Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method

Abstract The application of transfer matrix method (TMM) to the vibration analysis of three-dimensional (3D) pipelines conveying fluid is performed in this paper. Based on the equations of motion, in which the steady combined force is essentially included, a 3D straight pipe element and a curved pipe element conveying fluid are formulated by introducing dynamic stiffness matrix in order to apply the TMM. The natural frequencies of simple pipe systems with straight or circular shape are calculated to demonstrate the validity of the proposed treatment. Using TMM, the natural frequencies, frequency response functions and instability of 3D-shaped pipeline systems are analyzed, representing some fresh results. It is shown that, in the application of TMM to the vibration analysis of curved or 3D pipelines conveying fluid, the steady combined force has to be included, otherwise the obtained results may be not reliable.

[1]  Lin Wang,et al.  Size-dependent vibration characteristics of fluid-conveying microtubes , 2010 .

[2]  Youn-sik Park,et al.  Vibration analysis of a 3-dimensional piping system conveying fluid by wave approach , 1996 .

[3]  J. R. Yeh,et al.  The mechanics of multiple transverse cracking in composite laminates , 1989 .

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

[5]  U. Lee,et al.  Stability and dynamic analysis of oil pipelines by using spectral element method , 2009 .

[6]  Usik Lee,et al.  Vibration analysis of one-dimensional structures using the spectral transfer matrix method , 2000 .

[7]  C. D. Mote,et al.  Dynamic Stability of Axially Moving Materals , 1972 .

[8]  Michael P. Païdoussis,et al.  Pipes Conveying Fluid: A Model Dynamical Problem , 1993 .

[9]  M. Anklin,et al.  Coriolis mass flowmeters: Overview of the current state of the art and latest research , 2006 .

[10]  S. S. Chen.  FLOW-INDUCED IN-PLANE INSTABILITIES OF CURVED PIPES. , 1972 .

[11]  Yongan Huang,et al.  A NEW MATRIX METHOD FOR SOLVING VIBRATION AND STABILITY OF CURVED PIPES CONVEYING FLUID , 2002 .

[12]  James L. Hill,et al.  The Effect of Initial Forces on the Hydroelastic Vibration and Stability of Planar Curved Tubes , 1974 .

[13]  W. C. Hurty,et al.  Probabilistic Description of the Response of Linear Structures to Random Inputs , 1970 .

[14]  Ni Qiao,et al.  Bifurcations and chaotic motions of a curved pipe conveying fluid with nonlinear constraints , 2006 .

[15]  C. W. S. To,et al.  Vibration of Piping Systems Containing a Moving Medium , 1985 .

[16]  U. Lee,et al.  Spectral element modelling and analysis of a pipeline conveying internal unsteady fluid , 2006 .

[17]  G. Steven Gipson,et al.  Instability of Internally Damped Curved Pipes , 1990 .

[18]  A. Mioduchowski,et al.  Vibration and instability of carbon nanotubes conveying fluid , 2005 .

[19]  C. D. Mote.  Dynamic stability of an axially moving band , 1968 .

[20]  Hong Hee Yoo,et al.  New fluid velocity expression in an extensible semi-circular pipe conveying fluid , 2007 .

[21]  Ni Qiao,et al.  Vibration and stability of an axially moving beam immersed in fluid , 2008 .

[22]  Myung Jin Choi,et al.  Transfer matrix modelling for the 3-dimensional vibration analysis of piping system containing fluid flow , 1996 .

[23]  Shoei‐sheng Chen,et al.  Out-of-Plane Vibration and Stability of Curved Tubes Conveying Fluid , 1973 .

[24]  Ni Qiao,et al.  In-plane vibration analyses of curved pipes conveying fluid using the generalized differential quadrature rule , 2008 .

[25]  Usik Lee,et al.  The spectral element model for pipelines conveying internal steady flow , 2003 .

[26]  Andre P. Mazzoleni,et al.  Dynamic stability of a semi-circular pipe conveying harmonically oscillating fluid , 2008 .

[27]  Jintai Chung,et al.  In-plane and out-of-plane motions of an extensible semi-circular pipe conveying fluid , 2008 .

[28]  Michael P. Païdoussis,et al.  Dynamics of microscale pipes containing internal fluid flow: Damping, frequency shift, and stability , 2010 .

[29]  T. E. Unny,et al.  Hydroelastic Instability of Uniformly Curved Pipe-Fluid Systems , 1970 .

[30]  Ni Qiao,et al.  Dynamical behaviors of a fluid-conveying curved pipe subjected to motion constraints and harmonic excitation , 2007 .

[31]  G. H. Koo,et al.  Dynamic characteristics of KALIMER IHTS hot leg piping system conveying hot liquid sodium , 2000 .

[32]  Huijie Shen,et al.  The vibrational properties of a periodic composite pipe in 3D space , 2009 .

[33]  C. Dupuis,et al.  Application of the transfer matrix method to non-conservative systems involving fluid flow in curved pipes , 1985 .

[34]  Shoei‐sheng Chen,et al.  Vibration and Stability of a Uniformly Curved Tube Conveying Fluid , 1972 .

[35]  M. Païdoussis.  The canonical problem of the fluid-conveying pipe and radiation of the knowledge gained to other dynamics problems across Applied Mechanics , 2008 .

[36]  M. Païdoussis.  Fluid-Structure Interactions: Slender Structures and Axial Flow , 2014 .

[37]  M. P. Païdoussis,et al.  On the dynamics of curved pipes transporting fluid. Part I: Inextensible theory , 1988 .

[38]  M. P. Paı¨doussis.  The canonical problem of the fluid-conveying pipe and radiation of the knowledge gained to other dynamics problems across Applied Mechanics , 2008 .

[39]  C. D. Mote,et al.  On the Dynamic Analysis of Curved and Twisted Cylinders Transporting Fluids , 1976 .

[40]  L. Wang,et al.  Application of the differential transformation method to vibration analysis of pipes conveying fluid , 2011, Appl. Math. Comput..