Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Divergence instability of multiple-parameter circulatory systems

Authors: K. Huseyin and H. H. E. Leipholz
Journal: Quart. Appl. Math. 31 (1973), 185-197
MSC: Primary 70.34
DOI: https://doi.org/10.1090/qam/436698
MathSciNet review: 436698
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The free vibrations and stability of a discrete linear non-dissipative system subjected to the combined effect of several independent circulatory and conservative loads are studied. Attention is restricted to systems which exhibit only divergence-type instability and are incapable of flutter. Two theorems concerning the basic properties of the characteristic surfaces (loading-frequency relationship) and the stability boundary are established. One of the several other theorems insures that the stability boundary of the corresponding conservative system will always provide a lower bound for the actual stability boundary of the non-conservative system. This particular result is valid for all types of divergence-instability problems, including those which can exhibit flutter after divergence. The theorems established are quite general in the sense that they are valid for all systems in the class considered, without further analytical conditions. Practical implications of the general results are briefly discussed.

References [Enhancements On Off] (What's this?)

  • [1] K. Huseyin and J. Roorda, The loading-frequency relationship in multiple eigenvalue problems, Trans. ASME Ser. E J. Appl. Mech. 38 (1971), 1007–1011. MR 0292352
  • [2] H. H. E. Leipholz, Stability theory, Academic Press, Inc., New York and London, 1970
  • [3] H. Ziegler, Principles of structural stability, Blaisdell Publishing Co., Waltham, Mass., 1968
  • [4] V. V. Bolotin, Nonconservative problems of the theory of elastic stability, Moscow, 1961
  • [5] G. Herrmann and R. W. Bungay, On the stability of elastic systems subjected to nonconservative forces, Trans. ASME Ser. E. J. Appl. Mech. 31 (1964), 435–440. MR 0166978
  • [6] H. H. E. Leipholz, Uber ein Kriterium für die Gültigheit der Statischen Methode zur Bestimmung der Knicklast von elastischen Stäben unter nichtkonservativer Belastung, Ing. Arc. 32, S. 286-296 (1963)
  • [7] K. Huseyin, The elastic stability of structural systems with independent loading parameters, Int. J. Solids Struct. 6, 677-691 (1970)
  • [8] K. Huseyin, The convexity of the stability boundary of symmetric systems, Acta Mech. 8, 205-221 (1969)
  • [9] Koncay Huseyin, The stability boundary of systems with one degree of freedom. I, II, Meccanica—J. Italian Assoc. Theoret. Appl. Mech. 5 (1970), 306–311; ibid. 5 (1970), 312–316 (English, with Italian summary). MR 0323211
  • [10] H. H. E. Leipholz and K. Huseyin, On the stability of one-dimensional continuous systems with polygenic forces, Meccanica VI, 4, 253-257 (1971)
  • [11] S. N. Prasad and G. Herrmann, Some theorems on stability of discrete circulatory systems, Acta Mech. 6 (1968), 208–216 (English, with German summary). MR 0239865, https://doi.org/10.1007/BF01170385
  • [12] H. H. E. Leipholz, Application of Liapunov's direct method to the stability problem of rods subjected to follower forces, SMD Report No. 26, December 1969
  • [13] Olga Taussky, Positive-definite matrices and their role in the study of the characteristic roots of general matrices, Advances in Math. 2 (1968), 175–186. MR 0227200, https://doi.org/10.1016/0001-8708(68)90020-0
  • [14] R. Zurmühl, Matrices, Springer, Berlin, 1958
  • [15] K. Huseyin, Instability of symmetric structural systems with independent loading parameters, Quart. Appl. Math. 28, 571-586 (1970)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 70.34

Retrieve articles in all journals with MSC: 70.34

Additional Information

DOI: https://doi.org/10.1090/qam/436698
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society