Free Vibration Analysis of Waves in a Microstretch Elastic Plate

Rajneesh  Kumar; Geeta Partap

doi:10.6180/jase.2010.13.3.01

Free Vibration Analysis of Waves in a Microstretch Elastic Plate

Rajneesh Kumar This email address is being protected from spambots. You need JavaScript enabled to view it.¹ and Geeta Partap²

¹Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India - 136 119
²Department of Mathematics, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, Punjab, India - 144011

Received: January 28, 2008
Accepted: March 12, 2010
Publication Date: September 1, 2010

Download Citation: ||https://doi.org/10.6180/jase.2010.13.3.01

ABSTRACT

The free vibration analysis of waves in a homogeneous isotropic microstretch elastic plate subjected to stress free conditions is investigated. The secular equations for homogeneous isotropic microstretch elastic plate for symmetric and skew-symmetric wave modes are derived. The mathematical model has been simplified by using the Helmholtz decomposition technique and the frequency equations for different mechanical situations are obtained and discussed. The special cases such as short wavelength and regions of secular equations are deduced and discussed. The dispersion curves for symmetric and skew-symmetric modes are computed numerically and presented graphically. Results of some earlier workers have been deduced as particular cases.

Keywords: Microstretch elastic plate, Secular equations, Phase velocity, Micropolar elastic plate

REFERENCES

[1] Eringen, A.C., “Micropolar elastic solids with stretch,” In Prof. Dr. Mustafa Inan Anisina, pp. 1- 18, Ari. Kitapevi Matbaassi, Istanbul (1971).
[2] Eringen, A.C., “Theory of thermo-microstretch,” Int. J. Engng. Sci., Vol. 28, pp. 1291 – 1301 (1990).
[3] Eringen, A.C., “Theory of thermo-microstretch fluids and bubbly liquids,” Int. J. Engng. Sci., Vol. 28, 133-143 (1990b).
[4] Liu,X., Hu,G., “Inclusion problem of microstretch continuum,” Int. J. Engng. Sci., Vol. 42, pp. pp. 849 – 860 (2004).
[5] Svanadze, M., “Fundamental solution of the system of equations of steady oscillations in the theory of microstretch elastic solids,” Int. J. Engng. Sci., Vol. 42, pp. 1897 – 1910 (2004).
[6] De Cicco, S., “Stress concentration effects in microstretch elastic solids,” Int. J. Engng. Sci., Vol.41, pp. 187 – 199 (2003).
[7] Kumar, R., Singh R., Chadha, T.K., “Axisymmetric problem in microstretch elastic solids,” Indian Journal of Mathematics, Vol.44, pp.147 – 164 (2002).
[8] Kumar, R., Singh R., Chadha, T.K., “Plane strain problem in microstretch elastic solid,” Sadhana, Vol. 28, pp. 975 – 990 (2003).
[9] Kumar, R., Partap, G., “Reflection of plane waves in a heat flux dependent microstretch thermoelastic solid half space,” Int. J. of Applied Mechanics and Engineering, Vol.10, pp. 253 – 266 (2005).
[10] Eringen, A.C., Microcontinuum Field Theories I: Foundations and Solids, Springer Verlag, New York (1999).
[11] R.Kumar and G. Partap, “Rayleigh Lamb waves in micropolar isotropic elastic plate,” Applied Mathematics and Mechanics, Vol. 27, pp. 1049 – 1059 (2006).
[12] Graff, K.F, Wave motion in Elastic Solids, Dover publications, Inc. New York (1991).
[13] Lamb, H. , “On waves in an elastic plate,” Phil. Trans.Roy. Soc., London, Ser. A, Vol. 93, pp. 114 – 128 (1917).