Large deflection geometrically nonlinear bending of sandwich beams with flexible core and nanocomposite face sheets reinforced by nonuniformly distributed graphene platelets

2019 ◽  
Vol 22 (3) ◽  
pp. 866-895 ◽  
Author(s):  
S Jedari Salami
Keyword(s):  
Sandwich Panel ◽  
Sandwich Beam ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Face Sheet ◽  
Sandwich Beams ◽  
Nonlinear Bending ◽  
Graphene Platelet ◽  
The Face ◽  
Graphene Platelets

This study investigates the nonlinear bending response of a novel class of sandwich beams with flexible core and face sheets reinforced with graphene platelets that are functionally graded distributed through the thickness. Nonlinear governing equations are established based on extended high-order sandwich panel theory and Von Kármán type of geometrical nonlinearity. In this theory, the face sheets follow the first-order shear deformation theory, and the two-dimensional elasticity is adopted for the core. These nonlinear differential equations are discretized into algebraic systems by means of the Ritz-based method from which the static bending solution can be achieved. The effective Young’s modulus of functionally graded graphene platelet-reinforced composite (GPLRC) face sheets is determined through the modified Halpin–Tsai micromechanics model, and associated Poisson’s ratio is evaluated by employing the rule of mixture. Comparison studies are provided for a sandwich beam with graphene-reinforced face sheets and conventional nanocomposite beam reinforced by graphene platelets due to lack of results for introduced sandwich beams. Besides, three-point bending test was carried out in order to assure the validity of nonlinear bending analysis of a sandwich beam based on extended high-order sandwich panel theory. Afterwards, parametric studies are given to examine the influences of graphene platelet distribution pattern, weight fraction, and core-to-face sheet thickness ratio together with the total number of layers on the linear and nonlinear bending performances of the sandwich beams. Numerical results demonstrate that distributing more graphene platelets near the upper and lower surface layers of the face sheets, named X-GPLRC, is capable to improve the bending strength and decrease the local deflection of the top face sheet, and this recovery effect becomes more significant as graphene platelet weight fraction increases. The results also reveal that the graphene platelet distribution pattern of the face sheets plays an important role to decrease the transverse shear stress of the core by dispersing more graphene platelets near surfaces of the face sheets (X-GPLRC). So, reducing the local deflection of the top face sheet tends to be much more safety of the soft core from any failure. Besides, sandwich beams with a lower weight fraction of graphene platelets in face sheets that are symmetrically distributed in such a way, called O-GPLRC, are also less sensitive to the nonlinear deformation.

Free vibration analysis of sandwich beams with carbon nanotube reinforced face sheets based on extended high-order sandwich panel theory

2016 ◽  
Vol 20 (2) ◽  
pp. 219-248 ◽  
Author(s):  
S Jedari Salami
Keyword(s):  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Sandwich Panel ◽  
Sandwich Beam ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
High Order ◽  
Reinforced Composite ◽  
The Face ◽  
Composite Face

Free vibration analysis of a sandwich beam with soft core and carbon nanotube reinforced composite face sheets, hitherto not reported in the literature, based on extended high-order sandwich panel theory is presented. Distribution of fibers through the thickness of the face sheets could be uniform or functionally graded. In this theory, the face sheets follow the first-order shear deformation theory. Besides, the two-dimensional elasticity is used for the core. The field equations are derived via the Ritz-based solution which is suitable for any essential boundary conditions. Chebyshev polynomials multiplying boundary R-functions are used as admissible functions and evidence of their good performance is given. A detailed parametric study is conducted to study the effects of nanotube volume fraction and their distribution pattern, core-to-face sheet thickness ratio, and boundary conditions on the natural frequencies and mode shapes of sandwich beams with functionally graded carbon nanotube reinforced composite face sheets and soft cores. Since the extended high-order sandwich panel theory can be used with any combinations of core and face sheets and not only the soft cores that the other theories demand, the results for the same beam with functionally graded carbon nanotube reinforced composite face sheets and stiff core are also provided for comparison. It is concluded that the sandwich beam with X and V distribution figures of face sheets, no matter what the boundary conditions, has higher vibration performance than the beam with UD-CNTRC face sheets.

scholarly journals Fundamental Frequency Analysis of Sandwich Beams with Functionally Graded Face and Metallic Foam Core

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Lin Mu ◽  
Guiping Zhao
Keyword(s):  
Fundamental Frequency ◽  
Plate Theory ◽  
Order Theory ◽  
Functionally Graded ◽  
Face Sheet ◽  
Metallic Foam ◽  
Sandwich Beams ◽  
Classical Plate Theory ◽  
The Core ◽  
The Face

This study is interested in assessing a way to analyze fundamental frequency of sandwich beams with functionally graded face sheet and homogeneous core. The face sheet, which is an exponentially graded material (EGM) varying smoothly in the thickness direction only, is composed of a mixture of metal and ceramic. The core which is made of foam metal is homogeneous. The classical plate theory (CPT) is used to analyze the face sheet and a higher-order theory (HOT) is used to analyze the core of sandwich beams, in which both the transverse normal and shear strains of the core are considered. The extended Galerkin method is used to solve the governing equations to obtain the vibration equations of the sandwich beams suitable for numerical analysis. The fundamental frequency obtained by the theoretical model is validated by using the finite element code ABAQUS and comparison with earlier works. The influences of material and geometric properties on the fundamental frequency of the sandwich beams are analyzed.

