scholarly journals Geometrical Influences on the Vibration of Layered Plates

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Saira Javed ◽  
F. H. H. Al Mukahal ◽  
S. B. A. El Sayed
Keyword(s):  
Aspect Ratio ◽  
Eigenvalue Problem ◽  
Deformation Theory ◽  
Angular Displacement ◽  
Spline Approximation ◽  
Shear Deformation Theory ◽  
Frequency Variation ◽  
Layered Plates ◽  
Nonuniform Thickness ◽  
Support Conditions

This paper aims to study the influence of different geometric properties and support conditions on the vibration of layered plates of nonuniform thickness under shear deformation theory. The layered plates are supposed to have arbitrarily nonuniform thickness as linear, exponential, and sinusoidal. The spline approximation is used to approximate translational and angular displacement functions. Eigen frequency parameters are calculated by solving eigenvalue problem. The geometrical influences such as number of lay-ups, different ply orientations, each ply consisting of different material, side-to-thickness ratio, and aspect ratio are taken into consideration to examine the frequency variation of plates for two different support conditions.

Buckling analysis of nanocomposite sandwich plates with piezoelectric face sheets based on flexoelectricity and first-order shear deformation theory

2018 ◽  
Vol 22 (7) ◽  
pp. 2186-2209 ◽  
Author(s):  
Saeed Amir ◽  
Mohammad Khorasani ◽  
Hassan BabaAkbar-Zarei
Keyword(s):  
Aspect Ratio ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Sandwich Plate ◽  
Piezoelectric Materials ◽  
Shear Deformation Theory ◽  
Buckling Load ◽  
Sandwich Plates ◽  
Critical Buckling Load ◽  
First Order

In piezoelectric materials and at the nano-scale, there is a coupling between electrical polarization and strain gradients fields, which is called flexoelectricity. The effects of this phenomenon seem to be negligible in micro/macro scales. The current study has attempted to have a cohesive concentration on the buckling behaviors of sandwich plates. To achieve the abovementioned aim with a higher accuracy, the flexoelectric effect assumes to be existing on the top and bottom face sheets and the core is a composite plate. Also, based on statistics, the first-order shear deformation theory seems to lead to more accurate results. Therefore, in the present research we follow this method to obtain results. The analytical method is applied to solve higher order governing equations. In addition, the critical buckling voltage is calculated considering the flexoelectricity, and it is found that the effects of flexoelectricity play significant roles in determining the critical buckling voltage. Moreover, it is revealed that the thickness of the flexoelectric face sheets and the aspect ratio of the sandwich plate play the same role in critical buckling load variations. It means that the critical buckling load decreases when the thickness of the flexoelectric face sheets or the aspect ratio of the sandwich plate increases and vice versa. The results of the present work can be used for the optimum design and control of similar systems such as micro-electro-mechanical and nano-electromechanical devices.

scholarly journals ELASTOSTATIC BENDING OF A 2D-FGSW BEAM UNDER NONUNIFORM DISTRIBUTED LOADS

2019 ◽  
Vol 57 (3) ◽  
pp. 381
Author(s):  
Nguyen Van Chinh ◽  
Le Cung Inh ◽  
Le Thi Ngoc Anh
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Functionally Graded ◽  
Material Distribution ◽  
Distributed Load ◽  
Bending Behavior ◽  
Loading Type

Elastostatic bending behavior of a two-directional functionally graded sandwich (2D-FGSW) beam under various types of nonuniform distributed load is studied.  Based on a 3D-quasi shear deformation theory, a finite element model is derived and employed in the study. Elastostatic response of the beam is computed for the beam with different boundary conditions and aspect ratio. The effects of the material distribution and the loading type on the deflections and stresses distribution are investigated and highlighted.  The influence of the aspect ratio on the behavior of the beam is also examined and discussed.

scholarly journals Free Vibration of Annular Circular Plates Based on Higher-Order Shear Deformation Theory: A Spline Approximation Technique

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Saira Javed ◽  
F. H. H. Al Mukahal
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Spline Approximation ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Approximation Technique ◽  
Circular Plates ◽  
Equilibrium Equations ◽  
Material Parameters

