Effect of gravity on the vibration of vertical cantilevers

Virgin, Lawrence N.; Santillan, Sophia T.; Holland, David

doi:10.1016/j.mechrescom.2006.12.006

Cited by 38 publications

(14 citation statements)

References 7 publications

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“…Naguleswaran [15,16] analyzed the free vibration of a vertical cantilever and calculated natural frequencies when axial load is gravity load and generally linearly varying loading, respectively. Virgin et al [17] also studied free vibration of hanging and standing beams and revealed the effect of gravity on natural frequencies. The analysis of a rotating tapered cantilever with centrifugal force has been formulated [18,19].…”

Section: Introductionmentioning

confidence: 99%

Vibration of a Rayleigh cantilever beam with axial force and tip mass

Tang

2013

Journal of Constructional Steel Research

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Section: Introductionmentioning

confidence: 99%

Vibration of a Rayleigh cantilever beam with axial force and tip mass

Tang

2013

Journal of Constructional Steel Research

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“…For self-weighted vertical beams, the load is also purely axial, though non-constant, and some linear analyses can be found in Refs. [7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of horizontal self-weighted beams and cables with bending stiffness subjected to thermal loads

Treyssède

2010

Journal of Sound and Vibration

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This paper aims at proposing an analytical model for the vibration analysis of horizontal beams that are self-weighted and thermally stressed. Geometrical non-linearities are taken into account on the basis of large displacement and small rotation. Natural frequencies are obtained from a linearisation of equilibrium equations. Thermal force and thermal bending moment are both included in the analysis. Torsional and axial springs are considered at beam ends, allowing various boundary conditions. A dimensionless analysis is performed leading to only four parameters, respectively related to the self-weight, thermal force, thermal bending moment and torsional spring stiffness. It is shown that the proposed model can be efficiently used for cable problems with small sag-to-span ratios (typically less than 1/8, as in Irvine's theory). For beam problems, the model is validated thanks to finite element solutions and a parametric study is conducted in order to highlight the combined effects of thermal loads and self-weight on natural frequencies. For cable problems, solutions are first compared with existing results in the literature obtained without thermal effects or bending stiffness. Good agreement is found. A parametric study combining the effects of sag-extensibility, thermal change and bending stiffness is finally given

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“…Xi et al [13] investigated the free transverse vibrations of standing and hanging Rayleigh beam-columns subjected to a vertically orientated gravity load; by seeking a nontrivial solution of the partial differential equation of motion for the transverse deflection, the natural frequencies and mode shapes of the beam-columns were calculated. In addition, through both experimental and theoretical analyses, Virgin et al [14] confirmed that the natural frequencies of very slender vertical cantilevers are affected by their orientation due to gravity. In addition, Anye and Ziguo [15] transformed the fourth order differential equation of a Rayleigh beam into a second-order Fredholm integral equation and obtained the frequency equation by the integral equation method.…”

Section: Introductionmentioning

confidence: 95%

Natural Frequencies and Mode Shapes of Drill Pipe in Subsea Xmas Tree Installation

Xiao

Qin

Liu

et al. 2020

Mathematical Problems in Engineering

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In this study, experimental and numerical investigations on the vibration characteristics of a drill pipe during the lowering of a subsea Xmas tree were presented. A fourth-order partial differential equation with variable coefficients was established based on Euler–Bernoulli beam theory. The natural frequencies and mode shapes are obtained by using the differential transformation method. Four drill pipe models of different sizes were used in the experiments which were measured using piezoelectric acceleration sensors and fiber Bragg grating sensors, respectively. The factors that affect the natural frequencies and mode shapes, such as length, diameter, lumped mass, and boundary conditions, were analyzed. The results show that all factors have remarkable effects on the natural frequency, but changes in the length and diameter of the pipe have little effect on the mode shapes; the main factors affecting the mode shape are the boundary conditions and lumped mass. The results of the numerical calculation were validated by a comparison with the experimental results and showed good agreement.

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Effect of gravity on the vibration of vertical cantilevers

Cited by 38 publications

References 7 publications

Vibration of a Rayleigh cantilever beam with axial force and tip mass

Vibration of a Rayleigh cantilever beam with axial force and tip mass

Vibration analysis of horizontal self-weighted beams and cables with bending stiffness subjected to thermal loads

Natural Frequencies and Mode Shapes of Drill Pipe in Subsea Xmas Tree Installation

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