Effect of Thermal Gradient on Vibration of Non-Homogeneous Square Plate with Exponentially Varying Thickness

Authors

  • A Khanna Department of Mathematics, DAV College Sadhaura, Yamuna Nagar, Haryana
  • D Kumar Department of Mathematics, Maharishi Markandeshwar University- Mullana
  • R Deep Department of Mathematics, Maharishi Markandeshwar University- Mullana
Abstract:

Vibrations of plate and plate type structures made up of composite materials have a significant role in various industrial mechanical structures, aerospace industries and other engineering applications. The main aim of the present paper is to study the two dimensional thermal effect on the vibration of non-homogeneous square plate of variable thickness having clamped boundary. It is assumed that temperature varies bi-parabolic i.e. parabolic in x-direction & parabolic in y-direction and thickness is considered to vary exponentially in x direction. Also, density is taken as the function of “x” due to non-homogeneity present in the plate’s material.  Rayleigh Ritz technique is used to calculate the natural frequency for both the modes of vibration for the various values of taper parameter, non-homogeneity constant and thermal gradient. All the calculations are carried out for an alloy of Aluminum, Duralumin, by using mathematica.

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Journal title

volume 7  issue 4

pages  477- 484

publication date 2015-12-30

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