Analytical approximation of nonlinear vibration of string with large amplitudes

Omran, Mojtaba Parvizi; Amani, Amin; Lemu, Hirpa G.

doi:10.1007/s12206-013-0301-x

Cited by 8 publications

(7 citation statements)

References 30 publications

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“…Investigation of nonlinear vibration of string with large amplitudes has been conducted by Omran et al 22 In engineering application, however, the maximum stress and deformation are usually considered only rather than their change rule. In this section, energy conservation method is used to analyze the drillstring dynamics.…”

Section: Effects Of Large Axial Impact On Drillstring Dynamicsmentioning

confidence: 99%

Effects of axial impact load on the dynamics of an oilwell drillstring

Tang

Zhu

Lin

2019

Advances in Mechanical Engineering

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This article studies the dynamics of oilwell drillstring under large and small axial impact loads. For the case of large impact load, the drillstring is regarded as a continuous bar under the impact load of a falling mass, and the energy conservation method is implemented. A sensitivity analysis is conducted to investigate the effect of cross-sectional area of the drill string on the impact stress. Results show that the design of drillstring with different cross-sectional areas is not a suitable method. In order to understand the effect of high-frequency small axial impact (applied from percussion tools or downhole generators) on the drillstring vibration, a mechanical model in which the drillstring is regarded as a 2-degreeof-freedom system under a harmonic force is developed. Sensitivity analysis on the effects of impact generator placement and impact frequency on drillstring dynamics are conducted. Results show that the impact generator should be installed near the drill bit and that high frequency is recommended to be used.

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Section: Effects Of Large Axial Impact On Drillstring Dynamicsmentioning

confidence: 99%

Effects of axial impact load on the dynamics of an oilwell drillstring

Tang

Zhu

Lin

2019

Advances in Mechanical Engineering

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“…The obtained results are compared in the next section. Obtained solutions using AFF, IAFF, MMA and Runge-Kutta are compared to the results of variational Iteration Method (VIM) (Taghipour et al, 2014), Hamiltonian Approach (HA) (Taghipour et al, 2014) and Variational approach method (VAM) which is reproduced using the derived equations in (Omran et al, 2013) in Table 1 and Table 2. Comparing the results in tables 1 and 2, the computed response of the cable under the large amplitude vibration using VAM, AFF and MMA are near eachother, while those of the IAFF is far apart from other methods.…”

Section: Cos( ) ( Cos( )) ( Cos( ))mentioning

confidence: 99%

“…The obtained period parameter T  from AFF, IAFF and MMA are compared to that of VAM (Omran et al, 2013), second-order analytical approximation constructed by harmonic balance method (Gottlieb, 1990), Firstorder, second-order and third-order analytical approximation developed by coupling Newton's method with the harmonic balance method (NHB) (Lai et al, 2008) and the exact solution (Lai et al, 2008). Moreover, utilizing IAFF for this problem is not appropriate since its error is more than other mentioned methods.…”

Section: Period Parametermentioning

confidence: 99%

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Approximate solutions of large amplitude vibration of a string

Mahabadi

Pazhooh

2018

Lat. Am. j. solids struct.

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In the present study, the response of a flexible string with large amplitude transverse vibration is studied utilizing amplitude-frequency formulation, improved amplitude-frequency formulation and max-min approach. In order to verify the accuracy of these approaches, obtained results are compared with other methods such as variational approach method, variational iteration method, coupling Newton's method with the harmonic balance method and Hamiltonian approach. It has been found that for this problem, while amplitude-frequency formulation and max-min approach give the same results, improved amplitude frequency formulation is not an appropriate choice.Keywords nonlinear vibration, string, amplitude-frequency formulation, improved amplitude-frequency formulation and max-min approach.

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“…1. Figure 1 Schematic of a constant tension vibrating string with large amplitude (Omran et al, 2013).…”

Section: The Governing Equation Of Strings With Large Amplitudementioning

confidence: 99%

Explicit solution of the large amplitude transverse vibrations of a flexible string under constant tension

Nikkar

2014

Lat. Am. j. solids struct.

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This paper presents the analytical simulation of string with large amplitudes using the Variational Iteration Method (VIM) and Hamiltonian Approach (HA). In order to verify the precision of the presented methods, current results were compared with He's Variational Approach and Runge-Kutta 4 th order. It has been found that these methods are well suited for a range of parameters and the approximate frequencies and periodic solutions show a good agreement with other techniques. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering.

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Analytical approximation of nonlinear vibration of string with large amplitudes

Cited by 8 publications

References 30 publications

Effects of axial impact load on the dynamics of an oilwell drillstring

Effects of axial impact load on the dynamics of an oilwell drillstring

Approximate solutions of large amplitude vibration of a string

Explicit solution of the large amplitude transverse vibrations of a flexible string under constant tension

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