Static and dynamic analysis of micro beams based on strain gradient elasticity theory

Kong, Shengli; Zhou, Shenjie; Nie, Zhifeng; Wang, Kai

doi:10.1016/j.ijengsci.2008.08.008

Cited by 490 publications

(180 citation statements)

References 29 publications

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“…Soon after that, the modified strain gradient elasticity theory attracted many researchers in order to analyze size-dependent structures. For instance, Kong et al [31] predicted the static and dynamic responses of microbeams using modified strain gradient theory within the framework of Euler-Bernoulli beam theory. They revealed that the static deformation obtained by the non-classical continuum theory is generally lower than that of the classical beam model.…”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Resonant Frequency and Flexural Sensitivity of Atomic Force Microscope Microcantilevers Based on the Modified Strain Gradient Theory

Ansari

Pourashraf

Gholami

et al. 2015

International Journal of Optomechatronics

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In the present study, the resonant frequency and flexural sensitivity of atomic force microscope (AFM) microcantilevers are predicted incorporating size effects. To this end, the modified strain gradient elasticity theory is applied to the classical Euler-Bernoulli beam theory to develop a non-classical beam model which has the capability to capture sizedependent behavior of microcantilevers. On the basis of Hamilton's principle, the sizedependent analytical expressions corresponding to the frequency response and sensitivity of AFM cantilevers are derived. It is observed that by increasing the contact stiffness, the resonant frequencies of AFM cantilevers firstly increase and then tend to remain constant at an especial value. Moreover, the resonant frequencies of AFM cantilevers obtained via the developed non-classical model is higher than those of the classical beam theory, especially for the values of beam thickness close to the internal material length scale parameter.

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Section: Introductionmentioning

confidence: 99%

Size-Dependent Resonant Frequency and Flexural Sensitivity of Atomic Force Microscope Microcantilevers Based on the Modified Strain Gradient Theory

Ansari

Pourashraf

Gholami

et al. 2015

International Journal of Optomechatronics

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“…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.

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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.

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“…Numerous studies have been accomplished to investigate the size-dependent static bending and vibrational analysis of microstructures based on the MSGT. The static deformation and vibrational behavior of an Euler-Bernoulli microbeam was studied by Kong et al [2009] using the MSGT. developed a micro-scaled Timoshenko beam model based on the MSGT and Hamilton's principle.…”

Section: Introductionmentioning

confidence: 99%

Buckling and postbuckling behavior of functionally graded Timoshenko microbeams based on the strain gradient theory

Ansari

Shojaei

Mohammadi

et al. 2012

J. Mech. Mater. Struct.

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Presented herein is a comprehensive study on the buckling and postbuckling analysis of microbeams made of functionally graded materials (FGMs) based on the modified strain gradient theory. The present model is developed in the skeleton of the Timoshenko beam theory and the von Karman geometric nonlinearity, and enables one to consider size effects through introducing material length scale parameters. Also, the current model can be reduced to the modified couple stress and classical models if two or all material length scale parameters are set equal to zero, respectively. Utilizing a power law function, the volume fraction of the ceramic and metal phases of the functionally graded microbeam is expressed. The stability equations and corresponding boundary conditions are derived using Hamilton's principle and then solved through the generalized differential quadrature (GDQ) method in conjunction with a direct approach without linearization. The effects of the length scale parameter, slenderness ratio, material gradient index and boundary conditions on the buckling and postbuckling behavior of microbeams are carefully studied. Furthermore, the non-dimensional critical axial load of microbeams predicted by modified strain gradient and classical theories for the first three postbuckling modes is investigated and it is observed that the classical theory underestimates the non-dimensional critical axial load, especially at higher postbuckling modes. In addition, the influence of imperfections on the deflection of microbeams in prebuckled and postbuckled states is discussed.

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Static and dynamic analysis of micro beams based on strain gradient elasticity theory

Cited by 490 publications

References 29 publications

Size-Dependent Resonant Frequency and Flexural Sensitivity of Atomic Force Microscope Microcantilevers Based on the Modified Strain Gradient Theory

Size-Dependent Resonant Frequency and Flexural Sensitivity of Atomic Force Microscope Microcantilevers Based on the Modified Strain Gradient Theory

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

Buckling and postbuckling behavior of functionally graded Timoshenko microbeams based on the strain gradient theory

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