Summary
The stability of a uniform cantilever column supported by a Maxwell type viscoelastic foundation and subjected to a constant tangential force is investigated. Stability conditions are obtained for the entire range of system parameters through an application of Routh-Hurwitz criteria. Unlike the case of conservative loading, the Maxwell foundation is shown to produce a stabilizing effect on this nonconservative problem. Furthermore, an optimum combination of foundation parameters exist to yield the maximum flutter load. An approximate analysis is also presented through an application of the Galerkin's method. It is shown that a two-term approximation may not be adequate to yield meaning-ful results in a certain range of system parameters.
Similar content being viewed by others
References
Herrmann, G.: Stability of equilibrium of elastic systems subjected to nonconservative forces. Appl. Mech. Rev.20, 103–108 (1967).
Sundararajan, C.: The vibration and stability of elastic systems subjected to follower forces. Shock and Vibration Digest7 (89), 89–105 (1975).
Peterson, C.: Einige weitere Lösungen nichtkonservativer Knickprobleme. Stahlbau41, 198–203 (1972).
Smith, T. E., Herrmann, G.: Stability of a beam on an elastic foundation subjected to a follower force. J. Appl. Mech.39, 628–629 (1972).
Sundararajan, C.: Stability of columns on elastic foundations subjected to conservative and nonconservative forces. J. Sound and Vibration37, 79–85 (1974).
Hauger, W., Vetter, K.: Influence of an elastic foundation on the stability of a tangentially loaded column. J. Sound and Vibration47, 296–299 (1976).
Anderson, G. L.: The influence of a Wieghardt type elastic foundation on the stability of some beams subjected to distributed tangential forces. J. Sound and Vibration44, 103–118 (1976).
Wahed, I. F. A.: The instability of a cantilever on an elastic foundation under the influence of a follower force. J. Mech. Engng. Sci.17, 219–222 (1975).
Kar, R. C.: Stability of a nonuniform viscoelastic cantilever beam on a viscoelastic foundation under the influence of a follower force. SM Archives5 (4), 457–473 (1980).
Leipholz, H.: Stability Theory, p. 211. New York: Academic Press 1970.
Plaut, R. H., Infante, E. F.: The effect of external damping on the stability of Beck's column. Intl. Solids J. and Structures6, 491–496 (1970).
Morgan, M. R., Sinha, S. C.: Influence of a viscoelastic foundation on the stability of Beck's column: an exact analysis. J. Sound and Vibration, to appear.
Popov, E. P.: The dynamics of automatic control systems, p. 241. New York: Pergamon Press 1962.
Author information
Authors and Affiliations
Additional information
With 6 Figures
Rights and permissions
About this article
Cite this article
Sinha, S.C., Pawlowski, D.R. Stability analysis of a tangentially loaded column with a maxwell type viscoelastic foundation. Acta Mechanica 52, 41–50 (1984). https://doi.org/10.1007/BF01175963
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01175963