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

Affiliation(s)

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

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.

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.

Cite this paper

nullH. 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.

nullH. Najafi and A. Sheikhani, "Analyzing the Stability of a

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

[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