A new Timoshenko beam model for simulation of mechanical system with large deformation

2016 ◽  
Vol 59 (11) ◽  
pp. 1639-1645
Author(s):  
Guan Zhou ◽  
Ren Hui ◽  
WanZhong Zhao ◽  
ChunYan Wang ◽  
Bing Xu
Keyword(s):  
Mechanical System ◽  
Large Deformation ◽  
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.

Development of an Active Curved Beam Model Using a Moving Frame Method

2016 ◽  
Author(s):  
Hidenori Murakami
Keyword(s):  
Large Deformation ◽  
Timoshenko Beam ◽  
Virtual Work ◽  
Three Dimensional ◽  
Moving Frame ◽  
Beam Model ◽  
Principle Of Virtual Work ◽  
Beam Equations ◽  
Moving Frame Method ◽  
Frame Method

In order to develop an active large-deformation beam model for slender, flexible or soft robots, the d’Alembert principle of virtual work is derived for three-dimensional elastic solids from Hamilton’s principle. This derivation is accomplished by refining the definition of the Cauchy stress tensor as a vector-valued 2-form to exploit advanced geometrical operations available for differential forms. From the three-dimensional principle of virtual work, both the beam principle of virtual work and beam equations of motion with consistent boundary conditions are derived, adopting the kinematic assumption of rigid cross-sections of a deforming beam. In the derivation of the beam model, Élie Cartan’s moving frame method is utilized. The resulting large-deformation beam equations apply to both passive and active beams. The beam equations are validated with the previously reported results expressed in vector form. To transform passive beams to active beams, constitutive relations for internal actuation are presented in rate-form. Then, the resulting three-dimensional beam models are reduced to an active planar beam model. Finally, to illustrate the deformation due to internal actuation, an active Timoshenko-beam model is derived by linearizing the nonlinear planar equations. For an active, simply-supported Timoshenko-beam, the analytical solution is presented.

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.

Development of an Active Curved Beam Model—Part II: Kinetics and Internal Activation

2017 ◽  
Vol 84 (6) ◽  
Author(s):  
Hidenori Murakami
Keyword(s):  
Large Deformation ◽  
Timoshenko Beam ◽  
Virtual Work ◽  
Constitutive Relations ◽  
Differential Forms ◽  
Three Dimensional ◽  
Beam Model ◽  
Cauchy Stress ◽  
Principle Of Virtual Work ◽  
Beam Equations

Utilizing the kinematics, presented in the Part I, an active large deformation beam model for slender, flexible, or soft robots is developed from the d'Alembert's principle of virtual work, which is derived for three-dimensional elastic solids from Hamilton's principle. This derivation is accomplished by refining the definition of the Cauchy stress tensor as a vector-valued 2-form to exploit advanced geometrical operations available for differential forms. From the three-dimensional principle of virtual work, both the beam principle of virtual work and beam equations of motion with consistent boundary conditions are derived, adopting the kinematic assumption of rigid cross sections of a deforming beam. In the derivation of the beam model, Élie Cartan's moving frame method is utilized. The resulting large deformation beam equations apply to both passive and active beams. The beam equations are validated with the previously reported results expressed in vector form. To transform passive beams to active beams, constitutive relations for internal actuation are presented in rate form. Then, the resulting three-dimensional beam models are reduced to an active planar beam model. To illustrate the deformation due to internal actuation, an active Timoshenko beam model is derived by linearizing the nonlinear planar equations. For an active, simply supported Timoshenko beam, the analytical solution is presented. Finally, a linear locomotion of a soft inchworm-inspired robot is simulated by implementing active C1 beam elements in a nonlinear finite element (FE) code.

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
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