Analytical Solution for Free Vibration of Sandwich Structures with a Functionally Graded Syntactic Foam Core

2010 ◽  
Vol 636-637 ◽  
pp. 1143-1149 ◽  
Author(s):  
O. Rahmani ◽  
K. Malekzadeh ◽  
S. Mohammad ◽  
R. Khalili
Keyword(s):  
Free Vibration ◽  
Sandwich Panel ◽  
Sandwich Structures ◽  
Numerical Study ◽  
Sandwich Beam ◽  
Syntactic Foam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Foam Core ◽  
The Face

In this study, after a brief introduction to recent investigations on syntactic foam, the free vibration of sandwich structures with syntactic foam as a functionally graded flexible core based on higher order sandwich panel theory is investigated. The formulation uses the classical beam theory for the face sheets and an elasticity theory for the functionally graded core. In the following a numerical study of free vibration of a simply-supported sandwich beam is carried out and corresponding eigenmodes are obtained.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

2021 ◽  
pp. 095440622110084
Author(s):  
Amin Ghorbani Shenas ◽  
Parviz Malekzadeh ◽  
Sima Ziaee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Natural Frequencies ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Point Mass ◽  
Attached Mass ◽  
Graphene Platelets ◽  
Twisted Beam

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams

2021 ◽  
Vol 2 (110) ◽  
pp. 72-85
Author(s):  
S.H. Bakhy ◽  
M. Al-Waily ◽  
M.A. Al-Shammari
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
Functionally Graded Materials ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Gradient Index ◽  
Sandwich Beams ◽  
Graded Materials ◽  
The Impact

Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.

Design and Characterization of Small-Scale Sandwich Beams Fabricated by Photolithography and Electrodeposition

2000 ◽  
Author(s):  
Yuki Sugimura
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Shear Stiffness ◽  
Open Architecture ◽  
Small Scale ◽  
Sandwich Beams ◽  
The Face ◽  
Micrometer Size

Abstract Small-scale sandwich beams with core structures having cell diameters and wall widths on the order of 500 μm and 100 μm, respectively, have been produced through fabrication methods that combine photolithography and electrodeposition. Two core configurations have been examined: 1) regular hexagonal honeycomb and 2) high-aspect ratio hexagonal shells having an open architecture. The bending response of the sandwich beams has been examined and compared with the beam theory predictions. Shear stiffness of the honeycomb core was considerably high and therefore the bending behavior was dominated by the face sheets. The bending of the sandwich specimens with the hexagonal shells, on the other hand, was largely dependent on the core. The sandwich beam dimensions investigated in this study have not been optimized for weight minimization and structural efficiency. Further advances in fabrication methods to produce micrometer-size features and high-aspect ratio cores will enable realization of structurally efficient, lightweight sandwich beams and panels that can be used as multifunctional components in small-scale devices.

scholarly journals Elasticity Solutions for In-Plane Free Vibration of FG-GPLRC Circular Arches with Various End Conditions

2020 ◽  
Vol 10 (14) ◽  
pp. 4695
Author(s):  
Dongying Liu ◽  
Jing Sun ◽  
Linhua Lan
Keyword(s):  
Free Vibration ◽  
Weight Fraction ◽  
Distribution Patterns ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Scaled Model ◽  
Circular Arch ◽  
End Conditions ◽  
Elasticity Solutions ◽  
Graphene Platelets

In-plane free vibration of functionally graded graphene platelets reinforced nanocomposites (FG-GPLRCs) circular arches is investigated by using the two-dimensional theory of elasticity. The graphene platelets (GPLs) are dispersed along the thickness direction non-uniformly, and the material properties of the nanocomposites are evaluated by the modified Halpin-Tsai multi-scaled model and the rule of mixtures. A state-space method combined with differential quadrature technique is employed to derive the governing equation for in-plane free vibration of FG-GPLRCs circular arch, the semi-analytical solutions are obtained for various end conditions. An exact solution of FG-GPLRCs circular arch with simply-supported ends is also presented as a benchmark to valid the present numerical method. Numerical examples are performed to study the effects of GPL distribution patterns, weight fraction and dimensions, geometric parameters and boundary conditions of the circular arch on the natural frequency in details.

Three-dimensional static and free vibration analysis of graphene platelet–reinforced porous composite cylindrical shell

2020 ◽  
Vol 26 (19-20) ◽  
pp. 1627-1645 ◽  
Author(s):  
Alireza Rahimi ◽  
Akbar Alibeigloo ◽  
Mehran Safarpour
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Distribution Patterns ◽  
Functionally Graded ◽  
Fourier Series Expansion ◽  
Graphene Platelet ◽  
Vibration Behavior ◽  
Reinforced Composite ◽  
Graphene Platelets

Because of promoted thermomechanical performance of functionally graded graphene platelet–reinforced composite ultralight porous structural components, this article investigates bending and free vibration behavior of functionally graded graphene platelet–reinforced composite porous cylindrical shell based on the theory of elasticity. Effective elasticity modulus of the composite is estimated with the aid of modified version of Halpin–Tsai micromechanics. Rule of mixtures is used to obtain mass density and Poisson’s ratio of the graphene platelet–reinforced composite shell. An analytical solution is introduced to obtain the natural frequencies and static behavior of simply supported cylindrical shell by applying the state-space technique along the radial coordinate and Fourier series expansion along the circumferential and axial direction. In addition, differential quadrature method is used to explore the response of the cylindrical shell in the other cases of boundary conditions. Validity of the applied approach is examined by comparing the numerical results with those published in the available literature. A comprehensive parametric study is conducted on the effects of different combinations of graphene platelets distribution patterns and porosity distribution patterns, boundary conditions, graphene platelets weight fraction, porosity coefficient, and geometry of the shell (such as mid-radius to thickness ratio and length to mid-radius ratio) on the bending and free vibration behavior of the functionally graded graphene platelet–reinforced composite porous cylindrical shell. The results of this study provide useful practical tips for engineers designing composite structures.

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