A shear deformable conical shell formulation in the framework of couple stress theory

Zeighampour, Hamid; Beni, Yaghoub Tadi; Mehralian, Fahimeh

doi:10.1007/s00707-015-1318-2

Cited by 48 publications

(13 citation statements)

References 57 publications

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“…For the first time, couple stress theory was presented by Mindlin in 1962 [39]. So far, many scientists have studied the behavior of nanoscale elements using this theory [40][41][42][43][44]. Chen and Yang [45] developed the couple stress theory for anisotropic behavior.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent vibration analysis of graphene-PMMA lamina based on non-classical continuum theory

Zeverdejani

Beni

2019

Science and Engineering of Composite Materials

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This paper studies the free vibration of polymer nanocomposite reinforced by graphene sheet. In this work, the new size dependent formulation is presented for nanocomposites based on couple stress theory. For this purpose, the first shear deformation theory is applied. The effect of scale parameter is investigated based on anisotropic couple stress theory. Vibration equations of the composite lamina are extracted using Hamilton’s principle. Numerical results are provided for Poly methyl methacrylate/graphene composite.Mechanical properties of the composite are obtained from molecular dynamics simulation. Based on eigenvalue procedure, an analytical solution is obtained for the natural frequency of composite lamina. In the results section, the effect of dimensional and physical parameters are investigated on lamina natural frequency. It is observed that graphene defects caused to diminish the lamina frequency. Furthermore, it is revealed that the increase in graphene volume fraction leads to natural frequency be greater.

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Section: Introductionmentioning

confidence: 99%

Size-dependent vibration analysis of graphene-PMMA lamina based on non-classical continuum theory

Zeverdejani

Beni

2019

Science and Engineering of Composite Materials

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“…Therefore, researchers have recently begun to use continuum theories which take the effect of material length scale (MLS) parameter into consideration. Those theories include non-local elasticity theory [1][2][3][4][5][6][7][8], couple stress theory [9][10][11][12][13][14][15][16][17][18], strain gradient theory [19][20][21][22], and surface stress theory [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Size-dependent vibration of sandwich cylindrical nanoshells with functionally graded material based on the couple stress theory

Zeighampour

Shojaeian

2017

J Braz. Soc. Mech. Sci. Eng.

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Vibration of functionally graded sandwich (FGS) cylindrical nanoshell is investigated. For this purpose, the first shear deformable shell theory as well as material length scale parameter as considered by the couple stress theory is used, and Hamilton's principle is employed to derive the equations of motion of the FGS cylindrical nanoshell and the boundary conditions. In the end, using Navier solution, the natural frequency is determined for three types of FGS cylindrical nanoshells. Results of the new model are compared with the classical theory. According to the results, the rigidity of the FGS cylindrical nanoshell in the couple stress theory is higher than that in the classical theory, which leads to increased natural frequency. Besides, the effect of the material length scale parameter on natural frequency of the FGS cylindrical nanoshell in different wavenumbers and lengths is considerable.

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“…By substituting equation (16) into equation (15), the final equation for kinetic energy of CNT is obtained as follows…”

Section: Couple Stress Theory For Anisotropic Cylindrical Shellmentioning

confidence: 99%

“…Elements for modeling nanostructures include nano-beams, nano-discs, and nano-shells. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] Carbon nanotube (CNT) is one of the most commonly used elements in nanostructures which are used in a variety of composite materials and nano systems. CNTs are hollow cylinder made of the convolution of graphene sheets around an axis.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

Beni

Mehralian

Zeverdejani

2017

Journal of Low Frequency Noise, Vibration and Active Control

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In the present work, using the couple stress theory, a new model is provided for vibrating behavior of anisotropic carbon nanotubes. Carbon nanotubes have many applications, and careful analysis of their behavior is important. So far, using the isotropic models, several studies have been conducted on carbon nanotube vibration. According to the arrangement of carbon atoms on the nanotube walls, their properties will be different in various directions. Therefore, the behavior of carbon nanotubes must be considered as anisotropic materials. In this article, initially, using the Hamilton's principle, motion equations, and boundary conditions of carbon nanotubes are extracted based on couple stress theory. Afterwards, the equations are solved using the analytical solution method. In the results section, the effect of different parameters, particularly the anisotropic effect, on the carbon nanotube natural frequency is investigated.

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A shear deformable conical shell formulation in the framework of couple stress theory

Cited by 48 publications

References 57 publications

Size-dependent vibration analysis of graphene-PMMA lamina based on non-classical continuum theory

Size-dependent vibration analysis of graphene-PMMA lamina based on non-classical continuum theory

Size-dependent vibration of sandwich cylindrical nanoshells with functionally graded material based on the couple stress theory

Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

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