A size-dependent shear deformation beam model based on the strain gradient elasticity theory

2013 ◽  
Vol 70 ◽  
pp. 1-14 ◽  
Author(s):  
Bekir Akgöz ◽  
Ömer Civalek
Keyword(s):  
Elasticity Theory ◽  
Shear Deformation ◽  
Strain Gradient ◽  
Gradient Elasticity ◽  
Beam Model ◽  
Strain Gradient Elasticity ◽  
Size Dependent ◽  
Model Based ◽  
Strain Gradient Elasticity Theory ◽  
Gradient Elasticity Theory

Bending Analysis of Cantilever Micro-Beams Based on Strain Gradient Elasticity Theory

2013 ◽  
Vol 694-697 ◽  
pp. 172-175
Author(s):  
Sheng Li Kong
Keyword(s):  
Elasticity Theory ◽  
Strain Gradient ◽  
Gradient Elasticity ◽  
Beam Model ◽  
Strain Gradient Elasticity ◽  
Size Dependent ◽  
Deformation Problem ◽  
Strain Gradient Elasticity Theory ◽  
The Difference ◽  
Gradient Elasticity Theory

The bending deformation problem of cantilever micro-beams is solved analytically on the basis of strain gradient elasticity theory. The governing equations and boundary conditions are obtained by using Hamiltons principle. The size effect on deflections of the cantilever micro-beams is analyzed. It is found that the deflections of the cantilever micro-beams predicted by the newly model are size-dependent. The difference between the natural frequencies predicted by the newly established model and classical beam model is assessed.

Size Dependent Vibration Behavior of an AFM with Sidewall and Top-Surface Probes Based on the Strain Gradient Elasticity Theory

2015 ◽  
Vol 07 (03) ◽  
pp. 1550046 ◽  
Author(s):  
Mohammad Abbasi
Keyword(s):  
Elasticity Theory ◽  
Strain Gradient ◽  
Gradient Elasticity ◽  
Strain Gradient Theory ◽  
Strain Gradient Elasticity ◽  
Size Dependent ◽  
Vibration Behavior ◽  
Vertical Extension ◽  
Strain Gradient Elasticity Theory ◽  
Gradient Elasticity Theory

In this paper, the size-dependent vibration behavior of an atomic force microscope with assembled cantilever probe (ACP) is analyzed utilizing the modified strain gradient elasticity theory. The proposed ACP comprises a horizontal cantilever, a vertical extension and two tips located at the free ends of the cantilever and extension. Because the vertical extension is located between the clamped and free ends of the microcantilever, the cantilever is modeled as two beams. The results of the current model are compared to those evaluated by both modified couple stress and classical beam theories. The results indicate that the resonant frequency and sensitivity of the proposed ACP is strongly size-dependent especially when the contact stiffness is very low or it is very high. The results also declare that utilizing the strain gradient theory is essential in the analysis of the vibration behavior of the proposed ACP.

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