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Lyapunov Stability of a Class of Operator Integro‐differential Equations with Applications to Viscoelasticity
Author(s) -
Drozdov A.
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19960325)19:5<341::aid-mma775>3.0.co;2-m
Subject(s) - mathematics , lyapunov function , operator (biology) , flutter , mathematical analysis , viscoelasticity , stability (learning theory) , differential operator , differential equation , lyapunov stability , supersonic speed , nonlinear system , aerodynamics , mechanics , physics , biochemistry , chemistry , repressor , quantum mechanics , machine learning , computer science , transcription factor , gene , thermodynamics
The Lyapunov stability is analysed for a class of integro‐differential equations with unbounded operator coefficients. These equations arise in the study of non‐conservative stability problems for viscoelastic thin‐walled elements of structures. Some sufficient stability conditions are derived by using the direct Lyapunov method. These conditions are formulated for arbitrary kernels of the Volterra integral operator in terms of norms of the operator coefficients. Employing these conditions the supersonic flutter of a viscoelastic panel is studied and explicit expressions for the critical gas velocity are derived. Dependence of the critical flow velocity on the material characteristics and compressive load is analysed numerically.