zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Application of a hybrid method to the nonlinear dynamic analysis of a flexible rotor supported by a spherical gas-lubricated bearing system. (English) Zbl 1180.76017
The author employs a hybrid numerical method combining the differential transformation method and the finite difference method to study the nonlinear dynamic behavior of a flexible rotor supported by a spherical gas-lubricated bearing system. The analytical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and quasi-periodic responses of the rotor center and the journal center. Furthermore, the results reveal the changes in the dynamic behavior of the bearing system as the rotor mass and bearing number are increased. The analytical results are found to be in good agreement with those from other numerical methods. Therefore, the proposed method provides effective means of gaining insights into the nonlinear dynamics of spherical gas-film rotor-bearing systems.

76D08Lubrication theory
70K43Quasi-periodic motions and invariant tori (nonlinear dynamics)
Full Text: DOI
[1] Gross, W. A.; Zachmanaglou, E. C.: Perturbation solutions for gas-lubricating films. ASME journal of basic engineering 83, 139-144 (1961)
[2] Castelli, V.; Elrod, H. G.: Solution of the stability problem for 360 degree self-acting, gas-lubricated bearing. ASME journal of basic engineering 87, 199-212 (1961)
[3] Holmes, A. G.; Ettles, C. M.; Mayes, I. W.: Aperiodic behavior of a rigid shaft in short journal bearings. International journal for numerical method in engineering 12, 695-702 (1978) · Zbl 0372.73053
[4] Sykes, J. E. H.; Holmes, R.: The effect of bearing misalignment on the non-linear vibration of aero-engine rotor--damper assemblies. Proceeding institution of mechanical engineers 204, 83-99 (1990)
[5] Kim, Y. B.; Noah, S. T.: Bifurcation analysis of a modified jeffcott rotor with bearing clearances. Nonlinear dynamics 1, 221-241 (1990)
[6] Zhao, J. Y.; Linnett, I. W.; Mclean, L. J.: Subharmonic and quasi-periodic motion of an eccentric squeeze film damper-mounted rigid rotor. ASME journal of vibration and acoustics 116, 357-363 (1994)
[7] Brown, R. D.; Addison, P.; Chan, A. H. C.: Chaos in the unbalance response of journal bearings. Nonlinear dynamics 5, 421-432 (1994)
[8] Adiletta, G.; Guido, A. R.; Rossi, C.: Chaotic motions of a rigid rotor in short journal bearings. Nonlinear dynamics 10, 251-269 (1996)
[9] Adiletta, G.; Guido, A. R.; Rossi, C.: Nonlinear dynamics of a rigid unbalanced rotor in short bearings. Part I: Theoretical analysis. Nonlinear dynamics 14, 57-87 (1997) · Zbl 0910.70008
[10] Adiletta, G.; Guido, A. R.; Rossi, C.: Nonlinear dynamics of a rigid unbalanced rotor in short bearings. Part II: Experimental analysis. Nonlinear dynamics 14, 157-189 (1997) · Zbl 0910.70008
[11] Sundararajan, P.; Noah, S. T.: Dynamics of forced nonlinear systems using shooting/arc-length continuation method -- application to rotor systems. ASME journal of vibration and acoustics 119, 9-20 (1997)
[12] Chen, C. L.; Yau, H. T.: Chaos in the imbalance response of a flexible rotor supported by oil film bearings with nonlinear suspension. Nonlinear dynamics 16, 71-90 (1998) · Zbl 0909.76019
[13] Wang, Cheng-Chi; Chen, Cha’o-Kuang: Bifurcation analysis of self-acting gas journal bearings. ASME journal of tribology 123, No. 4, 755-768 (2001)
[14] Wang, Cheng-Chi; Lo, Cheng-Ying; Chen, Cha’o-Kuang: Nonlinear dynamic analysis of a flexible rotor supported by externally pressurized porous gas journal bearings. ASME journal of tribology 124, 553-561 (2002)
[15] Chen, C. L.; Lin, S. H.; Chen, C. K.: Application of Taylor transformation to nonlinear predictive control problem. Applied mathematics modelling 20, No. September, 609-710 (1996) · Zbl 0860.93008
[16] Jang, M. J.; Chen, C. L.; Liu, Y. C.: Two-dimensional differential transform for partial differential equations. Applied mathematics and computation 121, 261-270 (2001) · Zbl 1024.65093