Home > Research > Publications & Outputs > Bounding properties for eigenvalues of a transc...

Research

Associated organisational unit

Links

Text available via DOI:

View graph of relations

Bounding properties for eigenvalues of a transcendental dynamic stiffness matrix by using a quadratic matrix pencil

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Bounding properties for eigenvalues of a transcendental dynamic stiffness matrix by using a quadratic matrix pencil. / Ye, Jianqiao; Williams, F W .
In: Journal of Sound and Vibration, Vol. 184, No. 1, 06.07.1995, p. 173-183.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Ye, J & Williams, FW 1995, 'Bounding properties for eigenvalues of a transcendental dynamic stiffness matrix by using a quadratic matrix pencil', Journal of Sound and Vibration, vol. 184, no. 1, pp. 173-183. https://doi.org/10.1006/jsvi.1995.0310

APA

Ye, J., & Williams, F. W. (1995). Bounding properties for eigenvalues of a transcendental dynamic stiffness matrix by using a quadratic matrix pencil. Journal of Sound and Vibration, 184(1), 173-183. https://doi.org/10.1006/jsvi.1995.0310

Vancouver

Ye J, Williams FW. Bounding properties for eigenvalues of a transcendental dynamic stiffness matrix by using a quadratic matrix pencil. Journal of Sound and Vibration. 1995 Jul 6;184(1):173-183. doi: 10.1006/jsvi.1995.0310

Author

Ye, Jianqiao ; Williams, F W . / Bounding properties for eigenvalues of a transcendental dynamic stiffness matrix by using a quadratic matrix pencil. In: Journal of Sound and Vibration. 1995 ; Vol. 184, No. 1. pp. 173-183.

Bibtex

@article{6fb997a7c79f4791b927473fe64c23f6,
title = "Bounding properties for eigenvalues of a transcendental dynamic stiffness matrix by using a quadratic matrix pencil",
abstract = "An approximate representation of a transcendental dynamic stiffness matrix K(rho) by a simple quadratic matrix pencil A-rho B-rho(2)C is studied in this paper. The matrix pencil is formed by expressing the elements of K as parabolic functions based on choosing three fixed values of the eigenparameter rho. General bounds on the exact eigenvalues of the transcendental eigenvalue problem provided by the quadratic matrix pencil are shown to exist, provided that the three fixed values are below the lowest pole of the transcendental stiffness matrix considered and that the three coefficient matrices are positive definite. Numerical examples illustrate and confirm these bounding properties. Furthermore, the bounding properties are extended to constrained dynamic stiffness matrices. e.g., matrices formed by using Lagrangian multipliers to couple individual stiffness matrices of several different responses when a single response does not satisfy the desired boundary conditions. ",
author = "Jianqiao Ye and Williams, {F W}",
year = "1995",
month = jul,
day = "6",
doi = "10.1006/jsvi.1995.0310",
language = "English",
volume = "184",
pages = "173--183",
journal = "Journal of Sound and Vibration",
issn = "0022-460X",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - Bounding properties for eigenvalues of a transcendental dynamic stiffness matrix by using a quadratic matrix pencil

AU - Ye, Jianqiao

AU - Williams, F W

PY - 1995/7/6

Y1 - 1995/7/6

N2 - An approximate representation of a transcendental dynamic stiffness matrix K(rho) by a simple quadratic matrix pencil A-rho B-rho(2)C is studied in this paper. The matrix pencil is formed by expressing the elements of K as parabolic functions based on choosing three fixed values of the eigenparameter rho. General bounds on the exact eigenvalues of the transcendental eigenvalue problem provided by the quadratic matrix pencil are shown to exist, provided that the three fixed values are below the lowest pole of the transcendental stiffness matrix considered and that the three coefficient matrices are positive definite. Numerical examples illustrate and confirm these bounding properties. Furthermore, the bounding properties are extended to constrained dynamic stiffness matrices. e.g., matrices formed by using Lagrangian multipliers to couple individual stiffness matrices of several different responses when a single response does not satisfy the desired boundary conditions. 

AB - An approximate representation of a transcendental dynamic stiffness matrix K(rho) by a simple quadratic matrix pencil A-rho B-rho(2)C is studied in this paper. The matrix pencil is formed by expressing the elements of K as parabolic functions based on choosing three fixed values of the eigenparameter rho. General bounds on the exact eigenvalues of the transcendental eigenvalue problem provided by the quadratic matrix pencil are shown to exist, provided that the three fixed values are below the lowest pole of the transcendental stiffness matrix considered and that the three coefficient matrices are positive definite. Numerical examples illustrate and confirm these bounding properties. Furthermore, the bounding properties are extended to constrained dynamic stiffness matrices. e.g., matrices formed by using Lagrangian multipliers to couple individual stiffness matrices of several different responses when a single response does not satisfy the desired boundary conditions. 

U2 - 10.1006/jsvi.1995.0310

DO - 10.1006/jsvi.1995.0310

M3 - Journal article

VL - 184

SP - 173

EP - 183

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

IS - 1

ER -