A Meshless Local Collocation Method for Natural Frequencies and Mode Shapes of Functionally Graded Plates

Abstract:

The novelty of this paper is the use of a meshless local collocation method based on the multiquadric radial basis functions for free vibration analysis of functionally graded plates. This method approximates the governing equations based on first-order shear deformation theory using the nodes in the support domain of any data center. The natural frequencies computed by the present method are in good agreement with the element-free solutions of Zhao et al.

• Periodical: Advanced Materials Research (Volumes 1033-1034)
• Pages: 855-859
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1033-1034.855
• Online since: October 2014
• Authors: Guo Qing Zhou*, Ji Wang, Song Xiang
• Keywords: Functionally Graded Plates, Local Collocation Method, Meshless, Natural Frequency, Radial Basis Function

References

[1] S. Vel, R.C. Batra: J. Sound. Vib. Vol. 272 (2004), P. 703.

[2] S. Abrate, Compos. Sci. Technol. Vol. 66 (2006), P. 2383.

[3] A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, R.M.N. Jorge: Compos. Struct. Vol. 75 (2006) P. 593.

[4] C.M.C. Roque, A.J.M. Ferreira, R.M.N. Jorge: J. Sound. Vib. Vol. 300 (2007) P. 1048.

[5] H. Matsunaga: Compos. Struct. Vol. 82 (2008) 499–512.

[6] S. Pradyumna, J.N. Bandyopadhyay: J. Sound. Vib. Vol. 318 (2008) P. 176.

[7] X. Zhao, Y.Y. Lee, K.M. Liew: J. Sound. Vib. Vol. 319 (2009) P. 918.

[8] X. Liu, G.R. Liu, K. Tai, K.Y. Lam: Proceedings of the 1st Asian Workshop on Meshfree Methods, World Scientific, Singapore, (2002) P. 35–40.

[9] X. Liu, G.R. Liu, K. Tai, K.Y. Lam: Comput. Math. Appl. Vol. 50 (2005) P. 1425.

[10] G.R. Liu, B.B.T. Kee, L. Chun: Comput. Method. Appl. M. Vol. 195 (2006) P. 4843.

[11] C.K. Lee, X. Liu, S.C. Fan: Comput. Mech. Vol. 30 (2003) P. 396.

[12] S. Xiang, G.C. Li, W. Zhang, M.S. Yang: Compos. Struct. Vol. 93 (2011) P. 280.