Topology optimization design related to size effect using the modified couple stress theory

2021 ◽  
pp. 1-19
Author(s):  
Ning Gan ◽  
Qianxuan Wang
Keyword(s):  
Topology Optimization ◽  
Size Effect ◽  
Couple Stress ◽  
Optimization Design ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress

Flexural Vibration of an Atomic Force Microscope Cantilever Based on Modified Couple Stress Theory

2015 ◽  
Vol 15 (07) ◽  
pp. 1540025 ◽  
Author(s):  
Li-Na Liang ◽  
Liao-Liang Ke ◽  
Yue-Sheng Wang ◽  
Jie Yang ◽  
Sritawat Kitipornchai
Keyword(s):  
Size Effect ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Flexural Vibration ◽  
Modified Couple Stress Theory ◽  
Length Scale ◽  
Stress Theory ◽  
Atomic Force ◽  
Modified Couple Stress

This paper is concerned with the flexural vibration of an atomic force microscope (AFM) cantilever. The cantilever problem is formulated on the basis of the modified couple stress theory and the Timoshenko beam theory. The modified couple stress theory is a nonclassical continuum theory that includes one additional material parameter to describe the size effect. By using the Hamilton's principle, the governing equation of motion and the boundary conditions are derived for the AFM cantilevers. The equation is solved using the differential quadrature method for the natural frequencies and mode shapes. The effects of the sample surface contact stiffness, length scale parameter and location of the sensor tip on the flexural vibration characteristics of AFM cantilevers are discussed. Results show that the size effect on the frequency is significant when the thickness of the microcantilever has a similar value to the material length scale parameter.

Free vibrations of nanobeams under non-ideal supports based on modified couple stress theory

2021 ◽  
Vol 76 (5) ◽  
pp. 427-434
Author(s):  
Duygu Atcı
Keyword(s):  
Size Effect ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Linear Functions ◽  
Stress Theory ◽  
Fundamental Frequencies ◽  
Resonance Frequencies ◽  
Modified Couple Stress

Abstract In this study, free vibration analysis of nanobeams under various non-ideal supports have presented. Size effect of nanobeams has applied by utilizing modified couple stress theory. Hamilton’s principle has been used to derive the equation of motion. Governing equation has subjected to non-ideal boundary conditions which are modeled as linear functions including an introduced weighting factor (k). Obtained numerical results have verified by comparing with the published results. Results show that fundamental resonance frequencies of non-ideal clamped nanobeams are significantly decreased when it is compared to ideal supports. However, non-ideal simply supports creates a minor increase effect on fundamental frequencies with respect to clamped ones. Also, nano-size effect has investigated for non-ideal supports. It has found that, the smaller cross-sectional size of nanobeam causes increasing effect of non-ideal supports on fundamental frequencies.

Size Effect on Natural Frequency of Cantilever Micro-Beams Based on a Modified Couple Stress Theory

2013 ◽  
Vol 694-697 ◽  
pp. 221-224 ◽  
Author(s):  
Sheng Li Kong
Keyword(s):  
Size Effect ◽  
Natural Frequency ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
The Difference

The natural frequency of cantilever micro-beams is solved analytically on the basis of modified couple stress theory. The governing equations are obtained by a combination of the basic equations of modified couple stress theory and Hamiltons principle. The size effect on natural frequencies of the cantilever micro-beams is analyzed. It is found that the natural frequencies 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.

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