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

Subject Areas : Engineering

A Khanna ¹ , R Deep ² , D Kumar ³

1 - Department of Mathematics, DAV College Sadhaura, Yamuna Nagar, Haryana
2 - Department of Mathematics, Maharishi Markandeshwar University- Mullana
3 - Department of Mathematics, Maharishi Markandeshwar University- Mullana

Received: 2015-08-01 Accepted : 2015-10-09 Published : 2015-12-30

Keywords: Vibration, frequency, Thermal gradient, Taper constant, Non-homogeneity constant,

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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