Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature

2009 ◽  
Vol 87 (3) ◽  
pp. 257-264 ◽  
Author(s):  
Yang Li ◽  
Zhifei Shi
Keyword(s):  
Free Vibration ◽  
State Space ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Piezoelectric Beam ◽  
Functionally Graded Piezoelectric

Three-Dimensional Free Vibration Analysis of Functionally Graded Annular Plates on Elastic Foundations via State-Space Based Differential Quadrature Method

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
A. Jodaei ◽  
M. H. Yas
Keyword(s):  
Free Vibration ◽  
State Space ◽  
Present Method ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Elastic Foundations ◽  
Annular Plates

In this paper, free vibration of functionally graded annular plates on elastic foundations, based on the three-dimensional theory of elasticity, using state-space based differential quadrature method for different boundary conditions is investigated. The foundation is described by the Pasternak or two-parameter model. Assuming the material properties having an exponent-law variation along the thickness, a semi-analytical approach that makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is used to obtain the vibration frequencies. Supposed state variables in the present method are different from what have been used for functionally graded annular plate so far. They are a combination of three displacement parameters and three stresses parameters. Numerical results are given to demonstrate the convergency and accuracy of the present method. In addition, the influences of the Winkler and shearing layer elastic coefficients of the foundations and some parameters are also investigated.

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.

scholarly journals Piezoelectric Beam Finite Element Model and Its Reduction and Control

2021 ◽  
Vol 71 (1) ◽  
pp. 87-106
Author(s):  
Kutiš Vladimír ◽  
Paulech Juraj ◽  
Gálik Gálik ◽  
Murín Justín
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
State Space ◽  
State Space Model ◽  
Element Model ◽  
Functionally Graded ◽  
Fem Model ◽  
Space Model ◽  
Piezoelectric Beam ◽  
Reduced State

Abstract The paper deals with the development of the finite element method (FEM) model of piezoelectric beam elements, where the piezoelectric layers are located on the outer surfaces of the beam core, which is made of functionally graded material. The created FEM model of piezoelectric beam structure is reduced using the modal truncation method, which is one of model order reduction (MOR) method. The results obtain from reduced state-space model are compared with results obtain from finite element model. MOR state-space model is also used in the design of the linear quadratic regulator (LQR). Created reduced state-space model with feedback with the LQR controller is analysed and compared with the results from FEM model.

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