On the size-dependent behavior of functionally graded micro-beams

Asghari, Mohsen; Ahmadian, Mohammad Taghi; Kahrobaiyan, M. H.; Rahaeifard, M.

doi:10.1016/j.matdes.2009.12.006

Cited by 338 publications

(97 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…On the other hand, many researches showed that in micro and nano scales the materials have strong size dependence in deformation behavior (Papargyri-Beskou et al, 2003;Lazopoulos and Lazopoulos, 2010;Asghari et al, 2010;Park and Gao, 2006;Fu and Zhang, 2011;Kong et al, 2008Kong et al, , 2009Fathalilou et al, 2011). Size-dependent behavior is an inherent property of materials, which appears for a beam when the characteristic size such as thickness or diameter is close to the internal length-scale parameter of materials .…”

Section: Introductionmentioning

confidence: 99%

“…Recently, some researchers have applied the non-classic theories of elasticity to study the mechanical behavior of electrostatically actuated micro and nano beams Asghari et al, 2010;Fu and Zhang, 2011;Kong et al, 2008Kong et al, , 2009Fathalilou et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Gap Dependent Bifurcation Behavior of a Nano-Beam Subjected to a Nonlinear Electrostatic Pressure

Fathalilou

Sadeghi

Rezazadeh

2014

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

This paper presents a study on the gap dependent bifurcation behavior of an electro statically-actuated nano-beam. The sizedependent behavior of the beam was taken into account by applying the couple stress theory. Two small and large gap distance regimes have been considered in which the intermolecular vdW and Casimir forces are dominant, respectively. It has been shown that changing the gap size can affect the fundamental frequency of the beam. The bifurcation diagrams for small gap distance revealed that by changing the gap size, the number and type of the fixed points can change. However, for large gap regime, where the Casimir force is the dominant intermolecular force, changing the gap size does not affect the quality of the bifurcation behavior.

show abstract

On the size-dependent behavior of functionally graded micro-beams

Cited by 338 publications

References 25 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

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

Gap Dependent Bifurcation Behavior of a Nano-Beam Subjected to a Nonlinear Electrostatic Pressure

Contact Info

Product

Resources

About