Analysis of Natural Vibration of Visco-Elastic Rectangulr Plate with Thickness and Temperature Variation

Visco- Elastic Plates are being increasingly used in the aeronautical and aerospace industry as well as in other fields of modern technology. Plates with variable thickness are of great importance in a wide variety of engineering applications i.e. nuclear reactor, aeronautical field, naval structure, submarine, earth-quake resistors etc. A mathematical model is presented for the use of engineers and research workers in space technology, have to operate under elevated temperatures.It is assumed that temperature varies exponentially in x-direction : 0 1 1 1 x a e e e e T T ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? and thickness of plate varies parabolic in x & linear in y direction: 2 0 1 2 2 1 1 x y h h a b ? ? ? ?? ? ? ? ? ? ?? ? ? ?? ? To obtain frequency equation, the Rayleigh-Ritz method is used which allows satisfying all four boundary conditions. The frequency for first two modes of vibration is calculated for different values of thermal gradient and taper constants with the help of latest computational technique i.e. Mat Lab.