Observer-Based Stabilization of a Manipulator Based on the Timoshenko Beam Model

2014 ◽  
pp. 131-167
Author(s):  
Alexander L. Zuyev
Keyword(s):  
Timoshenko Beam ◽  
Beam Model ◽  
Timoshenko Beam Model

A new Timoshenko beam model based on modified gradient elasticity: Shearing effect and size effect of micro-beam

2019 ◽  
Vol 223 ◽  
pp. 110946 ◽  
Author(s):  
Bing Zhao ◽  
Jian Chen ◽  
Tao Liu ◽  
Wenhao Song ◽  
Jianren Zhang
Keyword(s):  
Size Effect ◽  
Timoshenko Beam ◽  
Gradient Elasticity ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Model Based

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.

Spectral operators generated by Timoshenko beam model

1999 ◽  
Vol 38 (4-5) ◽  
pp. 249-258 ◽  
Author(s):  
Marianna A. Shubov
Keyword(s):  
Timoshenko Beam ◽  
Beam Model ◽  
Timoshenko Beam Model

Terahertz Vibration of Short Carbon Nanotubes Modeled as Timoshenko Beams

2005 ◽  
Vol 72 (1) ◽  
pp. 10-17 ◽  
Author(s):  
J. Yoon ◽  
C. Q. Ru ◽  
A. Mioduchowski
Keyword(s):  
Carbon Nanotubes ◽  
Aspect Ratio ◽  
Timoshenko Beam ◽  
Large Diameter ◽  
Higher Order ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Double Beam ◽  
Short Carbon ◽  
Double Wall

Short carbon nanotubes of smaller aspect ratio (say, between 10 and 50) are finding significant application in nanotechnology. This paper studies vibration of such short carbon nanotubes whose higher-order resonant frequencies fall within terahertz range. Because rotary inertia and shear deformation are significant for higher-order modes of shorter elastic beams, the carbon nanotubes studied here are modeled as Timoshenko beams instead of classical Euler beams. Detailed results are demonstrated for double-wall carbon nanotubes of aspect ratio 10, 20, or 50 based on the Timoshenko-beam model and the Euler-beam model, respectively. Comparisons between different single-beam or double-beam models indicate that rotary inertia and shear deformation, accounted for by the Timoshenko-beam model, have a substantial effect on higher-order resonant frequencies and modes of double-wall carbon nanotubes of small aspect ratio (between 10 and 20). In particular, Timoshenoko-beam effects are significant for both large-diameter and small-diameter double-wall carbon nanotubes, while double-beam effects characterized by noncoaxial deflections of the inner and outer tubes are more significant for small-diameter than large-diameter double-wall carbon nanotubes. This suggests that the Timoshenko-beam model, rather than the Euler-beam model, is relevant for terahertz vibration of short carbon nanotubes.

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