Nanomachining analysis of a multi-cracked atomic force microscope cantilever based on a modified couple stress theory

2015 ◽  
Vol 29 (30) ◽  
pp. 1550186
Author(s):  
Win-Jin Chang ◽  
Yu-Ching Yang ◽  
Haw-Long Lee
Keyword(s):  
Atomic Force Microscope ◽  
Couple Stress ◽  
Removal Rate ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Depth Of Cut ◽  
Time Curve ◽  
Stress Theory ◽  
Atomic Force ◽  
Modified Couple Stress

The vibration analysis of an atomic force microscope (AFM) cantilever with an arbitrary number of cracks during the nanomachining process is studied based on the modified couple stress theory. The cantilever with [Formula: see text] cracks is divided into [Formula: see text] segments by the cracks and a rotational spring is used to simulate each crack. An analytical expression for the vibration frequency and displacement of the cracked cantilever is derived. According to the analysis, in addition, the displacement increases with an increase in the number of cracks and crack flexibilities. For nanomachining, the displacement of the cantilever tip is related to the depth of cut. The area under the displacement-time curve implies the material removal rate. The present study is useful for the design of an AFM-based nanomachining cantilever with cracks.

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.

scholarly journals The Response of Nanobeams with Temperature-Dependent Properties Using State-Space Method via Modified Couple Stress Theory

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1276 ◽  
Author(s):  
Ahmed E. Abouelregal ◽  
Marin Marin
Keyword(s):  
Thermal Conductivity ◽  
State Space ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Temperature Dependent ◽  
Stress Theory ◽  
Atomic Force ◽  
Modified Couple Stress ◽  
Temperature Dependent Properties

At present, with the development in nanotechnology, nanostructures with temperature-dependent properties have been used in nano-electromechanical systems (NEMS). Thus, introducing an accurate mathematical model of nanobeams with temperature-dependent properties is a major and important topic for the design of NEMS. This paper aims to discuss nonlocal nanobeams analysis depending on the theories of Euler–Bernoulli and modified couple-stress (MCS). It also is assumed that the thermal conductivity of the nanobeam is dependent on the temperature. Physical fields of the nanobeam are obtained utilizing Laplace transform and state-space techniques. The effects of the size and nonlocal parameters, variability of thermal conductivity and couple stress on various distributions are presented graphically and studied in detail. Numerical results are presented as application scales and the design of nanoparticles, nanoscale oscillators, atomic force microscopes, and nanogenerators, in which nanoparticles as nanobeams act as essential and basic elements.

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