This research is based on higher-order shear deformation theory to analyse the free vibration of composite annular circular plates using the spline approximation technique. Equilibrium equations are derived, and differential equations in terms of displacement and rotational functions are obtained. Cubic or quantic spline is used to approximate the displacement and rotational functions depending upon the order of these functions. A generalized eigenvalue problem is obtained and solved numerically for eigenfrequency parameter and associated eigenvector of spline coefficients. Frequency of annular circular plates with different numbers of layers with each layer consisting of different materials is analysed. The effect of geometric and material parameters on frequency value is investigated for simply supported condition. A comparative study with existing results narrates the validity of the present results. Graphs and tables depict the obtained results. Some figures and graphs are drawn by using Autodesk Maya and Matlab software.

Free Vibration of Cross-Ply Laminated Plates with Variable Thickness Based on Shear Deformation Theory

2016 ◽  
Vol 13 (03) ◽  
pp. 1650016 ◽  
Author(s):  
K. K. Viswanathan ◽  
Z. A. Aziz ◽  
Saira Javed ◽  
Shaharuddin Salleh ◽  
Siti Aisyah Binti Tumiran ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Free Vibration ◽  
Variable Thickness ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Frequency Parameter ◽  
Laminated Plates ◽  
Simply Supported ◽  
Thickness Variations ◽  
Plates Of Variable Thickness

Free vibration of laminated cross-ply plates of variable thickness including transverse problem is solved numerically to obtain eigenvalues as frequency parameter and associated eigenvectors which are spline coefficients. The variation of frequency parameters with respect to the aspect ratio, side-to-thickness ratio, ply-angle, number of layer and thickness variations for two different materials under simply supported boundary conditions are analyzed.

scholarly journals Free Vibration of Composite Cylindrical Shells Based on Third-Order Shear Deformation Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Muneerah Saad AL Nuwairan ◽  
Saira Javed
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Cylindrical Shells ◽  
Spline Approximation ◽  
Shear Deformation Theory ◽  
Mode Shapes ◽  
Present Formulation ◽  
Third Order ◽  
Node Number

The focus of this study is to analyse the free vibration of cylindrical shells under third-order shear deformation theory (TSDT). The constitutive equations of the cylindrical shells are obtained using third-order shear deformation theory (TSDT). The surface and traverse displacements are expected to have cubic and quadratic variation. Spline approximation is used to approximate the displacements and transverse rotations. The resulting generalized eigenvalue problem is solved for the frequency parameter to get as many eigenfrequencies as required starting from the least. From the eigenvectors, the spline coefficients are computed from which the mode shapes are constructed. The frequency of cylindrical shells is analysed by varying circumferential node number, length dimension, layer number, and different materials. The authenticity of the present formulation is established by comparing with the available FEM results.

Size-Dependent Vibration of Axially Moving Viscoelastic Micro-Plates Based on Sinusoidal Shear Deformation Theory

2017 ◽  
Vol 09 (02) ◽  
pp. 1750026 ◽  
Author(s):  
Ali Ghorbanpour Arani ◽  
Elham Haghparast
Keyword(s):  
Aspect Ratio ◽  
Size Effect ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Modified Couple Stress Theory ◽  
Axially Moving ◽  
Sinusoidal Shear Deformation Theory

In the present research, vibration and instability of axially moving viscoelastic micro-plate is investigated. Sinusoidal shear deformation theory (SSDT) is utilized due to its accuracy of polynomial functions than other plate theories. Based on Kelvin’s model, the viscoelastic structural properties of micro-plate are taken into consideration. The modified couple stress theory (MCST) is employed because of its capability to interpret the size effect. Using Hamilton’s principle, equations of motion are obtained and solved by hybrid analytical–numerical solution at different boundary conditions. Influences of various parameters such as size effect, axially moving speed, viscoelastic structural damping coefficient, thickness and aspect ratio on the vibration characteristics of moving viscoelastic micro-plate are discussed in detail. The results indicated that the critical speed of moving micro-plate is strongly dependent on the aspect ratio, therefore, the low aspect ratio should be considered for optimum design of this kind of moving micro-devices. The results of this investigation can be used in design and manufacturing of axially moving systems at the micro-scale such as micro-magnetic tapes.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

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