Linear and Nonlinear Dynamics of Cantilevered Cylinders in Axial Flow. Part 2: The Equations of Motion

Lopes, Joseph L.; Paı̈doussis, M.P.; Semler, C.

doi:10.1006/jfls.2002.0448

Cited by 83 publications

(38 citation statements)

References 14 publications

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“…This was followed by a spontaneous second-mode oscillation. Lopes et al (2002) derived a nonlinear equation of motion to describe the dynamics of a slender cantilevered cylinder in axial flow, generally terminated by an ogival free end, using the inextensibility assumption, which is reasonable for cantilevered cylinders. Inviscid forces were modelled by an extension of Lighthill's slender-body theory to third-order accuracy.…”

Section: Introductionmentioning

confidence: 99%

Experiments on vertical slender flexible cylinders clamped at both ends and subjected to axial flow

Modarres‐Sadeghi

Paı̈doussis

Semler

et al. 2007

Phil. Trans. R. Soc. A.

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Three series of experiments were conducted on vertical clamped-clamped cylinders in order to observe experimentally the dynamical behaviour of the system, and the results are compared with theoretical predictions. In the first series of experiments, the downstream end of the clamped-clamped cylinder was free to slide axially, while in the second, the downstream end was fixed; the influence of externally applied axial compression was also studied in this series of experiments. The third series of experiments was similar to the second, except that a considerably more slender, hollow cylinder was used. In these experiments, the cylinder lost stability by divergence at a sufficiently high flow velocity and the amplitude of buckling increased thereafter. At higher flow velocities, the cylinder lost stability by flutter (attainable only in the third series of experiments), confirming experimentally the existence of a post-divergence oscillatory instability, which was previously predicted by both linear and nonlinear theory. Good quantitative agreement is obtained between theory and experiment for the amplitude of buckling, and for the critical flow velocities.

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Section: Introductionmentioning

confidence: 99%

Experiments on vertical slender flexible cylinders clamped at both ends and subjected to axial flow

Modarres‐Sadeghi

Paı̈doussis

Semler

et al. 2007

Phil. Trans. R. Soc. A.

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“…1, the equation of motion is commonly obtained using the extended Hamilton's principle. The equation of motion in the form of a partial differential equation is then discretized using, for example, Galerkin's method (see, e.g., [13,18]). However, as noted in [19], a more versatile method to obtain the discretized equations is using the Lagrange equations.…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

“…δx = δx| s=L , θ = θ| s=L etc. Thus, the expressions for F L , F N and F A over the end-piece can easily be obtained from equations (12) and (13); they can alternatively be obtained as in [18]. As seen from equation (14), the inviscid hydrodynamic force per unit length over the end-piece is f F A , where f accounts for departures from ideal inviscid hydrodynamic theory (slender-body theory) over the end-piece (see [9]); the parameter f is normally between 0 and 1: for a perfectly streamlined end-piece, f → 1, whereas for a perfectly blunt end-piece, f → 0.…”

Section: Virtual Work and Generalized Forcesmentioning

confidence: 99%

Dynamics and Stability of a Flexible, Slender Cylinder Flexibly Restrained at One End and Free at the Other and Subjected to Axial Flow

Kheiri

2016

Archive of Mechanical Engineering

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In this paper, Lagrange's equations along with the Ritz method are used to obtain the equation of motion for a flexible, slender cylinder subjected to axial flow. The cylinder is supported only by a translational and a rotational spring at the upstream end, and at the free end, it is terminated by a tapering end-piece. The equation of motion is solved numerically for a system in which the translational spring is infinitely stiff, thus acting as a pin, while the stiffness of the rotational spring is generally non-zero. The dynamics of such a system with the rotational spring of an average stiffness is described briefly. Moreover, the effects of the length of the cylinder and the shape of the end-piece on the critical flow velocities and the modal shapes of the unstable modes are investigated. IntroductionSince the study by Hawthorne [1] in the late 1950s on the dynamics of the Dracone, a flexible sausage-like container towed behind a small vessel, the dynamics and stability of flexible slender structures subjected to axial flow have been studied extensively by applied mechanics researchers; some examples are the studies by Païdoussis [2-4] on the dynamics of flexible cylinders in axial flow with various boundary conditions, the studies by Triantafyllou and Chryssostomidis [5,6] on the dynamics of a cantilevered beam and a pinned-free string subjected to axial flow, and those by Dowling [7,8] on the dynamics of neutrally and negatively buoyant elements of a towed system; for a comprehensive review of these studies, see [9].

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“…In his study, he found that at sufficiently high flow velocities, the pipeline might buckle as a column subjected to axial compression. Recently, Paidoussis [3][4][5] considered the problem of a pinned free cylinder (elastomer cylinder) in water flow in cantilever in three parts, both theoretical and experimental. Olunloyo et al [6] investigated the dynamics of a vibrating offshore pipeline on a moving seabed.…”

Section: Introductionmentioning

confidence: 99%

Temperature modulation of the vibrational responses of a flexible fluid-conveying pipe

Adelaja

2013

Open Engineering

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Abstract:In this study, the nonlinear transverse vibration of a flexible pipe conveying hot, pressurized fluid is investigated.The pipe which is subjected to a pinned-pinned end condition extends as a result of several operating variables such as internal fluid temperature variation, pre-stress and internal pressurization. The equation of motion is solved analytically by hybrid Fourier-Laplace transforms, and the effects of inlet temperature, temperature gradient, and coefficient of area deformation are investigated on the natural frequencies and transverse dynamic response of the pipeline. While the inlet temperature and temperature gradient are found to be inversely proportional to the natural frequencies and amplitude of the dynamic response, increase in the coefficient of area deformation has little effect on the natural frequencies for the particular case considered.

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Linear and Nonlinear Dynamics of Cantilevered Cylinders in Axial Flow. Part 2: The Equations of Motion

Cited by 83 publications

References 14 publications

Experiments on vertical slender flexible cylinders clamped at both ends and subjected to axial flow

Experiments on vertical slender flexible cylinders clamped at both ends and subjected to axial flow

Dynamics and Stability of a Flexible, Slender Cylinder Flexibly Restrained at One End and Free at the Other and Subjected to Axial Flow

Temperature modulation of the vibrational responses of a flexible fluid-conveying pipe

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