Analysis of Elasticity Solution of Bi-Direction Functionally Graded Piezoelectric Beam Subject to Voltage

Abstract:

This paper presents symplectic method for the derivation of exact solutions of functionally graded piezoelectric beam with the material properties varying exponentially both along the axial and transverse coordinates. In the approach, the related equations and formulas are developed in terms of dual equations, which can be solved by variables separation and symplectic expansion in Hamiltonian system. To verify advantages of the method, numerical examples of bi-directional functionally piezoelectric beam are discussed.

• Periodical: Applied Mechanics and Materials (Volumes 166-169)
• Pages: 824-827
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.166-169.824
• Online since: May 2012
• Authors: Y Z Yang
• Keywords: Functionally Graded Piezoelectric, Hamiltonian, Symplectic Expansion

References

[1] WQ Chen, HJ Ding.Acta Mechanics Vol. 153(2002),pp.207-216.

[2] BV Sankar, JT Tzeng.. AIAA Vol. 40(2002),pp.1228-1232.

[3] Zhong Z, Shang ET. Int.J.Solids.Struct. Vol. 40 (2002), p.5335–5352.

[4] HH Chang, JQ Tarn. Int.J.Solids.Struct. Vol.44 (2007), pp.1409-1422.

[5] MA Steinberg:Materials for aerospace(Scientific American,Newyork 1986).

[6] CF Lü,WQ Chen, RQ Xu, CW Lim. Int.J.Solids.Struct.Vol.45(2008),pp.258-275.

[7] CF Lü, CW Lim,, WQ Chen. Int.J. Num.Meth.Eng, 2009, 79(1):25-44.

[8] Li Zhao.The symplectic method for plane problem of functionally graded materials. Zhejiang University, 2010.

[9] WA Yao, WX Zhong, CW Lim.Symplectic elasticity (World Scientific, Singapore 2008).

[10] XP Ruan, CD Stephen, S Ahmad.Int.J.Solids.Struct., 2000, 3