Static Torsion of Bi-Directional Functionally Graded Microtube Based on the Couple Stress Theory Under Magnetic Field

This paper presents is a solution for static torsion in a microtube made of bi-directional functionally graded materials (BDFGMs). The material properties are assumed to vary according to the arbitrary function along radius and length of microtube. As for the torque effect of the axial magnetic field, the well-known Maxwell’s relation is used. Couple stress theory is employed to study the influence of small-scale on static torsion of microtube. The Navier equation and boundary conditions of the size-dependent BDFG microtube were derived by the minimum potential energy. These equations were solved by employing the generalized differential quadrature method (GDQM). Comparison between the results of this work with the analytical method for static torsion of microtube made of one direction FG material reveals the accuracy of this study. Finally, numerical results are presented to study the small-scale effect and heterogeneity constants on the static torsion of the bi-directional functionally graded microtube.

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Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406216653622 ◽

2016 ◽

Vol 231 (20) ◽

pp. 3866-3885 ◽

Cited By ~ 21

Author(s):

M Mohammadimehr ◽

S Shahedi ◽

B Rousta Navi

Keyword(s):

Magnetic Field ◽

Couple Stress ◽

Longitudinal Magnetic Field ◽

Couple Stress Theory ◽

Differential Quadrature Method ◽

Sandwich Beam ◽

Modified Couple Stress Theory ◽

Stress Theory ◽

Modified Couple Stress ◽

Generalized Differential

In this paper, the magneto-mechanical nonlinear vibration behavior of rectangular functionally graded carbon nanotube reinforced composite (FG-CNTRC) sandwich Timoshenko beam based on modified couple stress theory (MCST) is investigated by the generalized differential quadrature method. The FG-CNTRC sandwich beam consists of two FG-CNTRC face sheets and homogenous core subjected to longitudinal magnetic field. In the FG-CNTRC face sheets, carbon nanotubes are disseminated in different patterns as uniform distribution, FG-X, FG-V, and FG-O. Based on von Kármán geometric nonlinearity, the nonlinear governing equations are derived by the Hamilton’s principle. Accuracy and convergence of this study are validated by comparing the numerical results with those found in literature. Various parameters effects are examined on the nonlinear 1st frequency of the sandwich beam. The results reveal that composition of the CNTRC face sheets and homogenous core in sandwich beam can be achieved remarkable stiffness in comparison to only CNTRC beam or only homogenous beam. For achieving the highest stiffness of FG-CNTRC sandwich beam, the value of thickness ratio is obtained about 0.34 and 0.27 in the presence and absence of Pasternak foundation, respectively. Moreover, the linear and nonlinear 1st frequencies increase with an increase in the magnetic field for all of CNT distribution types of sandwich beam and different boundary conditions whereas the frequency ratio decreases. Also the highest and lowest nonlinear 1st frequencies are corresponding to FG-A and FG-V distributions of CNT in face sheets, respectively.

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Analysis of Lamb wave propagation in a functionally graded piezoelectric small-scale plate based on the modified couple stress theory

Composite Structures ◽

10.1016/j.compstruct.2021.113733 ◽

2021 ◽

pp. 113733

Author(s):

Cancan Liu ◽

Jiangong Yu ◽

Bo Zhang ◽

Xiaoming Zhang ◽

L. Elmaimouni

Keyword(s):

Wave Propagation ◽

Couple Stress ◽

Couple Stress Theory ◽

Modified Couple Stress Theory ◽

Functionally Graded ◽

Small Scale ◽

Stress Theory ◽

Modified Couple Stress ◽

Functionally Graded Piezoelectric ◽

Lamb Wave Propagation

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Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale Timoshenko beam

Journal of Vibration and Control ◽

10.1177/1077546317721871 ◽

2017 ◽

Vol 24 (18) ◽

pp. 4211-4225 ◽

Cited By ~ 17

Author(s):

Seyed Sajad Mirjavadi ◽

Behzad Mohasel Afshari ◽

Navvab Shafiei ◽

Samira Rabby ◽

Mohammad Kazemi

Keyword(s):

Timoshenko Beam ◽

Couple Stress Theory ◽

Differential Quadrature Method ◽

Beam Theory ◽

Functionally Graded ◽

Effect Of Temperature ◽

Two Dimensional ◽

Stress Theory ◽

Micro Scale ◽

Generalized Differential

This work is aimed to present analysis on the thermal vibrational behavior of two-dimensional functionally graded porous microbeams based on Timoshenko beam theory. According to the power law function, the material composition and so the material properties are varying along thickness and axis of the microbeam. The governing equations are derived on the basis of the couple stress theory and the generalized differential quadrature method is used to solve the equations. The temperature gradient is considered to be uniform and nonuniform across the thickness of the microbeam. The results are presented to show the effect of temperature change, porosity, functionally graded and axially functionally graded power indexes and also micro-scale parameter on the vibration of the microbeam.

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