A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets

2020 ◽  
Vol 245 ◽  
pp. 112321 ◽  
Author(s):  
Quang Huan Nguyen ◽  
Lieu B. Nguyen ◽  
Hoang B. Nguyen ◽  
H. Nguyen-Xuan
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
High Order ◽  
Instability Analysis ◽  
Graphene Platelets

scholarly journals An isogeometric formulation with a three-variable high order shear deformation theory for free vibration analysis of FG porous plates reinforced by graphene platelets

2021 ◽  
Vol 15 (2) ◽  
pp. 51-66
Author(s):  
Lieu B. Nguyen ◽  
Thi Bui Viet ◽  
Hong-Yen Nguyen
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Isogeometric Analysis ◽  
Deformation Theory ◽  
Porous Plate ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
High Order ◽  
Graphene Platelets

We present a generalized three-variable high order shear deformation theory (THSDT) using isogeometric analysis (IGA) to analyze free vibration of functionally graded porous (FGP) plates reinforced by graphene platelets (GPLs) in this work. It is named as FGP-GPLs for a short. The proposed theory only has got three degrees of freedom (DOFs) per node as the same way of numerically solutions in three-dimensional (3D) solids. THSDT fulfills the classical plate theory (CPT), the first-order shear deformation theory (FSDT) and even the higher-order shear deformation theory (HSDT). IGA is chosen to analyze because of its noteworthy advantages in numerical computational sides of plate problems. In addition, the displacement field of THSDT needs the high continuity in approximated formulation with high-order derivatives for a weak form of fourth order equation. According to IGA formulation based on the generalized THSDT, the shear locking phenomenon is free. The variables of THSDT are less than HSDTs which contain five DOFs per node. The influences of weight fractions, the coefficient porosity, dispersion patterns of GPLs and distribution types of porosity on structure’s natural frequencies are studied through some numerical examples. In order to prove the reliability and accuracy of present method, the numerical results are compared to available published works. Keywords: FG-porous plate; graphene platelet reinforcements; three-variable high order shear deformation theory (THSDT); isogeometric analysis; free vibration.

scholarly journals Vibration Characteristics Analysis of Composite Laminated Annular/Circular Plate Using High-Order Shear Deformation Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Guodong Jin ◽  
Lei Ma ◽  
Hong Zhang ◽  
Qingshan Wang
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Circular Plate ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
High Order ◽  
Laminated Plate ◽  
Circular Plates ◽  
Elastic Boundary

In this paper, the free vibration behaviors of composite laminated annular and circular plates under complex elastic boundary constraints are investigated. Firstly, Reddy’s high-order shear deformation theory (HSDT) and Jacobi polynomial method are effectively combined to establish the unified vibration analysis model of composite laminated annular and circular plates. Secondly, the simulation of complex elastic boundary and coupling boundary is realized by using artificial virtual spring technology. Then, the energy equation of the composite laminated plate is established by using Rayleigh–Ritz energy technology. Finally, the free vibration solution equation of the laminated plate is obtained through the Hamilton differential principle. The fast and uniform convergence of this method and the accuracy of the calculated results are verified by numerical examples and the model experimental method. On this basis, the parameterization study is conducted, and the effects of material parameters, geometric parameters, spring stiffness values, and lamination scheme on the vibration characteristics of the annular or circular plate are fully discussed, which can provide a theoretical basis for future research.

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

scholarly journals Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory

2021 ◽  
pp. 1-11
Author(s):  
Param D. Gajbhiye ◽  
Vishisht Bhaiya ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Shear Mode ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Thickness Shear

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.

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