Hostname: page-component-6d856f89d9-gndc8 Total loading time: 0 Render date: 2024-07-16T07:27:32.100Z Has data issue: false hasContentIssue false

Stability of rotating compressed rod with imperfections

Published online by Cambridge University Press:  24 October 2008

T. M. Atanacković
Affiliation:
University of Novi Sad, Yugoslavia

Abstract

The stability of a rotating compressed rod is studied as a two-parameter bifurcation problem. Imperfections in shape and loading are assumed to be present. A number of solutions and their local behaviour is analysed.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Antman, S. S. and Nachman, A.. Large buckled states of rotating rods. Nonlinear Anal. 4 (1980), 303327.CrossRefGoogle Scholar
[2]Atanacković, T. M.. Estimates of maximum deflection for a rotating rods. Quart. J. Mech. Appl. Math. 37 (1984), 515523.CrossRefGoogle Scholar
[3]Atanacković, T. M.. Buckling of rotating compressed rods. Acta Mech. 60 (1986), 4966.Google Scholar
[4]Bazley, N. and Zwahlen, B.. Remarks on the bifurcation of solutions of a nonlinear eigenvalue problem. Arch. Rational Mech. Anal. 28 (1968), 5158.Google Scholar
[5]Chillingworth, D.. Universal bifurcation problems. In Mechanics of Solids: The Rodney Hill 60th Anniversary Volume (Pergamon Press, 1982). pp. 101133.CrossRefGoogle Scholar
[6]Chow, S.-N. and Hale, J. K.. Methods of Bifurcation Theory (Springer-Verlag, 1982).Google Scholar
[7]Golubitsky, M. and Schaeffer, D.. A theory for imperfect bifurcation via singularity theory. Commun. Pure Appl. Math. 32 (1979), 2198.Google Scholar
[8]Iooss, G. and Joseph, D. D.. Elementary Stability and Bifurcation Theory (Springer-Verlag, 1980).Google Scholar
[9]Mitrinović, D. S.. Analytic Inequalities (Springer-Verlag, 1970).CrossRefGoogle Scholar
[10]Odeh, F. and Tadjbakhsh, I.. A nonlinear eigenvalue problem for rotating rods. Arch. Rational Mech. Anal. 20 (1965), 8194.CrossRefGoogle Scholar
[11]Parter, S. V.. Nonlinear eigenvalue problems for some fourth order equations. I. Maximal solutions. SIAM J. Math. Anal. 1 (1970), 437457.Google Scholar
[12]Parter, S. V.. Nonlinear eigenvalue problems for some fourth order equations. II. Fixed point methods. SIAM J. Math. Anal. 1 (1970), 458478.Google Scholar
[13]Poston, T. and Stewart, I.. Catastrophe Theory and its Applications (Pitman, 1978).Google Scholar
[14]Subrahanyam, M. B.. On application of control theory to integral inequalities. J. Math. Anal. Appl. 77 (1980), 4759.CrossRefGoogle Scholar
[15]Troesch, B. A.. Integral inequalities for two functions. Arch. Rational Mech. Anal. 24 (1967), 128140.CrossRefGoogle Scholar
[16]Troger, H.. Applications of bifurcation theory to the solution of nonlinear stability problems in mechanical engineering. In Numerical Methods for Bifurcation Problems, Proc. Conf. Univ. Dortmund (Birkhäuser-Verlag, 1984).Google Scholar
[17]Wang, C.-Y.. On the bifurcation solutions of an axially rotating rod. Quart. J. Mech. Appl. Math. 35 (1982), 391402.Google Scholar
[18]Wang, C.-Y.. Rotation of a free elastic rod. J. Appl. Mech. 49 (1982), 225227.CrossRefGoogle Scholar