Lyapunov Stability of a Class of Operator Integro-differential Equations with Applications to Viscoelasticity
Article first published online: 4 DEC 1998
Copyright © 1996 B.G. Teubner Stuttgart—John Wiley & Sons, Ltd.
Mathematical Methods in the Applied Sciences
Volume 19, Issue 5, pages 341–361, 25 March 1996
How to Cite
Drozdov, A. (1996), Lyapunov Stability of a Class of Operator Integro-differential Equations with Applications to Viscoelasticity. Math. Meth. Appl. Sci., 19: 341–361. doi: 10.1002/(SICI)1099-1476(19960325)19:5<341::AID-MMA775>3.0.CO;2-M
- Issue published online: 4 DEC 1998
- Article first published online: 4 DEC 1998
- Manuscript Received: 25 NOV 1993
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.