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Stability Analysis of a Nonlinear Viscoelastic Column
Author(s) -
Distéfano J. N.,
Sackman J. L.
Publication year - 1967
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19670470602
Subject(s) - viscoelasticity , nonlinear system , column (typography) , mathematics , stability (learning theory) , deflection (physics) , gravitational singularity , mathematical analysis , materials science , geometry , physics , classical mechanics , composite material , computer science , connection (principal bundle) , quantum mechanics , machine learning
A Volterra‐Fréchet functional expansion is used to represent the stress‐strain relation of a general nonlinear viscoelastic material. Application is made to the investigation of the stability of a centrally loaded nonlinear viscoelastic column. By investigating the singularities of the integral equation governing the deflection of the column subjected to a small perturbation, general conditions for instantaneous stability are derived. Asymptotic stability of the column is also investigated, and by the use of a general Tauberian theorem, conditions which ensure long time stability of the column are obtained.