Effect of Bi- Parabolic Thermal and Thickness Variation on Vibration of Visco- Elastic Orthotropic Rectangular Plate

Authors

  • Ashish Kumar Sharma Dept. of Mathematics, Pacific University, Udaipur, Raj., India
  • Subodh Kumar Sharma Govt. P.G College, Ambala Cantt., Haryana, India

Keywords:

visco-elastic, thickness, frequency, vibration, taper parameter, aspect ratio

Abstract

As a result of the technological developments in civil, mechanical and aeronautical engineering, visco-elastic plate structures gained popularity in the 20th century. The mainstream of visco- elastic materials are receptive to heat in space technology, highly speed space flights, internal combustion engines, satellites, certain parts of mechanical structures have to man oeuvre under elevated temperatures consequently the state of affairs are thermal sensitive. It is observed that thermal effects are recurrently overlooked in most of the cases so far they have to be taken in to concern. In this paper effect of bi-parabolically variation in temperature is premeditated on vibration of an orthotropic rectangular plate:

 and whose thickness also varies bi-parabolically as:

Frequency equation is derived by using Rayleigh–Ritz technique with a two-term deflection function. Time period, Deflection and Logarithmic decrement at different points for the first two modes of vibration are calculated for various values of thermal gradients, aspect ratio and taper constants.

References

[1] Leissa A.W. (1969). Vibration of plates: NASA SP-160: U.S. Govt. Printing office.
[2] Sharma Subodh Kumar and. Sharma Ashish Kr, (2014). Mechanical Vibration of Orthotropic Rectangular Plate with 2D Linearly Varying Thickness and Thermal Effect. International Journal of Research in Advent Technology, 2(6), pp. 184-190.
[3] Gupta A.K. and Khanna A., (2007). Vibration of visco-elastic rectangular plate with linearly thickness variation in both directions. J. Sound and Vibration, 301, pp.450-457.
[4] Vijaya Kumar, K., (1974). Natural frequencies of rectangular orthotropic plates with a pair of parallel edges simply supported, J. Sound and Vibration, 35 (3), 379-394.
[5] Leissa, A. W., (1977). Recent research in plate vibrations: Classical Theory. Shock and Vibration Digest, 9 (10), 13-24.
[6] Sobotka, Z. , (1978). Free vibration of visco-elastic orthotropic rectangular plates. Acta Technica, CSAV, 23 (6), 678-705
[7] Jain R.K., Soni S.R., (1973). Free vibrations of rectangular plates of parabolically varying thickness. Indian J. Pure App. Math., 4, 267-277.
[8] Young D., (1950). Vibration of rectangular plates by the Ritz method. J. App. Mech., Trans. ASME, 17, 448-453.

Published

2019-01-11