A New Method Based on Laplace Transform and Its Application to Stability of Pipe Conveying Fluid

Wen, Huabing; Yang, Yi; Li, P.; Li, Y. D.; Yu, Huang

doi:10.1155/2017/1472601

Cited by 9 publications

(6 citation statements)

References 11 publications

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“…According to the positive and negative of the real part of the eigenvalue ω, the stability of the system can be analyzed. 3,9 The first-order eigenvalue of the pinned-pinned-pinned straight-curved pipe conveying fluid varying with flow velocity is shown in Fig. 8.…”

Section: The Stability Of the Straight-curved Pipe Conveying Fluidmentioning

confidence: 99%

“…The two forms of pipe have differ-ent mechanical characteristics, and the reasons of instability caused by fluid in the pipes are also different. Based on the linear theory, Paidoussis, 1 Dai, Wang, Qian, et al, 2 Wen, Yang, Li, et al 3 studied the stability of straight pipe conveying fluid supported at both ends. The results show that with increasing the flow velocity of fluid, the pipe buckles firstly, and then loses stability with coupled-mode flutter.…”

Section: Introductionmentioning

confidence: 99%

“…As for cantilever pipes conveying fluid, fluid in the pipe could cause the pipe flutter. 3,9 The motion of cantilever pipe conveying fluid is very complex when some nonlinear factors are considered, and the change of any parameter of the system could result in a great change of the motion of pipe. [10][11][12] The history of the study on the curved pipe conveying fluid has not been long before.…”

Section: Introductionmentioning

confidence: 99%

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Analysis on a Kinetic Theoretical Model of the Straight-Curved Pipe Conveying Fluid

Wen¹,

Yang²,

Li³

et al. 2018

IJAV

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A kinetic theoretical model for the straight-curved pipe conveying fluid was proposed and studied in this paper. Firstly, the new equations of static equilibrium and motion about equilibrium position were derived by applying perturbation method to the motion equations of the curved pipe conveying fluid. Then, the kinetic equations of the straight pipe were derived by ignoring the terms containing the curvature of the curved pipe in these equations. Subsequently, considering different factors, four segmental kinetic theoretical models of the straight-curved pipe were built. Lastly, based on the present theoretical models and finite element method, the static deformations and natural frequencies of the pipes with three typical boundary conditions were simulated. The simulation results show that the applicability of these kinetic theoretical models is closely related to the boundary conditions: 1) For the pipes with any one of three boundary conditions, the geometrical non-linearity and the nonlinear force caused by the deformation of straight pipe segment, have a great effect on the static deformation of the pipes, while they have little effect on the natural frequencies of the pipes. 2) When the natural frequencies of the pinned-pinned pipe or the pinned-sliding bearing-pinned pipe are solved, the static deformation of the pipes must be considered.3) When the natural frequencies of the pinned-pinned-pinned pipe are solved, the static deformation of the pipe can be ignored.

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Section: The Stability Of the Straight-curved Pipe Conveying Fluidmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis on a Kinetic Theoretical Model of the Straight-Curved Pipe Conveying Fluid

Wen¹,

Yang²,

Li³

et al. 2018

IJAV

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show abstract

“…Incidentally, it is worth pointing out that equations (51) to (53) make sense for free vibration when the right sides of the equations vanish. The natural frequencies and mode shapes can be obtained readily according to Wen et al (2017). For beams with other boundary conditions, Green's functions can be obtained by the same procedures above.…”

Section: Green's Functions Associated With Different Boundary Conditionsmentioning

confidence: 99%

Closed-form solutions for vibrations of a magneto-electro-elastic beam with variable cross section by means of Green’s functions

Zhang

Chen

Yang

et al. 2018

Journal of Intelligent Material Systems and Structures

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In this article, closed-form solutions are obtained for vibrations of a magneto-electro-elastic beam with variable cross section. Based on Timoshenko beam assumptions, governing equation for the non-uniform beam with exponentially varying width is obtained. Laplace transform approach applied to the governing equation results in the corresponding Green’s functions for the beams with various boundary conditions. The equations, which are solved to obtain Green’s functions, are degenerated for the analyses of the characters of free vibration. For free vibrations of the beams under different mechanical boundary conditions, the effects of the non-uniformly cross-sectional parameters and magneto-electric boundary conditions on the dynamic characters are studied. In addition, the magneto-electric potential modal variables’ distributions through the thickness are presented. In the discussions of forced vibration, two points in the beam are selected to investigate frequency responses in terms of displacement and magneto-electric potential. Moreover, the influences of excitation frequency and cross-sectional parameter on through-the-thickness distributions of electric potentials are investigated.

show abstract

“…Some of the methods that have been proposed to study this class of problems include the Finite element method [58], differential quadrature method, transfer matrix method, dynamic stiffness method, Galerkin method, multiple scales method and recently, a new method based on Laplace transform [60].…”

Section: Chapter 1 Introduction 11 Motivationmentioning

confidence: 99%

Dynamics of Three-Dimensional Pipes Conveying Fluid Using the Reissner Beam Theory

Muoka¹

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A New Method Based on Laplace Transform and Its Application to Stability of Pipe Conveying Fluid

Cited by 9 publications

References 11 publications

Analysis on a Kinetic Theoretical Model of the Straight-Curved Pipe Conveying Fluid

Analysis on a Kinetic Theoretical Model of the Straight-Curved Pipe Conveying Fluid

Closed-form solutions for vibrations of a magneto-electro-elastic beam with variable cross section by means of Green’s functions

Dynamics of Three-Dimensional Pipes Conveying Fluid Using the Reissner Beam Theory

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