scholarly journals Vortex-induced vibration of pipes conveying fluid using the method of multiple scales

2012 ◽  
Vol 2 (2) ◽  
pp. 022006 ◽  
Author(s):  
Huliang Dai ◽  
Lin Wang
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vortex Induced Vibration ◽  
Pipes Conveying Fluid ◽  
Conveying Fluid

Nonlinear Free Vibration of Spinning Viscoelastic Pipes Conveying Fluid

2018 ◽  
Vol 10 (07) ◽  
pp. 1850076 ◽  
Author(s):  
Feng Liang ◽  
Xiao-Dong Yang ◽  
Wei Zhang ◽  
Ying-Jing Qian
Keyword(s):  
Oil And Gas ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Drill String ◽  
Mode Shapes ◽  
Flowing Fluid ◽  
Nonlinear Dynamical ◽  
Pipes Conveying Fluid ◽  
Spinning Speed ◽  
Conveying Fluid

Drill strings are one of the most significant rotor components employed in oil and gas exploitation. In this paper, an improved dynamical model of drill-string-like pipes conveying fluid is developed by taking into account the axial spin, fluid–structure interaction (FSI), damping as well as curvature and inertia nonlinearities. The partial differential equations of motion are derived by two sequential Euler angles and the Hamilton principle and then directly handled by the multiple scales method. The nonlinear amplitudes, frequencies and whirling mode shapes are all investigated towards various system parameters to display the nonlinear dynamical characteristics of such a special rotor system coupled with FSI. It is revealed that the nonlinear amplitudes and frequencies are explicitly dependent on the spinning speed, while the flowing fluid mainly contributes to the linear frequencies, and consequently influences the nonlinear amplitudes and frequencies. The FSI effect and axial spin can both improve the forward procession mode and suppress the backward one, while both procession modes will be suppressed by the viscoelastic damping. The pipe will ultimately present a forward as well as decayed whirling motion for the fundamental mode.

scholarly journals Dynamics of axially functionally graded conical pipes conveying fluid

2021 ◽  
Vol 37 ◽  
pp. 318-326
Author(s):  
Yuzhen Zhao ◽  
Dike Hu ◽  
Song Wu ◽  
Xinjun Long ◽  
Yongshou Liu
Keyword(s):  
Natural Frequency ◽  
Critical Velocity ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Reduction Factor ◽  
Functionally Graded ◽  
Function Type ◽  
Pipes Conveying Fluid ◽  
Volume Fraction Function ◽  
Conveying Fluid

Abstract In this paper, the dynamics of axially functionally graded (AFG) conical pipes conveying fluid are analyzed. The materials are distributed along the conical pipe axis as a volume fraction function. Either the elastic modulus or the density of the AFG conical pipe is assumed to vary from the inlet to the outlet. The governing equation of the AFG conical pipe is derived using the Hamiltonian principle and solved by the differential quadrature method. The effects of the volume fraction index, volume fraction function type and reduction factor on the natural frequency and critical velocity are analyzed. It is found that for a power function volume fraction type, the natural frequency and critical velocity increase with increasing volume fraction index and clearly increase when the volume fraction index is within the range (0, 10). For an exponential function volume fraction type, the natural frequency and critical velocity change rapidly within the range (−10, 10), besides the above range the relationship between the natural frequency, critical velocity and volume fraction index is approximate of little change. The natural frequency and critical velocity decrease linearly with increasing reduction factor.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

scholarly journals Dynamic analysis of a parametrically excited golden Muga silk embedded pneumatic artificial muscle

2018 ◽  
Vol 211 ◽  
pp. 02008 ◽  
Author(s):  
Bhaben Kalita ◽  
S. K. Dwivedy
Keyword(s):  
Dynamic Analysis ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Quadratic Function ◽  
Artificial Muscle ◽  
Equation Of Motion ◽  
Time Response ◽  
Phase Portraits ◽  
Pneumatic Artificial Muscle ◽  
Pneumatic Muscle

In this work a novel pneumatic artificial muscle is fabricated using golden muga silk and silicon rubber. It is assumed that the muscle force is a quadratic function of pressure. Here a single degree of freedom system is considered where a mass is supported by a spring-damper-and pneumatically actuated muscle. While the spring-mass damper is a passive system, the addition of pneumatic muscle makes the system active. The dynamic analysis of this system is carried out by developing the equation of motion which contains multi-frequency excitations with both forced and parametric excitations. Using method of multiple scales the reduced equations are developed for simple and principal parametric resonance conditions. The time response obtained using method of multiple scales have been compared with those obtained by solving the original equation of motion numerically. Using both time response and phase portraits, variation of few systems parameters have been carried out. This work may find application in developing wearable device and robotic device for rehabilitation purpose.

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