scholarly journals The Third-Order Shear Deformation Theory for Modeling the Static Bending and Dynamic Responses of Piezoelectric Bidirectional Functionally Graded Plates

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Nguyen Thai Dung ◽  
Phung Van Minh ◽  
Hoang Manh Hung ◽  
Dao Minh Tien
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Third Order ◽  
Feedback Parameter ◽  
Dynamic Behaviors ◽  
The Third ◽  
Graded Structures

This work is the first exploration of the static bending and dynamic response analyses of piezoelectric bidirectional functionally graded plates by combining the third-order shear deformation theory of Reddy and the finite element approach, which can numerically model mechanical relations of the structure. The present approach and mechanical model are confirmed through the verification examples. The geometrical and material study is conducted to evaluate the effects of the feedback coefficients, volume fraction parameter, and constraint conditions on the static and dynamic behaviors of piezoelectric bidirectional functionally graded structures, and this work presents a wide variety of static and dynamic behaviors of the plate with many interesting results. There are many meanings that have not been mentioned by any work, especially the working performance of the structure is better than that when the feedback parameter of the piezoelectric component is added, that is, the piezoelectric layer increases the working efficiency. Numerical investigations are the important basis for calculating and designing related materials and structures in technical practice.

The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate

2019 ◽  
Vol 50 (9-11) ◽  
pp. 267-290
Author(s):  
Ali Bakhsheshy ◽  
Hossein Mahbadi
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Scale Parameter ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
The Third

This article develops the modified couple stress theory to study the free vibration of bi-directional functionally graded microplates subjected to multidimensional temperature distribution. Third-order shear deformation and classical theories of plates are adapted for free vibration analysis of thick and thin microplates, respectively. Employing the third-order shear deformation theory, both normal and shear deformations are considered without the need for shear correction factor. Material of the bi-directional functionally graded microplate is graded smoothly through the length and thickness of the microplate. Gradient of the material is assumed to obey from the power law in terms of the volume fraction of the constituents. Assuming the uniform and nonuniform temperature distributions, the effect of thermal environment on dynamic behavior of the microplate is discussed in detail. Applying the Ritz method, the displacement field is expanded by admissible functions which satisfy the essential boundary conditions, and Hamilton principle is employed to determine the natural frequencies of the microplate. Developed model has been applied to determine the natural frequencies in problems of thin/thick, one-directional/bi-directional functionally graded, and homogeneous/nonhomogeneous microplates. Effects of parameters such as the thermal environment, power law indexes [Formula: see text] and length scale parameter on free vibration of these problems are studied in detail. The results show that higher values of length scale parameter and temperature rise decrease the natural frequency of the bi-directional functionally graded microplate. According to results obtained by classical and third-order shear deformation theories, the third-order shear deformation theory is proposed for vibration analysis of microplates with thickness-to-length ratio less than five.

Thermoelastic Stability of Imperfect Functionally Graded Plates Based on the Third Order Shear Deformation Theory

2006 ◽  
Author(s):  
B. Samsam Shariat ◽  
M. R. Eslami ◽  
A. Bagri
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Form Solution ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
The Third

Thermal buckling analysis of rectangular functionally graded plates with initial geometric imperfections is presented in this paper. It is assumed that the non-homogeneous mechanical properties vary linearly through the thickness of the plate. The plate is assumed to be under various types of thermal loadings, such as the uniform temperature rise and nonlinear temperature gradient through the thickness. A double-sine function for the geometric imperfection along the x and y-directions is considered. The equilibrium equations are derived using the third order shear deformation plate theory. Using a suitable method, equilibrium equations are reduced from 5 to 2 equations. The corresponding stability equations are established. Using these equations accompanied by the compatibility equation yield to the buckling loads in a closed form solution for each loading case. The results are compared with the known data in the literature.

scholarly journals A NEW C0 THIRD-ORDER SHEAR DEFORMATION THEORY FOR THE NONLINEAR FREE VIBRATION ANALYSIS OF STIFFENED FUNCTIONALLY GRADED PLATES

2021 ◽  
Vol 19 (2) ◽  
pp. 285
Author(s):  
Hoang Lan Ton-That
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Nonlinear Free Vibration ◽  
Third Order

Nonlinear free vibration of stiffened functionally graded plates is presented by using the finite element method based on the new C0 third-order shear deformation theory. The material properties are assumed to be graded in the thickness direction by a power-law distribution. Based on the Von Karman theory and the third-order shear deformation theory, the nonlinear governing equations of motion are derived from the Hamilton’s principle. An iterative procedure based on the Newton-Raphson method is employed in computing the natural frequencies and mode shape. The comparison between these solutions and the other available ones suggests that this procedure is characterized by accuracy and efficiency.

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