of pipes.Results and discussion: Subsequently, by investigating the reduced-order equations under specific parameters, the existence and stability of the two types of periodic motion of the pipe are studied. For macro pipes, the truncated mode numbers are set incrementally to calculate the coefficients of the reduced-order equations, investigate the distribution of the stability of the two types of periodic motions with the mass ratio, and carry out a longitudinal comparison (i.e., the comparison between the results obtained under different truncated mode numbers) as well as a horizontal comparison (i.e., the comparison of results between the finite dimensional analysis and the infinite dimensional analysis). It is found that the reasonable truncated mode number required to study this type of system is 15. Previous studies primarily focused on the convergence of frequency and amplitude when determining the truncated mode numbers. On this basis, our study further examines the convergence of motion forms with respect to the truncated mode numbers. Finally, based on the Galerkin discretization equations of 15 modes, the distribution of the stability of two types of the periodic motion of micro pipes with the mass ratio is analyzed. For macro- and micro-scale pipes, when the truncated mode number is 15, the error between the finite dimensional analysis results and the infinite dimensional analysis results is calculated to be about 7%. The above results are verified by obtaining the numerical solution to Galerkin discretization equations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Periodic motion of macro- and/or micro-scale cantilevered fluid-conveying pipes with O(2) symmetry: a finite dimensional analysis

Guo

2024

Front. Phys.

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“…The nonlinear mathematical formulation derived from the third-order 2 approximation is the well-known model to simulate their nonlinear responses in the pre-and postflutter regions. This approximation model has attracted a great number of research interests from both theoretical and experimental studies [18][19][20][21][22][23][24][25][26]. For cantilevered flexible pipes conveying fluid, the third-order approximation model is incapable of estimating their nonlinear behavior when they undergo extremely large deformations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear geometrically exact dynamics of fluid-conveying cantilevered hard magnetic soft pipe with uniform and nonuniform magnetizations

Dehrouyeh-Semnani

2023

Mechanical Systems and Signal Processing

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Stability and Nonlinear Response Analysis of Parametric Vibration for Elastically Constrained Pipes Conveying Pulsating Fluid

Hao

Ding

Mao

et al. 2022

Acta Mech. Solida Sin.

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Non-planar motions due to nonlinear interactions between unstable oscillatory modes in a cantilevered pipe conveying fluid

Cited by 12 publications

References 27 publications

Periodic motion of macro- and/or micro-scale cantilevered fluid-conveying pipes with O(2) symmetry: a finite dimensional analysis

Periodic motion of macro- and/or micro-scale cantilevered fluid-conveying pipes with O(2) symmetry: a finite dimensional analysis

Nonlinear geometrically exact dynamics of fluid-conveying cantilevered hard magnetic soft pipe with uniform and nonuniform magnetizations

Stability and Nonlinear Response Analysis of Parametric Vibration for Elastically Constrained Pipes Conveying Pulsating Fluid

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