Exact solutions for simply supported functionally graded piezoelectric laminates by Stroh-like formalism

2006 ◽  
Vol 72 (3) ◽  
pp. 352-363 ◽  
Author(s):  
Pin Lu ◽  
H.P. Lee ◽  
C. Lu
Keyword(s):  
Exact Solutions ◽  
Functionally Graded ◽  
Simply Supported ◽  
Functionally Graded Piezoelectric

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

2012 ◽  
Vol 166-169 ◽  
pp. 824-827 ◽  
Author(s):  
Y Z Yang
Keyword(s):  
Hamiltonian System ◽  
Exact Solutions ◽  
Material Properties ◽  
Functionally Graded ◽  
Symplectic Method ◽  
Elasticity Solution ◽  
Numerical Examples ◽  
Piezoelectric Beam ◽  
Functionally Graded Piezoelectric

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.

Modelling of functionally graded piezoelectric ultrasonic transducers

2007 ◽  
Author(s):  
Wilfredo M. Rubio ◽  
Flavio Buiochi ◽  
Julio C. Adamowski ◽  
Emilio C. N. Silva
Keyword(s):  
Functionally Graded ◽  
Ultrasonic Transducers ◽  
Functionally Graded Piezoelectric
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