STEADY-STATE RESPONSE OF PIPES CONVEYING PULSATING FLUID NEAR A 2:1 INTERNAL RESONANCE IN THE SUPERCRITICAL REGIME

The work investigates steady-state responses of a pipe conveying fluid with a harmonic component of flow speed superposed on a constant mean value in the supercritical regime. If the flow speed exceeds a critical value, the straight configuration of the pipe becomes unstable and bifurcates into two stable curved configurations. The transverse motion measured from each of the curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation. The Galerkin method is employed to discretize the governing equation into a set of coupled nonlinear ordinary differential equations with gyroscopic terms. For the pipes in the supercritical regime, the method of multiple scales is used to determine the steady-state in the vicinity of two-to-one resonance. In the presence of the internal resonance, the subharmonic, the superharmonic and the summation, and the difference resonances exist due to the pulsating fluid. The amplitude–frequency relationships are established with the emphasis on the effects of the viscosity, the pulsating amplitude, the nonlinearity, and the mean flow speed. Some nonlinear phenomena such as the appearance of the peak or jumps pertaining to modal interaction are demonstrated. The numerical integration results are in agreement with the analytical predictions.

[1]  Michael P. Païdoussis,et al.  Dynamic Stability of Periodic Pipes Conveying Fluid , 2014 .

[2]  Li-Qun Chen,et al.  External and internal resonances of the pipe conveying fluid in the supercritical regime , 2013 .

[3]  B. Gültekin Sınır,et al.  Pseudo-nonlinear dynamic analysis of buckled pipes , 2013 .

[4]  H. Sheng,et al.  EXACT EIGEN-RELATIONS OF CLAMPED-CLAMPED AND SIMPLY SUPPORTED PIPES CONVEYING FLUIDS , 2012 .

[5]  Liqun Chen,et al.  Internal resonance of pipes conveying fluid in the supercritical regime , 2012 .

[6]  Raouf A. Ibrahim,et al.  Mechanics of Pipes Conveying Fluids—Part II: Applications and Fluidelastic Problems , 2011 .

[7]  Raouf A. Ibrahim,et al.  Overview of Mechanics of Pipes Conveying Fluids—Part I: Fundamental Studies , 2010 .

[8]  M. P. Païdoussis,et al.  Nonlinear dynamics of extensible fluid-conveying pipes, supported at both ends , 2009 .

[9]  R. C. Kar,et al.  Nonlinear dynamics of a pipe conveying pulsating fluid with combination, principal parametric and internal resonances , 2008 .

[10]  R. C. Kar,et al.  Nonlinear dynamics of a pipe conveying pulsating fluid with parametric and internal resonances , 2007 .

[11]  Raymond H. Plaut,et al.  Postbuckling and vibration of end-supported elastica pipes conveying fluid and columns under follower loads , 2006 .

[12]  M. Rajković,et al.  Bifurcations in nonlinear models of fluid-conveying pipes supported at both ends , 2005, nlin/0509056.

[13]  N. Namachchivaya,et al.  Pipes conveying pulsating fluid near a 0:1 resonance: Local bifurcations , 2005 .

[14]  J. Jin,et al.  Parametric resonances of supported pipes conveying pulsating fluid , 2005 .

[15]  Ioannis K. Chatjigeorgiou,et al.  Nonlinear resonances of parametrically excited risers-numerical and analytic investigation for Ω=2ω 1 , 2005 .

[16]  Zsolt Szabó,et al.  Nonlinear Analysis of a Cantilever Pipe Containing Pulsatile Flow , 2003 .

[17]  Ali H. Nayfeh,et al.  Nonlinear Interactions: Analytical, Computational, and Experimental Methods , 2000 .

[18]  M. P. Païdoussis,et al.  NONLINEAR ANALYSIS OF THE PARAMETRIC RESONANCES OF A PLANAR FLUID-CONVEYING CANTILEVERED PIPE , 1996 .

[19]  J. Wickert.  Non-linear vibration of a traveling tensioned beam , 1992 .

[20]  Ali H. Nayfeh,et al.  Modal Interactions in Dynamical and Structural Systems , 1989 .

[21]  W. M. Liu,et al.  Efficient Numerical Analysis for Dynamic Stability of Pipes Conveying Fluids , 1989 .

[22]  Masatsugu Yoshizawa,et al.  Lateral vibration of a flexible pipe conveying fluid with pulsating flow , 1986 .

[23]  P. J. Holmes,et al.  Bifurcations to divergence and flutter in flow-induced oscillations: A finite dimensional analysis , 1977 .

[24]  M. P. Païdoussis,et al.  Experiments on Parametric Resonance of Pipes Containing Pulsatile Flow , 1976 .

[25]  M. Païdoussis,et al.  Dynamic stability of pipes conveying fluid , 1974 .