zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method. (English) Zbl 1201.76199
Summary: In the present paper the natural frequencies of fluid-conveying pipes with pinned-pinned boundary condition are derived explicitly in a systematical and straightforward way with the help of homotopy perturbation method. Numerical results are presented for two cases and the effect of fluid flow velocity on the natural frequencies is discussed. Good agreement with their experimental and FEM counterparts is found numerically over ranges of practical interest.
MSC:
76M25Other numerical methods (fluid mechanics)
65L99Numerical methods for ODE
References:
[1]Païdoussis, M. P.: Fluid-structure interactions: slender structures and axial flow, (1998)
[2]Blevins, R. D.: Flow-induced vibration, (1977)
[3]Housner, G. W.: Bending vibrations of a pipe line containing flowing fluid, Journal of applied mechanics 19, 205-208 (1952)
[4]He, J. H.: Homotopy perturbation technique, Computer methods in applied mechanics and engineering 178, 257-262 (1999)
[5]He, J. H.: The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied mathematics and computation 151, 287-292 (2004) · Zbl 1039.65052 · doi:10.1016/S0096-3003(03)00341-2
[6]He, J. H.: Application of homotopy perturbation method to nonlinear wave equations, Chaos, solitions and fractals 26, 695-700 (2005) · Zbl 1072.35502 · doi:10.1016/j.chaos.2005.03.006
[7]He, J. H.: Homotopy perturbation method for solving boundary value problems, Physics letters A 350, 87-88 (2006) · Zbl 1195.65207 · doi:10.1016/j.physleta.2005.10.005
[8]Biazar, J.; Eslami, M.; Ghazvini, H.: Homotopy perturbation method for systems of partial differential equations, International journal of nonlinear science and numerical simulations 8, No. 3, 411-416 (2007)
[9]Biazar, J.; Ghazvini, H.: Homotopy perturbation method for solving hyperbolic partial differential equations, Computers and mathematics with applications 56, 453-458 (2008) · Zbl 1155.65395 · doi:10.1016/j.camwa.2007.10.032
[10]Biazar, J.; Ghazvini, H.: Exact solutions for systems of Volterra integral equations of the first kind by homotopy perturbation method, Applied mathematical sciences 2, 2691-2697 (2008) · Zbl 1188.65170 · doi:http://www.m-hikari.com/ams/ams-password-2008/ams-password53-56-2008/index.html
[11]Sadighi, A.; Ganji, D. D.: Exact solutions of Laplace equation by homotopy-perturbation and Adomian decomposition methods, Physics letters A 367, 83-87 (2007) · Zbl 1209.65136 · doi:10.1016/j.physleta.2007.02.082
[12]Gregory, R. W.; Païdoussis, M. P.: Unstable oscillation of tubular cantilevers conveying fluid–I, Proceedings of the royal society of London A 293, 512-527 (1966) · Zbl 0151.39201 · doi:10.1098/rspa.1966.0187
[13]Nayfeh, A. H.: Perturbation methods, (1973) · Zbl 0265.35002
[14]H.L. Dodds, H. Runyan, Effect of high-velocity fluid flow in the bending vibrations and static divergence of a simply supported pipe, NASA Technical Note D-2870, 1965.
[15]Lees, A. W.: A perturbation approach to analyze the vibration of structures conveying fluids, Journal of sound and vibration 222, 621-634 (1999)
[16]Yang, X. H.; Guo, H. Y.; Lou, M.: Allowable span length of submarine pipeline considering damping, The ocean engineering 23, 1-5 (2005)