Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory

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

doi:10.1016/j.ijengsci.2010.06.003

Cited by 188 publications

(57 citation statements)

References 27 publications

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“…are compared with those given by Kahrobaiyan et al [28] in Figure 2. A reasonable agreement is observed.…”

Section: Resultsmentioning

confidence: 82%

“…Comparison between the calculated first and second resonant frequencies of AFM microcantilevers based on the present study and those of. [28] SIZE-DEPENDENT RESONANT FREQUENCY OF AFM MICROCANTILEVERS of material length scale parameter (h=l) and dimensionless contact stiffness (b 1 ) corresponding to different models. It can be seen that the first and second dimensionless resonant frequencies increase as h=l decreases for both the modified couple stress theory and the modified strain gradient theory.…”

Section: Resultsmentioning

confidence: 99%

“…The simplified couple stress theory contains an additional equilibrium relation which causes to create symmetric couple stress tensor. Kahrobaiyan et al [28] studied the resonant frequency and sensitivity of AFM microcantilevers based on the modified couple stress elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…are compared with those given by Kahrobaiyan et al [28] in Figure 2. A reasonable agreement is observed.…”

Section: Resultsmentioning

confidence: 82%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Furthermore, the impact of the width, length and thickness of the coating on Young's modulus is discussed since the geometry would have great influence on properties of microcantilevers. [37][38][39] The microcantilever is schematically shown in Fig. 1 (a), three theoretical models without considering the impact of coating are given in equations.…”

confidence: 99%

Young’s modulus of multi-layer microcantilevers

Deng

et al. 2017

AIP Advances

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A theoretical model for calculating the Young’s modulus of multi-layer microcantilevers with a coating is proposed, and validated by a three-dimensional (3D) finite element (FE) model using ANSYS parametric design language (APDL) and atomic force microscopy (AFM) characterization. Compared with typical theoretical models (Rayleigh-Ritz model, Euler-Bernoulli (E-B) beam model and spring mass model), the proposed theoretical model can obtain Young’s modulus of multi-layer microcantilevers more precisely. Also, the influences of coating’s geometric dimensions on Young’s modulus and resonant frequency of microcantilevers are discussed. The thickness of coating has a great influence on Young’s modulus and resonant frequency of multi-layer microcantilevers, and the coating should be considered to calculate Young’s modulus more precisely, especially when fairly thicker coating is employed.

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“…In this direction, the modified couple stress theory (MCST) was initiated by Yang et al (2002) in which only one length scale parameter is used in the constitutive equations leading to the symmetric couple stress tensor. Relevant works concerning the applicability of MCST in the analysis of microstructures can be found in (Ma et al (2008); Tsiatas (2009); Kahrobaiyan et al (2010); Ke et al (2011);Jomehzadeh et al (2011); Asghari (2012); Thai and Choi (2013)). In addition to these works, based on the modified couple stress and Kirchhoff plate theories, a size-dependent plate model was developed by Yin et al (2010) for the dynamic analysis of microplate.…”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Bending, Buckling and Free Vibration Analyses of Microscale Functionally Graded Mindlin Plates Based on the Strain Gradient Elasticity Theory

Ansari

Hasrati

Shojaei

et al. 2016

Lat. Am. j. solids struct.

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In this paper, a size-dependent microscale plate model is developed to describe the bending, buckling and free vibration behaviors of microplates made of functionally graded materials (FGMs). The size effects are captured based on the modified strain gradient theory (MSGT), and the formulation of the paper is on the basis of Mindlin plate theory. The presented model accommodates the models based upon the classical theory (CT) and the modified couple stress theory (MCST) if all or two scale parameters are set to zero, respectively. By using Hamilton's principle, the governing equations and related boundary conditions are derived. The bending, buckling and free vibration problems are considered and are solved through the generalized differential quadrature (GDQ) method. A detailed parametric and comparative study is conducted to evaluate the effects of length scale parameter, material gradient index and aspect ratio predicted by the CT, MCST and MSGT on the deflection, critical buckling load and first natural frequency of the microplate. The numerical results indicate that the model developed herein is significantly sizedependent when the thickness of the microplate is on the order of the material scale parameters.

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Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory

Cited by 188 publications

References 27 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

Young’s modulus of multi-layer microcantilevers

Size-Dependent Bending, Buckling and Free Vibration Analyses of Microscale Functionally Graded Mindlin Plates Based on the Strain Gradient Elasticity Theory

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