Effects of Damping on the Vibration Frequency of Atomic Force Microscope Cantilevers Using the Timoshenko Beam Model

2009 ◽  
Vol 48 (6) ◽  
pp. 065005 ◽  
Author(s):  
Haw-Long Lee ◽  
Win-Jin Chang
Keyword(s):  
Atomic Force Microscope ◽  
Timoshenko Beam ◽  
Vibration Frequency ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Atomic Force

Dynamic analysis of AFM by applying Timoshenko beam theory in tapping mode and considering the impact of interaction forces in a liquid environment

2014 ◽  
Vol 92 (6) ◽  
pp. 472-483 ◽  
Author(s):  
M. Damircheli ◽  
M.H. Korayem
Keyword(s):  
Dynamic Response ◽  
Atomic Force Microscope ◽  
Timoshenko Beam ◽  
Ambient Air ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Interaction Forces ◽  
Liquid Environment ◽  
Atomic Force ◽  
Simulation Results

In an atomic force microscope (AFM), the cantilever vibrates by excitation at a frequency near the fundamental frequency, and the changes in vibration parameters, which result from the nonlinear forces of interaction between sample and cantilever tip, can be used as a tool to reveal the properties of the sample. To properly describe the images acquired by the AFM and to approximate the properties of the investigated sample, it is essential to use analytical and numerical models that can accurately simulate the dynamics of the cantilever and sample. For short beams, the Timoshenko model seems to be very accurate. Considering the fact that short beams (cantilevers) have many applications including the imaging of biological samples in liquid environments, the use of this theory seems to be necessary. In this paper, by employing the Timoshenko beam model, the effect of rotational inertia and shear deformation has been taken into consideration. The interaction forces between sample and cantilever in liquid, ambient air, and vacuum environments are quite different in terms of magnitude and formulation, and they play a significant role in the system’s dynamic response. These forces include hydrodynamic forces, electrostatic double layer force, etc. Using an accurate model for the interaction forces will improve the simulation results significantly. In this paper, the frequency response of the atomic force microscope has been investigated by applying the Timoshenko beam model and considering the forces of interaction between sample and tip in the air and liquid environments. The results indicate that the resonant frequency changes and cantilever vibration amplitude diminishes in a liquid environment compared to the air environment. The simulation results have good agreement with the experimental ones. The frequency responses for the attractive and repulsive regions in the two environments are compared and it is demonstrated that the dynamic response is highly dependent on the hydrodynamic and interaction forces in the liquid medium.

Investigating vibrations of viscoelastic fluid-conveying carbon nanotubes resting on viscoelastic foundation using a nonlocal fractional Timoshenko beam model

2020 ◽  
pp. 239779142093170
Author(s):  
M Faraji Oskouie ◽  
R Ansari ◽  
H Rouhi
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Time Domain ◽  
Beam Model ◽  
Viscoelastic Foundation ◽  
Timoshenko Beam Model ◽  
Governing Equations ◽  
The Time Domain

On the basis of fractional viscoelasticity, the size-dependent free-vibration response of viscoelastic carbon nanotubes conveying fluid and resting on viscoelastic foundation is studied in this article. To this end, a nonlocal Timoshenko beam model is developed in the context of fractional calculus. Hamilton’s principle is applied in order to obtain the fractional governing equations including nanoscale effects. The Kelvin–Voigt viscoelastic model is also used for the constitutive equations. The free-vibration problem is solved using two methods. In the first method, which is limited to the simply supported boundary conditions, the Galerkin technique is employed for discretizing the spatial variables and reducing the governing equations to a set of ordinary differential equations on the time domain. Then, the Duffing-type time-dependent equations including fractional derivatives are solved via fractional integrator transfer functions. In the second method, which can be utilized for carbon nanotubes with different types of boundary conditions, the generalized differential quadrature technique is used for discretizing the governing equations on spatial grids, whereas the finite difference technique is used on the time domain. In the results, the influences of nonlocality, geometrical parameters, fractional derivative orders, viscoelastic foundation, and fluid flow velocity on the time responses of carbon nanotubes are analyzed.

Precise Frequency Calculation Model on BTA Boring Bar

2014 ◽  
Vol 532 ◽  
pp. 398-401
Author(s):  
Wu Zhao ◽  
Wei Tao Jia ◽  
Quan Bin Zhang ◽  
Zhan Qi Hu
Keyword(s):  
Timoshenko Beam ◽  
Calculation Model ◽  
Cutting Fluid ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Intrinsic Frequency ◽  
Boring Bar ◽  
Precise Calculation ◽  
Vibration Model ◽  
Frequency Calculation

For the purpose of precise calculation on intrinsic frequency of the deep-hole boring bar in trepanning heavy-duty processing, a new frequency calculation model is proposed, based on the synthetically investigation of the axial press effects, intermediate supported, Coriolis inertia effects induced by cutting fluid and other relevant various factors of boring bar. The boring bar can be decomposed into the two parts, corresponding to the liquid-solid coupling vibration model inside the work part and Timoshenko beam model outside the work part, respectively. Then assume the whole system as continuous equal span beam model to combine these two parts. Through nesting liquid-solid coupled vibration model (considering cutting fluid velocity) and Timoshenko beam model (containing axial pressure and lateral bending) among the continuous beam model (considering equal span), the precise calculation on intrinsic frequency of the boring system can be completed.

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