Rheological Response and Validity of Viscoelastic Model Through Propagation of Harmonic Wave in Non-Homogeneous Viscoelastic Rods

Subject Areas : Engineering

R Kakar ¹ (Principal, DIPS Polytechnic College, Hoshiarpur)
K Kaur ² (Faculty of Applied Sciences, BMSCE, Muktsar-152026, India)

Received: 2013-03-04 Accepted : 2013-04-27 Published : 2013-06-30

Keywords:

References:

[1] Alfrey T., 1944, Non-homogeneous stress in viscoelastic media, Quarterly of Applied Mathematics 2: 113-119.

[2] Barberan J., Herrera J., 1966, Uniqueness theorems and speed of propagation of signals in viscoelastic materials, Archive for Rational Mechanics and Analysis 23(3): 173-190.

[3] Achenbach J.D., Reddy D. P., 1967, Note on the wave-propagation in linear viscoelastic media, Zeitschrift für angewandte Mathematik und Physik (ZAMP), 18(1):141-144.

[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 36: 908-909.

[7] Biot M.A., 1940, Influence of initial stress on elastic waves, Journal of Applied Physics 11(8):522-530.

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

[9] White J.E., Tongtaow C., 1981, Cylindrical waves in transversely isotropic media, The Journal of the Acoustical Society of America 70(4):1147-1155.

[10] Mirsky I., 1965, Wave propagation in transversely isotropic circular cylinders, part I: Theory, Part II: Numerical results, The Journal of the Acoustical Society of America 37:1016-1026.

[11] Tsai Y.M., 1991, Longitudinal motion of a thick transversely isotropic hollow cylinder, Journal of Pressure Vessel Technology 113:585-589.

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

[13] 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, Grenoble, Berlin 273 – 303.

[14] Gurdarshan S., Avtar S., 1980, Propagation, reflection and transmission of longitudinal waves in non-homogeneous five parameter viscoelastic rods, Indian Journal of Pure and Applied Mathematics 11(9): 1249-1257.

[15] Kakar R., Kaur K., Gupta K.C., 2012, Analysis of five-parameter viscoelastic model under dynamic loading, Journal of Solid Mechanics 4(4): 426-440.

[16] Kaur K., Kakar R., Gupta K.C., 2012, A dynamic non-linear viscoelastic model, International Journal of Engineering Science and Technology 4(12): 4780-4787.

[17] Kakar R., Kaur K., 2013, Mathematical analysis of five parameter model on the propagation of cylindrical shear waves in non-homogeneous viscoelastic media, International Journal of Physical and Mathematical Sciences 4(1): 45-52.

[18] Kaur K., Kakar R., Kakar S., Gupta K.C., 2013, Applicability of four parameter viscoelastic model for longitudinal wave propagation in non-homogeneous rods, International Journal of Engineering Science and Technology 5(1): 75-90.

[19] Friedlander F.G., 1947, Simple progressive solutions of the wave equation, Mathematical Proceedings of the Cambridge Philosophical Society 43: 360-73.

[20] Karl F. C., Keller J. B., 1959, Elastic waves propagation in homogeneous and inhomogeneous media, Journal of Acoustical Society America 31: 694-705.

[21] Moodie T.B., 1973, On the propagation, reflection and transmission of transient cylindrical shear waves in non-homogeneous four-parameter viscoelastic media, Bulletin of the Australian Mathematical Society 8: 397-411.

[22] Carslaw H. S., Jaeger, J. C., 1963, Operational Methods in Applied Math, Second Ed., Dover Pub, New York.

[23] Bland D. R., 1960, Theory of Linear Viscoelasticity, Pergamon Press, Oxford.

[24] Christensen R. M., 1971, Theory of Viscoelasticity, Academic Press.