Buy article PDF
The purchased file will be sent to you
via email after the payment is completed.
US$ 35
|
Structural Engineering and Mechanics Volume 39, Number 5, September10 2011 , pages 669-682 DOI: https://doi.org/10.12989/sem.2011.39.5.669 |
|
|
|
Matrix-based Chebyshev spectral approach to dynamic analysis of non-uniform Timoshenko beams |
||
W.Y. Wang, J.Y. Liao and L.W. Hourng
|
||
| Abstract | ||
| A Chebyshev spectral method (CSM) for the dynamic analysis of non-uniform Timoshenko beams under various boundary conditions and concentrated masses at their ends is proposed. The matrixbased Chebyshev spectral approach was used to construct the spectral differentiation matrix of the governing differential operator and its boundary conditions. A matrix condensation approach is crucially presented to impose boundary conditions involving the homogeneous Cauchy conditions and boundary conditions containing eigenvalues. By taking advantage of the standard powerful algorithms for solving matrix eigenvalue and generalized eigenvalue problems that are embodied in the MATLAB commands, chebfun and eigs, the modal parameters of non-uniform Timoshenko beams under various boundary conditions can be obtained from the eigensolutions of the corresponding linear differential operators. Some numerical examples are presented to compare the results herein with those obtained elsewhere, and to illustrate the accuracy and effectiveness of this method. | ||
| Key Words | ||
| Chebyshev spectral method; modal analysis; spectral differentiation matrix; chebfun; Timoshenko beam | ||
| Address | ||
| W.Y. Wang: Department of Mechanical Engineering, National Central University, Taoyuan, Taiwan J.Y. Liao: System Development Center, Chung-Sun Institute of Science and Technology, Taoyuan, Taiwan L.W. Hourng: Department of Mechanical Engineering, National Central University, Taoyuan, Taiwan | ||