Thermal Vibrations of a Graphene Sheet Embedded in Viscoelastic Medium based on Nonlocal Shear Deformation Theory

2019 ◽  
Vol 24 (3) ◽  
pp. 485-493 ◽  
Author(s):  
Ashraf M. Zenkour ◽  
A. H. Al-Subhi
Keyword(s):  
Shear Deformation ◽  
Graphene Sheet ◽  
Deformation Theory ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Thermal Parameter ◽  
Thermal Vibration ◽  
Thermal Vibrations

The nonlocal first-order shear deformation plate theory is used to present the thermal vibration of a single-layered graphene sheet (SLGS) resting on a viscoelastic foundation. The viscous damping term is added to the elastic foundation to get a three-parameter visco-Pasternak medium. The nonlocal shear deformation theory is applied to obtain the equations of motion of the simply-supported SLGSs. The effects of the nonlocal parameter as well as the length of the SLGS, mode numbers, three-parameters of the foundation, and the thermal parameter are discussed carefully for the vibration problem. The validation of the present frequencies is discussed with excellent comparison to the existing literature. For future comparisons, additional thermal vibration results of SLGSs are investigated to take into consideration the effects of thermal, nonlocal, and visco-Pasternak mediums.

Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory

2018 ◽  
Vol 233 (1) ◽  
pp. 287-301 ◽  
Author(s):  
Behrouz Karami ◽  
Davood Shahsavari ◽  
Li Li ◽  
Moein Karami ◽  
Maziar Janghorban
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Thermal Buckling ◽  
Second Order ◽  
Functionally Graded ◽  
Electric Voltage ◽  
Size Dependent

The effective elastic-piezoelectric properties of nanostructures have been shown to be strongly size-dependent. In this paper, a nonlocal second-order shear deformation formulation is presented to study the size-dependent thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core. Temperature is considered as uniform and nonlinear distributions across plate’s thickness direction. Based on the developed nonlocal second-order shear deformation theory, the size-dependent equations of motion are derived. The nonlocal thermal buckling responses of simply supported nanoplates are solved via Navier method. The reliability of present approach is verified by comparing the existing results provided in the open literature. The influences of nonlocal parameter, gradient index, electric voltage, and Winkler–Pasternak parameters on the thermal buckling characteristics of functionally graded nanoplates are examined.

Enhanced First-Order Shear Deformation Theory for Laminated and Sandwich Plates

2005 ◽  
Vol 72 (6) ◽  
pp. 809-817 ◽  
Author(s):  
Jun-Sik Kim ◽  
Maenghyo Cho
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Sandwich Plates ◽  
First Order ◽  
Transverse Shear Strains

A new first-order shear deformation theory (FSDT) has been developed and verified for laminated plates and sandwich plates. Based on the definition of Reissener–Mindlin’s plate theory, the average transverse shear strains, which are constant through the thickness, are improved to vary through the thickness. It is assumed that the displacement and in-plane strain fields of FSDT can approximate, in an average sense, those of three-dimensional theory. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT variables as well as the improved transverse shear strains. This paper makes two main contributions. First an enhanced first-order shear deformation theory (EFSDT) has been developed using an available higher-order plate theory. Second, it is shown that the displacement fields of any higher-order plate theories can be recovered by EFSDT variables. The present approach is applied to an efficient higher-order plate theory. Comparisons of deflection and stresses of the laminated plates and sandwich plates using present theory are made with the original FSDT and three-dimensional exact solutions.

A NEW TRIANGULAR ELEMENT BASED ON HIGHER ORDER SHEAR DEFORMATION THEORY FOR FLEXURAL VIBRATION OF COMPOSITE PLATES

2002 ◽  
Vol 02 (02) ◽  
pp. 163-184 ◽  
Author(s):  
A. CHAKRABARTI ◽  
A. H. SHEIKH
Keyword(s):  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Higher Order ◽  
Triangular Element

A triangular element based on Reddy's higher order shear deformation theory is developed for free vibration analysis of composite plates. In the Reddy's plate theory, the transverse shear stress varies in a parabolic manner across the plate thickness and vanishes at the top and bottom surfaces of the plate. Moreover, it does not involve any additional unknowns. Thus the plate theory is quite simple and elegant. Unfortunately, such an attractive plate theory cannot be exploited as expected in finite element analysis, primarily due to the difficulties in satisfying the inter-element continuity requirement. This has inspired us to develop the present element, which has three corner nodes and three mid-side nodes with the same number of degrees of freedom. To demonstrate the performance of the element, numerical examples of isotropic and composite plates under different situations are solved. The results are compared with the analytical solutions and other published results, which show the accuracy and range of applicability of the proposed element in the problem of vibration analysis.

