摘要(英) |
Noise is all around us. We are disturbed by these unpleasant sound all the time. However, most of the time people prefer to stay in a quieter environment. If people stay in enclosed space, we can keep the noise down by the aid of the boundaries which is made by elastic material, and furthermore set a damper on it to enhance the efficiency. The coupling and the interaction between fluid and structure can be simulated by a mathematical model called the acoustic structure interaction problem. It can be transform into a equivalent quadratic eigenvalue problem by applying the Galerkin finite element method. Eigenvalues reflects the behavior of the couple system, among these eigenvalue, we are interested in finding the low frequency eigenvalues which are concerned in the field of industrial and science. By the numerical simulation, the choices of material and the position of damper can be adjusted according to different situations or requirements. |
參考文獻 |
[1] Thomas JR Hughes. The Finite Element Method: Linear Static and Dynamic
Finite Element Analysis. Courier Dover Publications, 2012.
[2] William Thomson. Theory of Vibration with Applications. CRC Press, 1996.
[3] A Bermúdez, RG Durán, R Rodríguez, and J Solomin. Finite element analysis
of a quadratic eigenvalue problem arising in dissipative acoustics. SIAM Journal
on Numerical Analysis, 38(1):267–291, 2000.
[4] Alfredo Bermudez and Rodolfo Rodriguez. Modelling and numerical solution
of elastoacoustic vibrations with interface damping. International Journal for
Numerical Methods in Engineering, 46(10):1763–1779, 1999.
[5] Sheng-Hong Lai. Parallel Computation of Acoustic Eigenvalue Problems Using
a Polynomial Jacobi-Davidson Method. Master’s thesis, National Central
University, 2010.
[6] Tsung-Ming Huang, Feng-Nan Hwang, Sheng-Hong Lai, Weichung Wang, and
Zih-Hao Wei. A parallel polynomial Jacobi–Davidson approach for dissipative
acoustic eigenvalue problems. Computers & Fluids, 45(1):207–214, 2011.
[7] Yu-Fen Cheng. A Parallel Two-level Polynomial Jacobi-Davidson Algorithm
for Large Sparse Dissipative Acoustic Eigenvalue Problems. Master’s thesis,
National Central University, 2012.
[8] W Larbi, J-F Deü, and R Ohayon. A new finite element formulation for internal
acoustic problems with dissipative walls. International Journal for Numerical
Methods in Engineering, 68(3):381–399, 2006.
[9] Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur, Seamus D. Garvey,
Mims Eprint, Nicholas J. Higham, D. Steven Mackey, Françoise Tisseur, and
Seamus D. Garvey. Scaling, sensitivity and stability in the numerical solution
of quadratic eigenvalue problems. 2006.
[10] P.E. Austrell. CALFEM: A Finite Element Toolbox : Version 3.4. Structural
Mechanics, LTH, 2004.
[11] Göran Sandberg, Per-Anders Wernberg, and Peter Davidsson. Fundamentals
of fluid-structure interaction. In Göran Sandberg and Roger Ohayon, editors,
Computational Aspects of Structural Acoustics and Vibration, CISM International
Centre for Mechanical Sciences, pages 23–101. Springer Vienna, 2009.
[12] Göran Sandberg and Roger Ohayon. Computational Aspects of Structural
Acoustics and Vibration. Springer, 2009.
[13] Hung-Yuan Fan, Wen-Wei Lin, and Paul Van Dooren. Normwise scaling of
second order polynomial matrices. SIAM Journal on Matrix Analysis and Applications,
26(1):252–256, 2004.
[14] Linda Kaufman. Some thoughts on the QZ algorithm for solving the generalized
eigenvalue problem. ACM Transactions on Mathematical Software, 3(1):65–75,
1977. |