Spectral Element Model for the Vibration of an Axially Moving Timoshenko Beam

2003 ◽  
Author(s):  
Hyungmi Oh ◽  
Hyuckjin Oh ◽  
Joohong Kim ◽  
Usik Lee
Keyword(s):  
Timoshenko Beam ◽  
Element Model ◽  
Spectral Element ◽  
Axially Moving ◽  
Axially Moving Timoshenko Beam

Frequency-Domain Spectral Element Model of a Uniform Spinning Shaft

2012 ◽  
Vol 224 ◽  
pp. 264-267
Author(s):  
Usik Lee ◽  
In Joon Jang ◽  
Il Wook Park
Keyword(s):  
Differential Equations ◽  
Timoshenko Beam ◽  
Variational Approach ◽  
Element Model ◽  
Spectral Element ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Shape Functions ◽  
Wave Solutions ◽  
Spinning Shaft

This paper presents a spectral element model for the spinning uniform shaft represented by the Timoshenko beam model. The bearing-supports are represented by equivalent springs. The variational approach is used to formulate the spectral element model from the frequency-dependent shape functions derived from exact wave solutions to the governing differential equations.

Longitudinal and Transverse Coupling Dynamic Properties of a Timoshenko Beam with Mass Eccentricity

2017 ◽  
Vol 17 (07) ◽  
pp. 1750077 ◽  
Author(s):  
Zhiyang Lei ◽  
Jinpeng Su ◽  
Hongxing Hua
Keyword(s):  
Timoshenko Beam ◽  
Control Method ◽  
Dynamic Properties ◽  
Element Model ◽  
Spectral Element ◽  
Coupling Mechanism ◽  
Beam Model ◽  
Coupling Coefficients ◽  
Coupling Vibration ◽  
Mass Eccentricity

Non-uniform mass distribution on a beam will lead to the coupling between lateral and axial vibrations of the beam. To simulate the mass eccentricity, a double-layered Timoshenko beam model is developed. Based on Hamilton’s principle, the coupled governing equations are derived and mass and stiffness coupling coefficients are also derived. Moreover, the spectral element method (SEM), with high frequency accuracy by employing the dynamic shape functions, is utilized to study the dynamic properties of the beam. In addition, a corresponding finite element model is established to verify the SEM model. The coupling vibration characteristics are investigated and the coupling mechanism is revealed. Furthermore, the effects of mass non--uniformity on the free vibration and forced vibration of the beam with classical and flexible boundary conditions are analyzed. Finally, an optimal control method for reducing the contributions of bending modes under the axial excitation is presented with the results displayed.

Control of an Axially Moving Timoshenko Beam Attached to a Moving Base

2021 ◽  
Author(s):  
Phuong-Tung Pham ◽  
Gyoung-Hahn Kim ◽  
Quoc-Chi Nguyen ◽  
Keum-Shik Hong
Keyword(s):  
Timoshenko Beam ◽  
Moving Base ◽  
Axially Moving ◽  
Axially Moving Timoshenko Beam

Spectral Element Model for the Vibration of a Bending-Shear-Torsion Coupled Composite Timoshenko Beam

2010 ◽  
Author(s):  
Usik Lee ◽  
Injoon Jang
Keyword(s):  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Spectral Element ◽  
Beam Model ◽  
Shape Functions ◽  
Laminated Beams ◽  
Composite Timoshenko Beam ◽  
Dynamic Shape

In this paper, a spectral element model is developed for axially loaded bending-shear-torsion coupled composite laminated beams. The composite laminated beams are represented by the Timoshenko beam model based on the first-order shear deformation theory. The spectral element model is formulated by using the variational method from frequency-dependent dynamic shape functions. The dynamic shape functions are derived from exact wave solutions to the governing differential equations of motion which are transformed into the frequency-domain by using the DFT theory. The numerical results show that the present spectral model provides extremely accurate natural frequencies for an example problem when compared to the results obtained by using the conventional finite element model which is also presented in this paper.

Sign in / Sign up

Export Citation Format

Share Document