On asymptotic stability of nonlinear hereditary phenomena
Authors:
J. N. Distéfano and J. L. Sackman
Journal:
Quart. Appl. Math. 24 (1966), 133-141
MSC:
Primary 73.41
DOI:
https://doi.org/10.1090/qam/202372
MathSciNet review:
202372
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Abstract: Conditions for long-term stability of nonlinear hereditary phenomena are derived from two Tauberian theorems. When the hereditary phenomena are time invariable (i.e., of the closed cycle type), then the asymptotic limits of the phenomena are evaluated. An application is made to the investigation of the stability of a rigid column restrained by a nonlinear viscoelastic element.
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- Raymond E. A. C. Paley and Norbert Wiener, Fourier transforms in the complex domain, American Mathematical Society Colloquium Publications, vol. 19, American Mathematical Society, Providence, RI, 1987. Reprint of the 1934 original. MR 1451142
- José Néstor Distéfano, Sulla stabilità in regime viscoelastico a comportamento lineare. I, II, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 27 (1959), 205–211, 356–361 (Italian). MR 116634
- J. N. Distéfano, Ancora sulla stabilità asintotica delle deflezioni di una trave viscoelastica, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 35 (1963), 504–508 (Italian). MR 167046
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V. Volterra and J. Pérès, Théorie Générale des Fonctionnelles, Gauthier-Villars, Paris, 1936
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V. Volterra, Leçons sur les Fonctions des Lignes, Gauthier-Villars, Paris, 1913
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H. R. Pitts, Tauberian Theorems, Oxford University Press, 1958
R. Paley and N. Wiener, Fourier Transforms in the Complex Domain, American Mathematical Society Colloquium Publications, 19 (1934) 59–63
J. N. Distefano, Sulla Stabilita in Regime Viscoelatica Comportamento Lineare, Rend. Acc. Naz. Lincei, fasc. 5, serie VIII, 27. (1959) and fasc. 6, serie VIII, 27 (1959)
J. N. Distefano, Ancora Sulla Stabilita Asintotica delle Deflezioni de una Trave Viscoelastica, Rend. Acc. Naz. Lincei, fasc. 6, serie VIII, 35 (1963)
V. Volterra, Theory of Functionals and of Integral and Integro-Differential Equations, Dover Pub., Inc., New York, 1959
V. Volterra and J. Pérès, Théorie Générale des Fonctionnelles, Gauthier-Villars, Paris, 1936
F. Tricomi, Integral Equations, Interscience, New York, 1957
V. Volterra, Leçons sur les Fonctions des Lignes, Gauthier-Villars, Paris, 1913
F. R. Shanley, Weight-Strength Analysis of Aircraft Structures, Second Ed., Dover Pub., Inc., New York, 1960
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Article copyright:
© Copyright 1966
American Mathematical Society
