Analysis of Five Parameter Viscoelastic Model Under Dynamic Loading

Subject Areas : Engineering

R Kakar ¹ , K Kaur ² , K.C Gupta ³

1 - Principal, DIPS Polytechnic College, Hoshiarpur
2 - Faculty of Science, BMSCTE, Muktsar
3 - Faculty of Science, BMSCTE, Muktsar

Received: 2012-12-02 Accepted : 2012-12-29 Published : 2012-12-30

Keywords: Shear waves, Viscoelastic media, Asymptotic method, dynamic loading,

Abstract :

The purpose of this paper is to analysis the viscoelastic models under dynamic loading.A five-parameter model is chosen for study exhibits elastic, viscous, and retarded elastic response to shearing stress. The viscoelastic specimen is chosen which closely approximates the actual behavior of a polymer. The module of elasticity and viscosity coefficients are assumed to be space dependent i.e. functions of in non-homogeneous case and stress-strain are harmonic functions of time The expression for relaxation time for five parameter viscoelastic model is obtained by using constitutive equation. The dispersion equation is obtained by using Ray techniques. The model is justified with the help of cyclic loading for maxima or minima.

References:

[1] Alfrey T., 1944, Non-homogeneous stress in viscoelastic media, Quarterly of Applied Mathematics 2:113.

[2] Barberan J., Herrera J., 1966, Uniqueness theorems and speed of propagation of signals in viscoelastic materials, Archive for Rational Mechanics and Analysis 23: 173.

[3] Achenbach J. D., Reddy D. P., 1967, Note on the wave-propagation in linear viscoelastic media, ZAMP 18: 141-143.

[4] Bhattacharya S., Sengupta P.R., 1978, Disturbances in a general viscoelastic medium due to impulsive forces on a spherical cavity, Gerlands Beitr Geophysik (Leipzig) 87(8):57–62.

[5] Acharya D. P., Roy, I., Biswas P. K., 2008, Vibration of an infinite inhomogeneous transversely isotropic viscoelastic medium with a cylindrical hole, Applied Mathematics and Mechanics 29(3):1-12.

[6] Bert C. W., Egle. D. M., 1969, Wave propagation in a finite length bar with variable area of cross-section, Journal of Applied Mechanics (ASME) 36: 908-909.

[7] Abd-Alla A. M., Ahmed S. M., 1996, Rayleigh waves in an orthotropic thermo-elastic medium under gravity field and initial stress, Earth Moon and Planets 75: 185-197.

[8] Batra R. C., 1998, Linear constitutive relations in isotropic finite elasticity, Journal of Elasticity 51: 243-245.

[9] Murayama S., Shibata T., 1961, Rheological properties of clays, 5th International Conference of Soil Mechanics and Foundation Engineering 1: 269-273.

[10] Schiffman R. L., Ladd C. C., Chen A. T. F., 1964, The secondary consolidation of clay, Rheology and Soil Mechanics, Proceedings of the International Union of Theoretical and Applied Mechanics Symposium 273 – 303.

[11] Anagnostopoulos S.A., 1988, Pounding of buildings in series during earthquakes, Earthquake Engineering & Structural Dynamics 16(3): 443-456.

[12] Jankowski R., Wilde K., Fujino Y., 1998, Pounding of superstructure segments in isolated elevated bridge during earthquakes, Earthquake Engineering & Structural Dynamics 27:487-502.

[13] Muthukumar S., Desroches R., 2006, A Hertz contact model with nonlinear damping for pounding simulation, Earthquake Engineering & Structural Dynamics 35: 811-828.

[14] Westermo B.D., 1989, The dynamics of interstructural connection to prevent pounding, Earthquake Engineering & Structural Dynamics 18: 687–699.

[15] Jankowski R., 2005, Non-linear viscoelastic modelling of earthquake-induced structural pounding, Earthquake Engineering & Structural Dynamics 34(6): 595-611.

[16] Lakes R.S., 1998, Viscoelastic solids, CRC Press, New York.