Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method

Xu, Mengrui; Xu, Shunfu; Guo, Haiyan

doi:10.1016/j.camwa.2010.04.049

Cited by 48 publications

(28 citation statements)

References 9 publications

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“…The case ω 0 = 0 shown in Fig. 17(a) describes the pipe conveying fluid without rotation, in which the solutions obtained here agree well with the simulations presented in reference [Xu et al, 2010]. When the time increases to be t = 0.04 as shown in Fig.…”

Section: Eigenvalue Studysupporting

confidence: 82%

Radial Basis Collocation Method for the Dynamics of Rotating Flexible Tube Conveying Fluid

Wang

Zhong

2015

Int. J. Appl. Mechanics

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A Meshfree Radial Basis Collocation Method (RBCM) associated with explicit and implicit time integration scheme is formulated to study the coupling dynamics of a rotating flexible tube conveying fluid, which involves a partial differential equation (PDE) with variable coefficients. Dispersion studies are performed and they indicate that the proposed RBCM has a very small dispersion error compared with conventional FEM and Galerkin-based meshfree methods. Numerical examples are conducted for the influence of initial flow rate of the fluid, discretization and shape parameter on the dispersion error. The critical time step is obtained from a Von Neumann stability analysis. For the eigenproblem, Hermite-type RBCM is proposed in order to construct square matrices and eigenvalue analysis gives the frequencies of the system. Subsequently, the influence of angular velocity, flow rate of the fluid and the time variation on the fundamental frequencies is studied. Though proposed for studying the dynamics of a rotating flexible tube conveying fluid, this solution scheme is applicable to other dynamical problems which have similar PDEs with variable coefficients.beam, which showed that the coupling between rotation and flexible deformation of the beam had significant effect on the stability of the system. After that extensive attempts have been made to explore the stability of such system [Yoo and Shin, 1998;Cai et al., 2004;Wright et al., 1982].The aforementioned pipe conveying fluid model and rotating cantilever beam model was first modeled by Panussis and Dimarogonas [2000] as a rotating flexible fluid-tube cantilever system and the model then found its application in the simulation of dynamics for dragonfly wings . Panussis and Dimarogonas [2000] studied the in-plane and out-of-plane lateral vibrations of a horizontally rotating cantilever tube conveying fluid, and presented the critical nondimensional circular frequency of the lateral vibration and critical nondimensional speed of the fluid flow. Wang and Zhong [2014] derived the governing partial differential equations of motion for an elastic tube conveying fluid rotating around a fixed axis based on extended Hamilton's principle, and investigated the stability and energy variation of the system. Vibration system consisting of a rotating cantilever pipe conveying fluid and a tip mass was examined by Yoon and Son [2007]. They illustrated the influences of the tip mass, the velocity of fluid, the angular velocity of cantilever pipe and the coupling of these factors on the dynamics of the system.The previous solution techniques for the rotating flexible cantilever tube conveying fluid model are mainly based on Galerkin method [Panussis and Dimarogonas 2000;Wang and Zhong, 2014] and Runge-Kutta method Yoon and Son, 2007]. However, the time step for solving dynamical problems using finite difference method should be quite small to ensure the stability, which involves high computational costs. Integration in Galerkin method also costs much computation. Therefore, we refer t...

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Section: Eigenvalue Studysupporting

confidence: 82%

Radial Basis Collocation Method for the Dynamics of Rotating Flexible Tube Conveying Fluid

Wang

Zhong

2015

Int. J. Appl. Mechanics

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“…(28) is analytical everywhere, so based on the power series method the solution can be assumed as [25,26] …”

Section: Power Series Methodsmentioning

confidence: 99%

Non-linear nonlocal vibration and stability analysis of axially moving nanoscale beams with time-dependent velocity

Rezaee

Lotfan

2015

International Journal of Mechanical Sciences

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“…Furthermore, Modarres-Sadeghi and Païdoussis 13 studied the possible postdivergence flutter instabilities of this complete nonlinear supported pipe's model with Houbolt's finite difference method 14 and AUTO Software package. Xu et al 15 proposed the analytical expression of natural frequencies of fluid-conveying pipes with the help of homotopy perturbation method. Those calculated frequencies were in good agreement with experiment results.…”

Section: Introductionmentioning

confidence: 99%

Flow‐Induced Vibration Analysis of Supported Pipes Conveying Pulsating Fluid Using Precise Integration Method

Liu

Xuan

2010

Mathematical Problems in Engineering

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Dynamic analysis of supported pipes conveying pulsating fluid is investigated in Hamiltonian system using precise integration method (PIM). First, symplectic canonical equations of supported pipes are deduced with state variable vectors composed of displacement and momentum. Then, PIM with linear interpolation formula is proposed to solve these equations. Finally, this approach's precision is testified by several numerical examples of pinned-pinned pipes with different fluid velocities and frequencies. The results show that PIM is an efficient and rapid approach for flow-induced dynamic analysis o f supported pipes.

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Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method

Cited by 48 publications

References 9 publications

Radial Basis Collocation Method for the Dynamics of Rotating Flexible Tube Conveying Fluid

Radial Basis Collocation Method for the Dynamics of Rotating Flexible Tube Conveying Fluid

Non-linear nonlocal vibration and stability analysis of axially moving nanoscale beams with time-dependent velocity

Flow‐Induced Vibration Analysis of Supported Pipes Conveying Pulsating Fluid Using Precise Integration Method

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