Vibration of circular functionally graded piezoelectric plates in pre-/postbuckled configurations of bifurcation/limit load buckling

Free vibration of pre-/postbuckled circular functionally graded piezoelectric (FGP) plates is studied in this research. The buckled configurations are considered to be resulting from either thermoelectrical bifurcation buckling or limit load buckling due to lateral loading of thermally preloaded pla...

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Bibliographic Details
Published in:Acta mechanica 2017-09, Vol.228 (9), p.2945-2964
Main Authors: Ashoori, A. R., Sadough Vanini, S. A.
Format: Article
Language:English
Subjects:
Bifurcations
Boundary conditions
Buckling
Classical and Continuum Physics
Conduction heating
Conductive heat transfer
Control
Dynamical Systems
Electricity
Engineering
Engineering Thermodynamics
Equations of motion
Finite element method
Free vibration
Functionally gradient materials
Hamilton's principle
Heat and Mass Transfer
Lateral loads
Limit load
Load
Matrix representation
Newton-Raphson method
Nonlinear equations
Original Paper
Piezoelectricity
Plates
Solid Mechanics
Theoretical and Applied Mechanics
Vibration
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Summary:Free vibration of pre-/postbuckled circular functionally graded piezoelectric (FGP) plates is studied in this research. The buckled configurations are considered to be resulting from either thermoelectrical bifurcation buckling or limit load buckling due to lateral loading of thermally preloaded plates. The nonlinear governing equations of motion and associated boundary conditions are extracted by the generalized form of Hamilton’s principle. The Ritz finite element method is then implemented to construct the matrix representation of governing equations which are solved by two different strategies including Newton–Raphson scheme and cylindrical arc-length method. The thermoelectromechanical properties of FGPM plates are considered to be graded in the thickness direction on the basis of a power law function. Moreover, two cases of thermal loading, i.e., uniform temperature rise and heat conduction across the thickness as well as two types of boundary conditions, including clamped and simply supported, are considered. Comparison studies are presented to validate the numerical results. Furthermore, extensive parametric studies are conducted to assess the influence of involved parameters.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-017-1857-9