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Analyzing the Stability of a n-DOF System with Viscous Damping

PP. 942-946
DOI: 10.4236/am.2011.28129    3,861 Downloads   7,139 Views  

ABSTRACT

In this paper we introduce a numerically stable method for determining the stability of n-DOF system without computing eigenvalues. In this sense, at first we reduce the second-order system to a standard eigenvalue problem with symmetric tridiagonal form. Then we compute the exact inertia by using an algorithm based on floating point arithmetic [1]. Numerical tests report the effectiveness of these methods.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

H. Najafi and A. Sheikhani, "Analyzing the Stability of a n-DOF System with Viscous Damping," Applied Mathematics, Vol. 2 No. 8, 2011, pp. 942-946. doi: 10.4236/am.2011.28129.

References

[1] K. V. Fernando, “Computation of Exact Inertia and Inclusions of Eigenvalues of Tridiagonal Matrices,” Linear Algebra and Its Applications, Vol. 422, No. 1, 2007, pp. 71-99. doi:10.1016/j.laa.2006.09.008
[2] D. Carlson and B. N. Datta, “The Lyapunov Matrix Equation ,” Linear Algebra and Its Applications, Vol. 28, 1979, pp. 43-52. doi:10.1016/0024-3795(79)90117-4
[3] A. C. Antoulas and D. C.Sorensen, “Lyapunov, Lanczos and Inertia,” Linear Algebra and Its Applications, Vol. 326, No. 1-3, 2001, pp. 137-150. doi:10.1016/S0024-3795(00)00288-3
[4] D. Carlson and B. N. Datta, “On the Effective Computation of the Inertia of a Nonhermitian Matrix,” Numerical Mathematics, Vol. 33, No. 3, 1979, pp. 315-322. doi:10.1007/BF01398647
[5] B. N. Datta, “Stability and Inertia,” Linear Algebra and Its Applications, Vol. 302-303, 2000, pp. 563-600. doi:10.1016/S0024-3795(99)00213-X

  
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