scholarly journals A Finite Element Formulation and Nonlocal Theory for the Static and Free Vibration Analysis of the Sandwich Functionally Graded Nanoplates Resting on Elastic Foundation

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Van-Ke Tran ◽  
Thanh-Trung Tran ◽  
Minh-Van Phung ◽  
Quoc-Hoa Pham ◽  
Trung Nguyen-Thoi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Material Properties ◽  
Free Vibration Analysis ◽  
Nonlocal Theory ◽  
Functionally Graded ◽  
Element Formulation ◽  
Proposed Model ◽  
Homogeneous Core

This article presents a finite element method (FEM) integrated with the nonlocal theory for analysis of the static bending and free vibration of the sandwich functionally graded (FG) nanoplates resting on the elastic foundation (EF). Material properties of nanoplates are assumed to vary through thickness following two types (Type A with homogeneous core and FG material for upper and lower layers and Type B with FG material core and homogeneous materials for upper and lower layers). In this study, the formulation of the four-node quadrilateral element based on the mixed interpolation of tensorial components (MITC4) is used to avoid “the shear-locking” problem. On the basis of Hamilton’s principle and the nonlocal theory, the governing equations for the sandwich FG nanoplates are derived. The results of the proposed model are compared with published works to verify the accuracy and reliability. Furthermore, the effects of geometric parameters and material properties on the static and free vibration behaviors of nanoplates are investigated in detail.

scholarly journals On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nguyen Van Dung ◽  
Nguyen Chi Tho ◽  
Nguyen Manh Ha ◽  
Vu Trong Hieu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Mechanical Response ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Engineering Practice

Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.

scholarly journals Buckling and Free Vibration Analysis of Laminated Sandwich Beams under Hygrothermal Conditions

2021 ◽  
Vol 2070 (1) ◽  
pp. 012170
Author(s):  
A Garg ◽  
S Gupta ◽  
HD Chalak
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Fourth Order ◽  
Vibration Analysis ◽  
Loading Condition ◽  
Free Vibration Analysis ◽  
Element Formulation ◽  
Sandwich Beams ◽  
Proposed Model ◽  
Zigzag Theory

Abstract In present work, an attempt has been made for carrying out free vibration and buckling analysis of laminated sandwich beams under hygrothermal conditions. The analysis is carried out using fourth order zigzag theory based on finite element formulation. The efficiency of proposed model is validated by comparing the present results with those available in literature. Geometric properties and loading condition widely affect the behavior of the laminated sandwich beams.

scholarly journals Free vibration of FG sandwich plates partially supported by elastic foundation using a quasi-3D finite element formulation

2020 ◽  
Author(s):  
Le Cong Ich ◽  
Pham Vu Nam ◽  
Nguyen Dinh Kien
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Layer Thickness ◽  
Elastic Foundation ◽  
Functionally Graded ◽  
Thickness Ratio ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Sandwich Plates ◽  
Layer Thickness Ratio

Free vibration of functionally graded (FG) sandwich plates partially supported by a Pasternak elastic foundation is studied. The plates consist of three layers, namely a pure ceramic hardcore and two functionally graded skin layers. The effective material properties of the skin layers are considered to vary in the plate thickness by a power gradation law, and they are estimated by Mori--Tanaka scheme. The quasi-3D shear deformation theory, which takes the thickness stretching effect into account, is adopted to formulate a finite element formulation for computing vibration characteristics.  The accuracy of the derived formulation is confirmed through a comparison study. The numerical result reveals that the foundation supporting area plays an important role on the vibration behavior of the plates, and the effect of the layer thickness ratio on the frequencies is governed by the supporting area. A parametric study is carried out to highlight the effects of material distribution, layer thickness ratio, foundation stiffness and area of the foundation support on the frequencies and mode shapes of the plates. The influence of the side-to-thickness ratio on the frequencies of the plates is also examined and discussed.

scholarly journals Finite Element Formulation for the Large-Amplitude Vibrations of FG Beams

2014 ◽  
Vol 61 (3) ◽  
pp. 469-482 ◽  
Author(s):  
Mehdi Javid ◽  
Milad Hemmatnezhad
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Power Law ◽  
Large Amplitude ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Geometrical Parameters ◽  
Element Formulation ◽  
Vibration Frequencies

Abstract On the basis of Euler-Bernoulli beam theory, the large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The von Karman type nonlinear strain-displacement relationship is employed where the ends of the beam are constrained to move axially. The material properties are assumed to be graded in the thickness direction according to the power-law and sigmoid distributions. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law index, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible.

scholarly journals An Edge-Based Smoothed Finite Element for Free Vibration Analysis of Functionally Graded Porous (FGP) Plates on Elastic Foundation Taking into Mass (EFTIM)

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Trung Thanh Tran ◽  
Quoc-Hoa Pham ◽  
Trung Nguyen-Thoi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Mass Parameter ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Triangular Element ◽  
Power Law Distribution ◽  
Edge Based

In this paper, free vibration analysis of the functionally graded porous (FGP) plates on the elastic foundation taking into mass (EFTIM) is presented. The fundamental equations of the FGP plate are derived using Hamilton’s principle. The mixed interpolation of the tensorial components (MITC) approach and the edge-based smoothed finite element method (ES-FEM) is employed to avoid the shear locking as well as to improve the accuracy for the triangular element. The EFTIM is a foundation model based on the two-parameter Winkler–Pasternak model but added a mass parameter of foundation. Materials of the plate are FGP with a power-law distribution and maximum porosity distributions in the forms of cosine functions. Some numerical examples are examined to demonstrate the accuracy and reliability of the proposed method in comparison with those available in the literature.

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