Free Vibration of Orthotropic Plate on Foundation with Four Edges Free by Finite Integral Transform Method

Abstract:

The double finite cosine integral transform method is exploited to obtain explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate on foundation with four edges free. In the analysis procedure, the classical Kirchhohh orthotropic rectangular plate is considered and the Winkler elastic foundation is utilized to represent the elastic foundation. Because only are the basic dynamic elasticity equations of the orthotropic thin plate on elastic foundation adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by present paper is reasonable and theoretical. In order to illuminate the correction of formulations, the numerical results are also presented to comparing with that of the other references.

• Periodical: Advanced Materials Research (Volumes 243-249)
• Pages: 4253-4256
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.243-249.4253
• Online since: May 2011
• Authors: Yong Zhong, Yuan Yuan Gao
• Keywords: Elastic Foundation, Finite Cosine Integral Transform, Mode Shape, Natural Frequency, Rectangular Orthotropic Plate with Four Edges Free

References

[1] A.W. Leissa: Vibration of Plates (Acoustical Society of America. 1993).

[2] G.B. Warburton: Proceeding of the Institute of Mechanical Engineers, Series A 168 (1954) 371–384

[3] A.W. Leissa: Journal of Sound and Vibration 31 (1973) 257–293

[4] G.B. Warburton: Journal of Earthquake Engineering and Structural Dynamics 7 (1979) 327–334

[5] G.B. Warburton, and S.L. Edney: Journal of Sound and Vibration 95 (1984) 537–552

[6] D.J. Gorman: Journal of Applied Mechanics 56 (1980) 893–899

[7] D.J. Gorman: Free Vibration analysis of rectangular plates (Elsevier North Holland, Inc. 1982).

[8] A.V. Bapat, N. Venkatramani, and S. Suryanarayan: Journal of Sound and Vibration 120 (1988) 127–140

[9] D. Zhou: Journal of Sound and Vibration 189 (1996) 81–88

[10] S. Hurlebaus, L. Gaul and J.T.-S. Wang: Journal of Sound and Vibration 244 (2001) 747–759

[11] Ian.H.Sneddon: The use of integral transforms (McGraw-Hill, Inc. 1972).

[12] Ian.H.Sneddon: The application of integral transform in elasticity (McGraw-Hill, Inc. 1981).

[13] Yang.T.Y: Computer and Structure (2) (1972) 573-616

[14] Zafrang A.E: Int. J. Num. Engrg. (38) 1995 887-903