scholarly journals Effect of elastic foundation on vibrational behavior of graphene based on first-order shear deformation theory

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881462
Author(s):  
Mohsen Motamedi ◽  
Amirhossein Naghdi ◽  
Ayesha Sohail ◽  
Zhiwu Li
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Circular Plates ◽  
First Order ◽  
Special Case ◽  
Good Agreement

In this study, an investigation of “the free vibrations of hollow circular plates’’ is reported. The study is based on elastic foundation and the results depicted are further extended to study the special case of “graphene sheets.’’ The first-order shear deformation theory is applied to study the elastic properties of the material. A hollow circular sheet is modeled and the vibrations are simulated with the aid of finite element method. The results obtained are in good agreement with the theoretical findings. After the validation, a model of graphene is presented. Graphene contains a layer of honeycomb carbon atoms. Inside a layer, each carbon atom C is attached to three other carbon atoms and produces a sheet of hexagonal array. A 25 nm × 25 nm graphene sheet is modeled and simulated using the validated technique, that is, via the first-order shear deformation theory. The key findings of this study are the vibrational frequencies and vibrational mode shapes.

A New First-Order Shear Deformation Theory for Free Vibrations of Rectangular Plate

2015 ◽  
Vol 07 (01) ◽  
pp. 1550008 ◽  
Author(s):  
Wei Xiang ◽  
Yufeng Xing
Keyword(s):  
Shear Deformation ◽  
Rectangular Plate ◽  
Deformation Theory ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Present Theory ◽  
Free Vibrations ◽  
Variable Theory ◽  
First Order ◽  
Geometrical Constraints

A new first-order shear deformation theory (FSDT) with pure bending deflection and shearing deflection as two independent variables is presented in this paper for free vibrations of rectangular plate. In this two-variable theory, the shearing deflection is regarded as the only fundamental variable by which the total deflection and bending deflection can be expressed explicitly. In contrast with the conventional three-variable first-order shear plate theory, present variationally consistent theory derived by using Hamiltonian variational principle can uniquely define the bending and the shearing deflections, and give two rotations by the differentiations of bending deflection. Due to more restrictive geometrical constraints on rotations and boundary conditions, the obtained natural frequencies are equal to or higher than those by conventional FSDT for the rectangular plate with at least one pair of opposite edges simply supported. This new theory is of considerable significance in theoretical sense for giving a simple two-variable FSDT which is variational consistent and involve rotary inertia and shear deformation. The relation and differences of present theory with conventional FSDT and other relative formulations are discussed in detail.

Nonlinear vibration of functionally graded sandwich shallow spherical caps resting on elastic foundations by using first-order shear deformation theory in thermal environment

2018 ◽  
Vol 22 (4) ◽  
pp. 1157-1183 ◽  
Author(s):  
Nguyen Thi Phuong ◽  
Vu Hoai Nam ◽  
Dang Thuy Dong
Keyword(s):  
Nonlinear Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Thermal Environment ◽  
Geometrical Nonlinearity ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
First Order ◽  
Spherical Caps

A semi-analytical approach to investigate the nonlinear vibration axisymmetric analysis of functionally graded sandwich shallow spherical caps under external pressure resting on elastic foundation in thermal environment is presented. The governing equations are derived by using the first-order shear deformation theory taking into account von Karman geometrical nonlinearity and Pasternak’s two-parameter elastic foundation. The motion equations are determined by Galerkin method and the obtained equation is numerically solved by using Runge–Kutta method. Results of nonlinear dynamic responses show the effects of foundation, material, geometric parameters, and temperature change on the nonlinear vibration of shells.

Examination of the plate twist specimen for thick specially orthotropic laminated composites and sandwich plates by using first-order shear deformation theory

2017 ◽  
Vol 21 (7) ◽  
pp. 2239-2265
Author(s):  
R. Guillén-Rujano ◽  
A. Hernández-Pérez ◽  
F. Avilés
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Theory Approach ◽  
First Order ◽  
Aspect Ratios ◽  
Good Agreement ◽  
Element Method

Analytical (closed-form) solutions are developed for the deflections and rotations of thick specially orthotropic plate twist specimens by using first-order shear deformation theory. Results are compared with outcomes from finite element method, previously reported experiments, and a classical laminated plate theory solution. A [(0/90)6]s cross-ply laminate and a sandwich panel with aluminum face sheets and a polyvinyl chloride (PVC) foam core are used as baseline materials. Overall, good agreement between first-order shear deformation theory and finite element method is obtained for compliance predictions. It is found that the proposed first-order shear deformation theory approach can be used to adequately calculate the deflections of specially orthotropic plates from low to moderately high side length to thickness ratios [Formula: see text]. Examination of the in-plane shear modulus ratio between face sheets and core ([Formula: see text]) points out that first-order shear deformation theory slightly underpredicts the compliance with respect to finite element method, specially for [Formula: see text] ratios larger than 100. Both solutions based on plate theories are suitable to estimate the compliance of cross-ply laminates with moderate [Formula: see text] ratios ([Formula: see text]). First-order shear deformation theory is able to properly predict the compliance of square and rectangular laminates with aspect ratios lower than 10. Good agreement between published compliance measurements and those predicted by first-order shear deformation theory is found for Maple plywoods, monolithic metals, and specially orthotropic sandwich panels.

Mechanical analysis of shrink-fitted thick FG cylinders based on first order shear deformation theory and FE simulation

2021 ◽  
pp. 095440622110127
Author(s):  
Mohammad Reza Salehi Kolahi ◽  
Hossein Rahmani ◽  
Hossein Moeinkhah
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Fe Simulation ◽  
Shear Deformation Theory ◽  
Mechanical Analysis ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
First Order ◽  
Analytical Functions ◽  
Plane Elasticity Theory

In this paper, the first order shear deformation theory is used to derive an analytical formulation for shrink-fitted thick-walled functionally graded cylinders. It is assumed that the cylinders have constant Poisson’s ratio and the elastic modulus varies radially along the thickness with a power function. Furthermore, a finite element simulation is carried out using COMSOL Multiphysics, which has the advantage of defining material properties as analytical functions. The results from first order shear deformation theory are compared with the findings of both plane elasticity theory and FE simulation. The results of this study could be used to design and manufacture for elastic shrink-fitted FG cylinders.

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