Exponential temperature effect on frequencies of a rectangular plate of non-linear varying thickness: a quintic spline technique

• Autorzy: Gupta A. K. , Mamta J.
• Języki publikacji: EN

Abstrakty

EN

The differential equation governing the transverse motion of an elastic rectangular plate of non-linear thickness variation with thermal gradient has been analyzed on the basis of classi- cal plate theory. Following Levy’s approach, i.e. the two parallel edges are simply supported, the fourth-order differential equation governing the motion of such plates of non-linear vary- ing thickness in one direction with exponentially temperature distribution has been solved by using the quintic splines interpolation technique for two different combinations of clamped and simply supported boundary conditions at the other two edges. An algorithm for com- puting the solution of this differential equation is presented for the case of equal intervals. The effect of thermal gradient together with taper constants on the natural frequencies of vibration is illustrated for the first three modes of vibration.

Słowa kluczowe

EN

exponentially temperature; non-linear; thickness variation; vibration; rectangular plate

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2014
• Tom: Vol. 52 nr 1
• Strony: 15--24
• Opis fizyczny: Bibliogr. 18 poz., tab.

Twórcy

autor

Gupta A. K.

• M.S. College, Department of Mathematics, Saharanpur, U.P., India

autor

Mamta J.

• M.S. College, Department of Mathematics, Saharanpur, U.P., India

Bibliografia

• 1. Gupta A.K., Johri T., Vats R.P., 2007, Thermal effect on vibration of non-homogeneous orthotropic rectangular plate having bi-directional parabolically varying thickness, Proceeding of International Conference in World Congress on Engineering and Computer Science 2007, San-Francisco, USA, 784-787
• 2. Gupta A.K., Johri T., Vats R.P., 2010a, Study of thermal gradient effect on vibrations of a non-homogeneous orthotropic rectangular plate having bi-direction linearly thickness variations, Meccanica, 45, 3, 393-400
• 3. Gupta A.K., Kaur H., 2008, Study of the effect of thermal gradient on free vibration of clamped visco-elastic rectangular plates with linearly thickness variation in both directions, Meccanica, 43, 4, 449-458
• 4. Gupta A.K., Khanna A., 2007, Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions, Journal of Sound and Vibration, 301, 3/5, 450-457
• 5. Gupta A.K., Kumar A., Gupta Y.K., 2010b, Vibration study of visco-elastic parallelogram plate of linearly varying thickness, International Journal of Engineering and Interdisciplinary Mathematics, 2, 1, 21-29
• 6. Gupta A.K., Kumar A., Kaur H., 2011a, Vibration of visco-elastic orthotropic parallelogram plate with linearly thickness variation in both directions, International Journal of Acoustics and Vibration, 16, 2, 72-80
• 7. Gupta A.K., Kumar M., Khanna A., Kumar S., 2010c, Thermal effect on vibrations of parallelogram plate of linearly varying thickness, Advanced Studies in Theoretical Physics, 17, 4, 817-826
• 8. Gupta A.K., Kumar M., Kumar S., Khanna A., 2011b, Thermal effect on vibration of parallelogram plate of bi-direction linearly varying thickness, Applied Mathematics, 2, 1, 33-38
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