An analysis is conducted of the free vibration response characteristics of a single-degree-of-freedom (SDOF) elasto-hereditary (viscoelastic) system. The viscoelasticity is characterized by a relaxation kernel consisting of one exponential term. For this problem analytical results are presented that define the regions of oscillatory and nonoscillatory response. A possible application of the described technique to multi-degree-of-freedom diagonalizable viscoelastic systems is shown.
Issue Section:
Research Papers
1.
Burton, T. A., 1985, Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, London.
2.
Carlni
A.
De Donato
O.
1992
, “Fundamental Solutions for Linear Viscoelastic Continua
,” Journal of Solids and Structures
, Vol. 29
, No. 23
, pp. 2989
–3009
.3.
Christensen, R. M., 1982, Theory of Viscoelasticity, Academic Press.
4.
Ferry, J. D., 1970, Viscoelastic Properties of Polymers, John Wiley and Sons, Inc.
5.
Flugge, W., 1967, Viscoelasticity, Blaisdell Publishing Company.
6.
Linz, P., 1985, Analytical and Numerical Methods for Volterra Equations, SIAM, Philadelphia.
7.
Korn, G. A., and Korn, T. M., 1968, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company.
8.
Muravyov
A.
1997
, “Analytical Solutions in the Time Domain for Vibration Problems of Discrete Viscoelastic Systems
,” Journal of Sound and Vibration
, Vol. 199
, No. 2
, pp. 337
–348
.9.
Muravyov
A.
Hutton
S. G.
1997
, “Closed-Form Solutions and the Eigenvalue Problem for Vibration of Discrete Viscoelastic Systems
,” Journal of Applied Mechanics
, Vol. 64
, No. 3
, 1997, pp. 684
–691
.10.
Rabotnov, Yu. N., 1969, Creep Problems in Structural Members, North-Holland Publishing Company, Amsterdam.
11.
Rabotnov, Yu. N., 1980, Elements of Hereditary Solid Mechamics, Mir Publishers, Moscow.
12.
Stepan, G., 1989, Retarded Dynamical Systems, Longman, Harlow.
This content is only available via PDF.
Copyright © 1998
by The American Society of Mechanical Engineers
You do not currently have access to this content.