Innovative Systems Design and Engineering www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 2, No 3 Study of Free Vibrations Of Visco-Elastic Square Plate Of Variable Thickness With Thermal Effect Anupam Khanna (Corresponding author) Dept. Of Mathematics, MMEC, MMU (MULLANA), Ambala, Haryana, INDIA 3/1413, Janakpuri, Saharanpur, UP, INDIA Tel: - +91-903409199, +91-8439448048, E-mail: anupam_rajie@yahoo.co.in Ashish Kumar Sharma Dept. Of Mathematics, MMEC, MMU (MULLANA), Ambala, Haryana, INDIA PO box Sunder Bani, Jammu & Kashmir, Pin code 185153, INDIA Tel: - +91-8529525643, +91-9858687507, E-mail: ashishk482@gmail.com Meenu Bhaita Dept. Of Mathematics, MMEC, MMU (MULLANA), Ambala, Haryana, INDIA H. No – G-12, Kissan Basti, Nilokheri (Karnal), Haryana, INDIA Tel: - +91-8529525643, +91-9858687507, E-mail: ashishk482@gmail.com The research is financed by Asian Development Bank. No. 2006-A171(Sponsoring information) Abstract Visco-elastic Square plates are widely used in various mechanical structures, aircrafts and industries. For a proper design of plate structures and efficient use of material, the behavior and strength characteristics of plates should be accurately determined. A mathematical model is presented for the use of engineers, technocrats and research workers in space technology, mechanical Sciences have to operate under elevated temperatures. Two dimensional thermal effects on frequency of free vibrations of a visco-elastic square plate of variable thickness are considered. In this paper, the thickness varies parabolically in both direction and thermal effect is varying linearly in one direction and parabolic in another direction. Rayleigh Ritz method is used to evaluate the fundamental frequencies. Both the modes of the frequency are calculated by the latest computational technique, MATLAB, for the various values of taper parameters and temperature gradient. Keywords: Visco-elastic, Plate, Square Plate,Vibration, Thermal gradient, Frequency. 1. Introduction