Vibration control of magnetostrictive plate under multi- physical loads via trigonometric higher order shear deformation theory

2015 ◽  
Vol 23 (19) ◽  
pp. 3057-3070 ◽  
Author(s):  
Ali Ghorbanpour Arani ◽  
Z Khoddami Maraghi ◽  
H Khani Arani
Keyword(s):  
Elastic Medium ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Feedback Gain ◽  
First Time ◽  
Free Vibration Response

For the first time in this research, a feedback control system is used to study the free vibration response of rectangular plate made of magnetostrictive material. In this regard, magnetostrictive plate (MsP) is analyzed by trigonometric higher order shear deformation theory that involved six unknown displacement functions and does not require shear correction factor. The MsP is supported by elastic medium as Pasternak foundation which considers both normal and shears modules. Also the MsP undergoes in-plane forces in x and y directions. Considering simply supported boundary condition, six equations of motion are derived using Hamilton’s principle and solved by differential quadrature method. Results indicate the effect of aspect ratio, thickness ratio, elastic medium, compression and tension loads on vibration behavior of MsP. Also, findings show the controller effect of velocity feedback gain to minimize the frequency as far as other parameters become ineffective. These findings can be used to active noise and vibration cancellation systems in many structures.

Dynamic Stiffness Analysis of a Beam Based on Trigonometric Shear Deformation Theory

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Jun Li ◽  
Hongxing Hua ◽  
Rongying Shen
Keyword(s):  
Shear Deformation ◽  
Stiffness Matrix ◽  
Deformation Theory ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Beam Element ◽  
Mode Shapes ◽  
Dynamic Stiffness Matrix ◽  
Stiffness Analysis

The dynamic stiffness matrix of a uniform isotropic beam element based on trigonometric shear deformation theory is developed in this paper. The theoretical expressions for the dynamic stiffness matrix elements are found directly, in an exact sense, by solving the governing differential equations of motion that describe the deformations of the beam element according to the trigonometric shear deformation theory, which include the sinusoidal variation of the axial displacement over the cross section of the beam. The application of the dynamic stiffness matrix to calculate the natural frequencies and normal mode shapes of two rectangular beams is discussed. The numerical results obtained are compared to the available solutions wherever possible and validate the accuracy and efficiency of the present approach.

scholarly journals Free vibration characteristics of thick doubly curved variable stiffness composite laminated shells using higher-order shear deformation theory

2018 ◽  
Vol 172 ◽  
pp. 03010 ◽  
Author(s):  
Anand Venkatachari ◽  
K. Ramajeyathilagam
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Variable Stiffness ◽  
Mode Shapes ◽  
Laminated Shells ◽  
Surface Displacements ◽  
Edge Conditions ◽  
Geometric Variables

In the present work, the natural frequencies of cylindrical and spherical laminated shells with variable stiffness are numerically studied using a shear flexible isogeometric finite element. The kinematics relies on cubic shear deformation theory in which cubic variation is assumed for the surface displacements and a quadratic variation for the traverse displacement along the thickness. A zig-zag function, used for the in-plane displacements, accounts for the abrupt discontinuity at the boundaries of the laminae. The Lagrangian equations of motion is deployed to solve the frequencies of curved panels. A detailed parametric analysis examines the influence of fibre centre/edge angles, shell geometric variables, material anisotropy and edge conditions on frequencies and mode shapes.

A Parametric Study on Natural Frequency of Sandwich Panel Using Refined Shear Model

2002 ◽  
Author(s):  
Qunli Liu ◽  
Yi Zhao
Keyword(s):  
Shear Deformation ◽  
Natural Frequency ◽  
Deformation Theory ◽  
Sandwich Panel ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Nonlinear Behavior ◽  
Flexural Vibration ◽  
Element Analysis ◽  
Theoretical Predictions

The natural frequency of a thick rectangular sandwich panel was studied using refined shear deformation theory. Both faceshheets and core materials are orthotropic. Nonlinear behavior of shear deformation of sandwich panel was described by a proposed polynomial function. The effect of transverse shear modulus of sandwich core on flexural vibration of the panel was investigated. Comparison was made among the classical thin plate theory, low order shear deformation theory and high order refined shear theory. Results from finite element analysis were also provided to verify the theoretical predictions.

Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory

2017 ◽  
Vol 21 (8) ◽  
pp. 2751-2778 ◽  
Author(s):  
Mohammad Arefi ◽  
Ashraf M Zenkour
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Radius Of Curvature ◽  
Governing Equations ◽  
Size Dependent ◽  
Magnetic Potentials ◽  
Sinusoidal Shear Deformation Theory

In this work, an analytical solution for bending analysis of the three-layer curved nanobeams is presented. The nanobeams are including a nanocore and two piezomagnetic face-sheets. The structure is subjected to applied electric and magnetic potentials while is resting on Pasternak's foundation. To reach more accurate results, sinusoidal shear deformation theory is employed to derive displacement field of the curved nanobeams. In addition, nonlocal electro-magneto-elasticity relations are employed to derive governing equations of bending based on the principle of virtual work. The analytical results are presented for simply supported curved nanobeam to discuss the influence of important parameters on the vibration and bending results. The important parameters are included spring and shear parameters of the foundation, applied electric and magnetic potentials, nonlocal parameter, and radius of curvature of curved nanobeam.

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.

Sign in / Sign up

Export Citation Format

Share Document