Natural frequency analysis of continuously graded carbon nanotube-reinforced cylindrical shells based on third-order shear deformation theory

Aragh, B. Sobhani; Farahani, E. Borzabadi; Barati, AH Nasrollah

doi:10.1177/1081286512438794

Cited by 36 publications

(14 citation statements)

References 60 publications

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“…Liang Ke et al investigated the nonlinear free vibration of FG‐CNTRC beam based on Timoshenko theory which the CNTs distribution was assumed to be graded in the thickness direction and was estimated though the rule of mixture. Based on the Eshelby–Mori–Tanaka approach and using generalized differential quadrature method (GDQM) approach, Aragh et al carried out the frequencies analysis of a FG‐CNTRC cylindrical panels. In this research, the CNTs were distributed in the thickness and radial direction .…”

Section: Introductionmentioning

confidence: 99%

Low velocity impact analysis of an axially functionally graded carbon nanotube reinforced cantilever beam

Ranjbar

Feli

2017

Polymer Composites

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In this article, a new analytical model is presented for low velocity impact on an axially functionally graded (AFG) carbon nanotube (CNT) reinforced cantilever beam. In order to estimate the material properties of the composite media, the refined rule of mixtures approach containing the efficiency parameters is employed. Based on the third order shear deformation beam theory, the beam deformation is formulated and the contact force is obtained with the aid of the nonlinear Hertz contact law. To derive the equations of motion, energy method with combining the polynomial Ritz method and generalized Lagrange equations are employed. To validate the accuracy of the analytical model, the convergence and comparison studies are carried out with those are reported in the literature in the special cases and simulating the process with ABAQUS software. Afterward, the influences of CNTs distribution, CNTs volume fraction, impact position, impactor initial velocity, and beam geometrical parameters on the contact force and beam deflection at the impact position are studied in detail. POLYM. COMPOS., 39:E969–E983, 2018. © 2017 Society of Plastics Engineers

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Section: Introductionmentioning

confidence: 99%

Low velocity impact analysis of an axially functionally graded carbon nanotube reinforced cantilever beam

Ranjbar

Feli

2017

Polymer Composites

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“…Hence, to examine the same, many attempts have already been made in the past to reveal the effective material properties of CNTRC via various theoretical, experimental, and simulation methodologies, such as molecular dynamic simulation, [18,19] the representative volume element method, [20] and the rule of mixture, [21][22][23][24][25][26] Mori-Tanaka, [27,28] Halpin-Tsai. Consequently, analysis of the structural responses, such as fundamental frequency, deflection, and the buckling strength of the CNTRC beams, [34,35] flat panels [36][37][38] , and curved shell panel [39][40][41][42] are recognized as the motivational research in the recent years. [33] Further, to achieve the effective material properties, for the first time, Shen [22] employed the concept of functionally grading of CNT distribution in the matrix and investigated the nonlinear static deflections of the CNTRC plate.…”

Section: Introductionmentioning

confidence: 99%

Elastic bending and stress analysis of carbon nanotube‐reinforced composite plate: Experimental, numerical, and simulation

Mehar

Panda

2017

Adv Polym Technol

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The deflection behavior of carbon nanotube-reinforced composite plate is investigated numerically using the finite-element method and the result accuracy is established via three-point experimental bending test data. The physical composite panel model is realized with the help of new mathematical model based on the higher order kinematic theory and the responses are computed using the in-house computer code in the MATLAB environment. Further, the efficacy of the current higher order finite-element model has been established by comparing the deflection responses with those of the references, simulation values (ANSYS), and the in-house experimentation including the experimental elastic properties. Finally, the effect of different design parameters,such as aspect ratio, thickness ratio, edge constraints including the types of load on the deflection and stress responses of the composite plate has been studied in detail. K E Y W O R D Scarbon nanotube, elastic bending, experimental mechanics, finite element method, higher order shear deformation theory, simulation

