The modified couple stress functionally graded Timoshenko beam formulation

Asghari, Mohsen; Rahaeifard, M.; Kahrobaiyan, M. H.; Ahmadian, M.T.

doi:10.1016/j.matdes.2010.08.046

Cited by 282 publications

(86 citation statements)

References 27 publications

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“…The modi ed couple stress formulations of functionally graded Euler-Bernoulli and Timoshenko beams were developed by Asghari et al [26,27]. The modi ed couple stress-based formulation of laminated Timoshenko beams was developed by Chen and Li [28].…”

Section: Introductionmentioning

confidence: 99%

Effect of size dependency on in-plane vibration of circular micro-rings

2017

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KEYWORDSMicro-ring; Modi ed couple stress theory; Resonant frequency.Abstract. In this paper, based on the modi ed couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-classical Euler-Bernoulli and Timoshenko beam theories. The ndings are compared with classical beam theories. Response of the micro-ring under application of static and dynamic loads is investigated and compared with the classical theories. Results show that when the thickness of the ring is in the order of the length scale of the ring material, the natural frequencies evaluated using the modi ed couple stress are considerably more than those predicted based on the classical beam theories, while the de ection and natural frequencies of the classical and non-classical beam theories approach one another for the rings with thickness much larger than the material length scale.

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Section: Introductionmentioning

confidence: 99%

Effect of size dependency on in-plane vibration of circular micro-rings

2017

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“…In the modified couple-stress theory, the strain energy density for an elastic material in the infinitesimal deformation is introduced as (Yang et al, 2002;Asghari et al, 2011) 1 : ( )…”

Section: Governing Equations Based On the Modified Couple-stress Theorymentioning

confidence: 99%

Analytical Couple-stress Solution for Size-dependent Large-amplitude Vibrations of FG Tapered-nanobeams

Baghani

Mohammadsalehi

Dabaghian

2016

Lat. Am. j. solids struct.

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In this paper, analytical couple-stress solution for size-dependent large-amplitude vibrations of FG (functionally-graded) taperednanobeams is presented. Using the modified couple-stress theory, the small scale effects are accounted for. Employing the Homotopy-Pade Analysis Method, efficient and accurate analytical expressions for the deflection and non-linear frequencies of the both single and double tapered nanobeam are presented. Very good agreement is observed between the present work results and some available results reported in the literature. This study may be helpful to investigate the size-dependent mechanical properties of MEMS\NEMS. Therefore, the proposed analytical solution can be used as an efficient tool for the material or geometrical parametric studies of small scale devices consisting of beams for their design and optimization which involves a large number of simulations.

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“…Also, Asghari et al [25,26] investigated the size-dependent behavior of FGM micro beams using the modified couple stress theory and the Euler-Bernoulli and Timoshenko beam models. Sadeghi et al [27] examined strain gradient elasticity formulation for analysis of FGM micro-cylinders.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of functionally graded stiffened micro-cylinder based on the modified couple stress theory

Jabbarian

Ahmadian

2017

Scientia Iranica

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Abstract. In this paper, free vibration of the micro-cylinder made by functionally graded material that is stiffened in circumferential direction, has been investigated based on the modified couple stress and first order shear deformation theories. Modified couple stress theory (MCST) has been used to catch size effects in micro scales. By using first order shear deformation theory and Hamilton principle, general equations of motion and corresponding boundary conditions have been derived. Free vibration of the structure has been investigated by implementing simply supported boundary condition as a common case. The effects of different parameters such as dimensionless length scale parameter, distribution of FGM properties, number of stiffeners, thickness and length on the natural frequencies were calculated and compared with classical continuum theory. Results show that effects of the size are considerable and also using stiffeners lead to increase in natural frequencies which is because of increase in stiffness of the cylinder.

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The modified couple stress functionally graded Timoshenko beam formulation

Cited by 282 publications

References 27 publications

Effect of size dependency on in-plane vibration of circular micro-rings

Effect of size dependency on in-plane vibration of circular micro-rings

Analytical Couple-stress Solution for Size-dependent Large-amplitude Vibrations of FG Tapered-nanobeams

Free vibration analysis of functionally graded stiffened micro-cylinder based on the modified couple stress theory

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