A Computational Model on: Vibration of Square Plate with Varying Thickness and Thermal effect in Two Directions

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A Computational Model on: Vibration of Square Plate with Varying Thickness and Thermal effect in Two Directions

Author Affiliations

¹Dept. of Mathematics, Govt. P.G College, Ambala Cantt., Haryana, INDIA
² Dept. of Mathematics, Pacific University, Udaipur, Rajasthan, INDIA

Res. J. Engineering Sci., Volume 2, Issue (7), Pages 6-9, July,26 (2013)

Abstract

A computational model presented here is to study the vibration of visco-elastic isotropic square plate with thermal effect on two direction varying thickness parabolically. Equation of frequency is derived by using Rayleigh-Ritz technique with a two-term deflection function. All the calculation made for the first two modes of vibration, for various values of thermal gradients and taper constant.

References

Leissa A.W., Vibration of plates, NASA SP-160 (1969)
Tomar J.S. and Gupta A.K., Effect of thermal gradient on frequencies of an orthotropic rectangular plate whose thickness varies in two directions, Journal sound and vibration, 98(2), 257-262 (1985)
Gupta A.K. and Lalit Kumar, Thermal effects on vibration of non-homogeneous visco-elastic rectangular plate of linearly varying thickness in two directions, Meccanica, 43, 47-54 (2008)
Gupta A.K. and Khanna A., Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions, J. Sound and Vibration, 301, 450-457 (2007)
Larrondo H.A., Avalos D.R., Laura P.A.A. and Rossi R.E., Vibration of simply supported rectangular plates with varying thickness and same aspect ratio cutouts , J. Sound and Vibration, 244, No.4, 738-746 (2001)
Gupta A.K. and Anupam Khanna, Free vibration of clamped visco-elastic rectangular plate having bi-direction exponentially thickness variations, Journal of Theoretical and Applied Mechanics,47(2), 457-471 (2009)
Khanna A. and Ashish Kumar Sharma,Thermally Induced Vibration of Non- Homogenous Visco-Elastic Plate of Variable thickness, Advances in Physics Theories and Applications, 1, 1-5 (2011)
Khanna A. and Ashish Kumar Sharma, Analysis of free Vibration of Visco-Elastic Square Plate of Variable Thickness with Temperature effect, International Journal of Applied Engineering Research, Dindigul, 2,(2), 312-317 (2011)
Khanna A. and Ashish Kumar Sharma, Mechanical Vibration of Visco-Elastic Plate with Thickness Variation, International Journal of Applied Mathematical Research, 1(2),150-158 (2012)
Khanna A. and Ashish Kumar Sharma, Vibration Analysis of Visco-Elastic Square Plate of Variable Thickness with Thermal Gradient, International Journal of Engineering and Applied Sciences, 3(4), 1-6 (2011)

[ref1] Leissa A.W., Vibration of plates, NASA SP-160 (1969)

[ref2] Tomar J.S. and Gupta A.K., Effect of thermal gradient on frequencies of an orthotropic rectangular plate whose thickness varies in two directions, Journal sound and vibration, 98(2), 257-262 (1985)

[ref3] Gupta A.K. and Lalit Kumar, Thermal effects on vibration of non-homogeneous visco-elastic rectangular plate of linearly varying thickness in two directions, Meccanica, 43, 47-54 (2008)

[ref4] Gupta A.K. and Khanna A., Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions, J. Sound and Vibration, 301, 450-457 (2007)

[ref5] Larrondo H.A., Avalos D.R., Laura P.A.A. and Rossi R.E., Vibration of simply supported rectangular plates with varying thickness and same aspect ratio cutouts , J. Sound and Vibration, 244, No.4, 738-746 (2001)

[ref6] Gupta A.K. and Anupam Khanna, Free vibration of clamped visco-elastic rectangular plate having bi-direction exponentially thickness variations, Journal of Theoretical and Applied Mechanics,47(2), 457-471 (2009)

[ref7] Khanna A. and Ashish Kumar Sharma,Thermally Induced Vibration of Non- Homogenous Visco-Elastic Plate of Variable thickness, Advances in Physics Theories and Applications, 1, 1-5 (2011)

[ref8] Khanna A. and Ashish Kumar Sharma, Analysis of free Vibration of Visco-Elastic Square Plate of Variable Thickness with Temperature effect, International Journal of Applied Engineering Research, Dindigul, 2,(2), 312-317 (2011)

[ref9] Khanna A. and Ashish Kumar Sharma, Mechanical Vibration of Visco-Elastic Plate with Thickness Variation, International Journal of Applied Mathematical Research, 1(2),150-158 (2012)

[ref10] Khanna A. and Ashish Kumar Sharma, Vibration Analysis of Visco-Elastic Square Plate of Variable Thickness with Thermal Gradient, International Journal of Engineering and Applied Sciences, 3(4), 1-6 (2011)