An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory

Ebrahimi, Farzad; Rastgo, A.

doi:10.1016/j.tws.2008.03.008

Cited by 160 publications

(52 citation statements)

References 14 publications

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“…The short-circuited boundary conditions is considered for both top and bottom piezoelectric layers. By employing a second order approximation for electric potential distribution along the z direction, we'll have: [Ebrahimi and Rastgo, 2008] …”

Section: Formulationmentioning

confidence: 99%

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Nonlinear Electromechanical Stability of a Functionally Graded Circular Plate Integrated With Functionally Graded Piezoelectric Layers

Arefi

2015

Lat. Am. j. solids struct.

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This research develops nonlinear electromechanical stability of a circular functionally graded plate integrated with functionally graded piezoelectric layers under compressive radial force. Geometric nonlinearity is considered in the strain-displacement relation using Von-Karman relation. The structure is loaded under mechanical and electrical loads. Distribution of electric potential is considered along the radial and thickness direction. The top and bottom of both piezoelectric layers is short-circuited. The effect of various values of non homogenous index for both functionally graded (FG) and functionally graded piezoelectric (FGP) layers can be considered on the responses of the system. Furthermore, a comprehensive study for evaluation of geometric parameters can be performed on the critical loads of the structure.

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Section: Formulationmentioning

confidence: 99%

“…Discharge equation that implies divergence of electric displacement vanishes through the piezoelectric section yields third equation as follows: [Ebrahimi and Rastgo, 2008] …”

Section: Formulationmentioning

confidence: 99%

Nonlinear Electromechanical Stability of a Functionally Graded Circular Plate Integrated With Functionally Graded Piezoelectric Layers

Arefi

2015

Lat. Am. j. solids struct.

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“…Containing various advantageous properties, FGMs are idoneous for various engineering applications, and has gained intense interest by several researchers [1][2][3][4][5][6][7]. Moreover, nanoscale beam structures have attracted the interest of some researchers in the field of nanomechanics.…”

Section: Introductionmentioning

confidence: 99%

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

Ebrahimi

Barati

2016

International Journal of Smart and Nano Materials

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In the present work, thermo-electro-mechanical buckling behavior of functionally graded piezoelectric (FGP) nanobeams is investigated based on higher-order shear deformation beam theory. The FGP nanobeam is subjected to four types of thermal loading including uniform, linear, and sinusoidal temperature rise as well as heat conduction through the beam thickness. Thermo-electromechanical properties of FGP nanobeam are supposed to change continuously in the thickness direction based on power-law model. To consider the influences of small-scale sizes, Eringen's nonlocal elasticity theory is adopted. Applying Hamilton's principle, the nonlocal governing equations of an FGP nanobeam in thermal environments are obtained and are solved using Naviertype analytical solution. The significance of various parameters, such as thermal loadings, external electric voltage, power-law index, nonlocal parameter, and slenderness ratio on thermal buckling response of size-dependent FGP nanobeams is investigated. ARTICLE HISTORY

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“…Jaroszewicz and Zoryj [7] have studied free vibration of circular thin plates of constant and linearly variable thickness using the method of partial discretization (MPD). Ebrahimi and Rastgo [8] investigated the natural vibration behavior of circular functionally graded plates with clamped edges based on classical plate theory. Yalcin et al [9] have studied free vibration of circular plates by using differential transformation method (DTM).…”

Section: Introductionmentioning

confidence: 99%

Green’s function approach to frequency analysis of thin circular plates

Żur¹

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract.The free vibration analysis of homogeneous and isotropic circular thin plates by using the Green's functions is considered. The formulae for construction of the influence function for all nodal diameters are presented in a closed form. The limited independent solutions of differential Euler equations were expanded in the Neumann power series using the method of successive approximation. This approach allows to obtain the analytical frequency equations as power series rapidly convergent to exact eigenvalues for different number of nodal diameters.

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An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory

Cited by 160 publications

References 14 publications

Nonlinear Electromechanical Stability of a Functionally Graded Circular Plate Integrated With Functionally Graded Piezoelectric Layers

Nonlinear Electromechanical Stability of a Functionally Graded Circular Plate Integrated With Functionally Graded Piezoelectric Layers

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

Green’s function approach to frequency analysis of thin circular plates

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