Smart Search 



Title of the article

ALTERNATIVE VARIANT FOR THE EXPLICATION THE REASON FOR HARD EXCITATIONS OF OSCILLATIONS IN THE PROBLEM OF THE NONLINEAR PANEL FLUTTER

Authors

Kulikov A.N., Associate Professor of the State University n.a. P.G. Demidova, Yaroslavl, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

In the section  
Year 2013 Issue 4 Pages 51-56
Type of article RAR Index UDK 533.6013.42:42.534.1 Index BBK  
Abstract

A well know problem of oscillations for plate in ultrasonic gas flow in considered if the damping coefficient is sufficiently small. It is shown that the resonances 1:1, 1:2, 1:3 of proper frequencies lead to the appearance of unstable oscillations for those velocities of the flow for which the state of equilibrium remains stable. The investigation of the nonlinear value boundary problems does not use Galerkin’s method.

Keywords nonlinear panel flutter, value boundary problem, stability, resonances, hard excitation of oscillations, bifurcations
  You can access full text version of the article
Bibliography
  • Bolotin V.V. Nekonservativnye zadachi teorii uprugoj ustojchivosti [Nonconservative problems of the theory of elastic stability]. Moscow, Fizmatlit, 1961. 337 p.
  • Gukenhejmer Dzh., Holms F. Nelinejnye kolebanija dinamicheskih sistem i bifurkacii vektornyh polej [Nonlinear oscillations of dynamical systems and bifurcations of vector fields]. Minsk, Izhevsk, In-t komp'juternyh issled, 2002. 559 p.
  • Volmir A.S. Obolochki v potoke zhidkosti i gaza [Shells in liquid and fluid on-streams]. Moscow, Nauka, 1979. 320 p.
  • Kulikov A.N., Liberman B.D. O novom podhode k issledovaniju zadach nelinejnogo panel'nogo flattera [New approach to the study of problems of nonlinear panel flutter]. Vestn. Jarosl. un-ta [Journal of Yaroslavl University]. Jaroslavl, 1976, pp. 118-133.
  • Dowell E.H. Flutter of a buckled plate as an example of chaoticmotion of a deterministic autonomous system. J. Sound. - Vib., vol. 85, no. 3, pр. 333-344.
  • Bolotin V.V. [et al.]. Nonlinear panel flutter is renote post-critical domains. J. NonlinearMechanics, 1998, vol. 33, no. 5, pр. 753-764.
  • Kolesov V.S. [et al.]. Ob odnoj matematicheskoj zadache teorii uprugoj ustojchivosti [On a mathematical problem in the theory of elastic stability]. PMM [RMM], 1978, vol. 42, no. 3, pp. 458-465.
  • Kulikov A.N. Zhestkoe vozbuzhdenie kolebanij harakterno dlja flattera pri malom kojefficiente dempfirovanija [Hard excitation of oscillations typical for a flutter at low damping coefficient]. Izv. RAEN. Differ. Uravnenija [RANS news. Differential equations], 2006, vol. 29, no. 11, pp. 131-134.
  • Kulikov A.N. Bifurkacii avtokolebanij plastinki pri malom kojefficiente dempfirovanija v sverhzvukovom potoke gaza [Bifurcation of self-oscillations of the plate with a small damping ratio in a supersonic gas flow]. PMM [RMM], 2009, vol. 73, no. 2, pp. 271-281.
  • Kulikov A.N. Rezonans 1:3 – odna iz vozmozhnyh prichin nelinejnogo panel'nogo flattera [Resonance 1: 3 - one possible reason for the nonlinear panel flutter]. ZhVMiMF [ZhVMandMF], 2011, vol. 51, no. 7, pp. 1266-1279.
  • Kulikov A.N. Nelinejnyj panel'nyj flatter: opasnost' zhestkogo vozbuzhdenija kolebanij [Nonlinear panel flutter: danger of hard drive vibrations]. Izv. RAEN. Differ. Uravnenija [RANS news. Differential equations], 1992, vol. 28, no. 6, pp. 1080-1082.
  • Bekbulatova A.O., Kulikov A.N. Rezonans 1:2 kak istochnik zhestkogo vozbuzhdenija kolebanij [Resonance 1: 2 as the source of hard drive vibrations]. Sovr. problemy matemat. i informat. [Modern problems of mathematics and informatics], 2002, no. 5, pp. 22-27.
  • Kulikov A.N. Nelinejnyj panel'nyj flatter. Rezonans sobstvennyh chastot - odna iz vozmozhnyh prichin zhestkogo vozbuzhdenija kolebanij [Nonlinear panel flutter. The resonance of eigen frequency - one of the possible causes of hard drive vibrations]. Vestn. Nizhegorod. un-ta [Nizhny Novgorod University Gazette], 2011, vol. 4, pp. 193-194.
  • Kulikov A.N. Resonance of proper frequency 1:2 as a reason for hard excitation of oscillations of the plate ultrasonic gas. Trudy mezhdunarodnogo kongressa ENOC-2008 [Proceedings of the International Congress ENOC-2008]. Russia, Saint-Petersburg, 2008, pp. 1636-1643.
  • Babakov I.M. Teorija kolebanij [Theory of oscillations]. Moscow, Nauka, 1968. 559 p.
  • Nejmark M.A. Linejnye differencial'nye operatory [Linear differential operators]. Moscow, Nauka, 1969. 528 p.
  • Bahvalov N.S. Chislennye metody [Numerical methods]. Moscow, Nauka, 1973. 632 p.
  • Kulikov A.N. Bifurkacii malyh periodicheskih reshenij v sluchae blizkom k rezonansu 1:2 dlja odnogo klassa nelinejnyh jevoljucionnyh uravnenij [Bifurcation of small periodic solutions in the case of near-resonance 1:2 for a class of nonlinear evolution equations]. Dinamich. sistemy [Dynamical systems], 2012, vol. 2(30), no. 3-4, pp. 241-258.
  • Kulikov A.N. Rezonansnaja dinamika kak prichina zhestkogo vozbuzhdenija kolebanij v nekotoryh zadachah teorii uprugoj ustojchivosti [Resonance dynamics as the cause of hard excitation of oscillations in some problems of the theory of elastic stability]. Dinamich. sistemy [Dynamical systems], 2013, no. 1-2, pp. 49-68.
  • Bautin N.N., Leontovich E.A. Metody i priemy kachestvennogo issledovanija dinamicheskih sistem na ploskosti [Methods and techniques of the qualitative study of dynamical systems on the plane]. Moscow, Nauka, 1990. 488 p.