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“…Similarly to the theory of laminated and composite beams [83][84][85][86][87][88][89][90] the literature is very rich in the different theories to model laminated composite plates and shells. Thin flat plates can be modeled by the classical or Kirchhoff plate theory, 91,92 while for relatively thick plates the first-order shear deformation theory (FSDT or Mindlin), [93][94][95][96][97][98][99][100] second-order shear deformation theory (SSDT), [101][102][103][104][105] general third-order theory (TSDT), [106][107][108] Reddy third-order theory, [109][110][111][112] other higher-order shear deformation theories (HSDT), [113][114][115] layerwise theories, [116][117][118][119][120][121] and the 3D elasticity solutions 122,123 are developed. These theories have been utilized to model curved shells [124][125][126] and delaminated and cracked laminates …”

Section: Department Of Applied Mechanics Budapest University Of Techmentioning

confidence: 99%

Natural vibration-induced parametric excitation in delaminated Kirchhoff plates

Szekrényes

2015

Journal of Composite Materials

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This paper revisits the problem of free vibration of delaminated composite plates with Lévy type boundary conditions. The governing equations are derived for laminated Kirchhoff plates including through-width delamination. The plate is divided into two subplates in the plane of the delamination. The kinematic continuity of the undelaminated part is established by using the system of exact kinematic conditions. The free vibration analysis of orthotropic simply supported Lévy plates reveals that the delaminated parts are subjected to periodic normal and in-plane shear forces. This effect induces parametric excitation leading to the susceptibility of the plates to dynamic delamination buckling during the vibration. An important aspect is that depending on the vibration mode the internal forces have a two-dimensional distribution in the plane of the delamination. To solve the dynamic stability problem the finite element matrices of the delaminated parts are developed. The distribution of the internal forces in the direction of the delamination front was considered. The mode shapes including a half-wave along the width of the plate accompanied by delamination buckling are shown based on the subsequent superimposition of the buckling eigenshapes. The analysis reveals that the vibration phenomenon is amplitude dependent. Also, the phase plane portraits are created for some chosen cases showing some special trajectories. KeywordsDelamination, free vibration, laminated plate theory, dynamic stability, parametric excitation, harmonic balance, finite element method IntroductionDelaminations are typical defects in composite and sandwich structures induced by indentations (e.g. local loading by spherical indentors), 1,2 low-velocity impact and free edge effects (normal and shear stress concentration between layers at free edges), 3-6 finally by fabrication defects. 7,8 The cracks and delaminations reduce significantly the strength and stiffness of composite laminates.9-11 The material defects also influence the dynamic behavior of the structures.12-20 One of the widely known dynamic phenomena is parametric excitation, which takes place in machine tools, 21 [73][74][75][76][77][78] and sandwich beams. 79In Burlayenko and Sadowski, 80 the foam/core debonding in sandwich plates was investigated during free vibration. However, the existence of the parametric excitation was not revealed in any of the former papers.To the best of the author's knowledge, the existence of the parametric excitation in the course of free vibration of delaminated composite beams was first revealed in Szekre´nyes 81 and was solved effectively by the FE and harmonic balance methods in Szekre´nyes.82 It was also shown that the delamination buckling takes place only if the free vibration amplitude exceeds the so-called critical amplitude at a specified point of the beam. The existence of the critical amplitude was also proved experimentally. The parametric excitation in delaminated plates is possible to appear, as well. 9,10,[127][128][129] subseq...

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Natural frequency analysis of continuously graded carbon nanotube-reinforced cylindrical shells based on third-order shear deformation theory

Cited by 36 publications

References 60 publications

Low velocity impact analysis of an axially functionally graded carbon nanotube reinforced cantilever beam

Low velocity impact analysis of an axially functionally graded carbon nanotube reinforced cantilever beam

Elastic bending and stress analysis of carbon nanotube‐reinforced composite plate: Experimental, numerical, and simulation

Natural vibration-induced parametric excitation in delaminated Kirchhoff plates

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