Engineering Transactions, 44, 2, pp. 169-180, 1996

Dynamic Instability of Plates Made of Nonlinear Viscoelastic Materials

G. Cederbaum
Ben-Gurion University of The Negev, Beer-Sheva
Israel

D. Touati
Ben-Gurion University of The Negev, Beer-Sheva
Israel

The dynamic stability analysis of isotropic plates made of a nonlinear viscoelastic material is performed within the concept of the Lyapunov exponents. The material behaviour is modelled according to the Leaderman representation of nonlinear viscoelasticity. The influence of the various parameters involved on the possibility of instability to occur is investigated. lt is also shown that in some cases the system is chaotic.

Full Text: PDF

References

V.V. BOLOTIN, The dynamic stability of elastic systems, Holden Day, San Francisco 1964.

R.M. EVAN-IWANOWSKI, On the parametric response of structures, Appl. Mech. Rev., 18, 699-702, 1965.

R.M. EVAN-IWANOWSKI, Resonant oscillations in mechanical systems, Elsevier, Amsterdam 1976.

V.I. MATYASH, Dynamic stability of hinged viscoelastic bar, Mech. Poly., 2, 293-300, 1964.

K.K. STEVENS, On the parametric excitation of a viscoelastic column, AIAA J., 12, 2111-2116, 1966.

W. SZYSKOWSKI and P.G. GLUCKNER, The stability of viscoelastic perfect columns. A dynamic approach, Int. J. Sol. Struct., 6, 545-559, 1985.

P.G. GLUCKNER and W. SZYSKOWSKI, On the stability of column made of time dependent materials, Encyc. Civ. Engng. Prac. Technomic., 23, 1, 577-626, 1987.

J. ABOUDI, G. CEDERBAUM and I. ELISHAKOFF, Stability of viscoelastic plates by Lyapunov exponents, J. Sound Vib., 139, 459-468, 1990.

G. CEDERBAUM, J. ABOUDI and I. ELISHAKOFF, Dynamic stability of viscoelastic composite plates via the Lyapunov exponents, Int. Solid Struct., 28, 317-327, 1991.

J. SMART and J.G. WILLIAMS, A comparison of single integral nonlinear viscoelasticity theories, J. Mech. Phys. Sol., 20, 313-324, 1972.

H. LEADERMAN, Large longitudinal retarded elastic deformation of rubberlike net­work polymers, Trans. Soc. Rheol., 6, 361-382, 1962.

R.A. SCHAPERY, On the characterizaion of nonlinear viscoelastic materials, Pol. Engng. Sci., 9, 295, 1969.

B. BERNSTEIN, E.A. KEARSLEY and L.J. ZAPAS, A study of stress relaxation with finite strain, Trans. Soc. Rheol., 2, 391-410, 1963.

L.J. ZAPAS and T. CRAFT, Correlation of large longitudinal deflections with different strain histories, J. Res. Nat. Bur. Stan. Phy. Chem., 69A, 6, 541-546, 1965.

N.G. CHETAEV, Stability of motion, Program Press, Oxford 1961.

S. TIMOSHENKO, Theory of elastic stability, Me Graw-Hill, New York 1963.

A.H. NAYFEH and D.T. MOOK, Nonlinear oscillations, John Wiley and Sons, New York 1979.

W. HAHN, Stability of motion, Springer-Verlag, Berlin 1967.

N.G. CHETAEV, On certain questions related to the problem of stability of unsteady motion, Prikl. Matem. Mekh., 24, 1, 5-22, 1960.

I. GOLDHIRSCH, P.L. SULEM and S.A. ORSZAG, Stability and Lyapunov stability of dynamical systems. Differenial approach and numerical method, Physica., 27D, 311-337, 1987.

Matlab for Unix computers, Math. Works Inc., USA 1991.

N.W. MC LACHLAN, Theory and application of Mathieu functions, Dover, New York 1964.

G. CEDERBAUM and M. MOND, Stability properties of a viscoelastic column under a periodic force, J. Appl. Mech., 59, ,16-19, 1992.

G. CEDERBAUM, Parametric excitation of viscoelastic plates, Struct. Mech., 20, 1, 37-51, 1992.

F.C. MOON, Chaotic vibrations, Wiley, New York 1987.

A. WOLF, J.B. SWIFT, H.L. SWINNEY and J.A. VASTANO, Determining Lyapunov exponents from a time series, Physica., 16D, 285-317, 1985.




Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland