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Quadratic representation of a nonlinear dynamic stiffness matrix and related eigenvalue problems

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Quadratic representation of a nonlinear dynamic stiffness matrix and related eigenvalue problems. / Ye, J Q ; Williams, F W .
In: Computer Methods in Applied Mechanics and Engineering, Vol. 146, No. 3-4, 15.07.1997, p. 313-323.

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

Harvard

Ye, JQ & Williams, FW 1997, 'Quadratic representation of a nonlinear dynamic stiffness matrix and related eigenvalue problems', Computer Methods in Applied Mechanics and Engineering, vol. 146, no. 3-4, pp. 313-323. https://doi.org/10.1016/S0045-7825(96)01239-X

APA

Ye, J. Q., & Williams, F. W. (1997). Quadratic representation of a nonlinear dynamic stiffness matrix and related eigenvalue problems. Computer Methods in Applied Mechanics and Engineering, 146(3-4), 313-323. https://doi.org/10.1016/S0045-7825(96)01239-X

Vancouver

Ye JQ, Williams FW. Quadratic representation of a nonlinear dynamic stiffness matrix and related eigenvalue problems. Computer Methods in Applied Mechanics and Engineering. 1997 Jul 15;146(3-4):313-323. doi: 10.1016/S0045-7825(96)01239-X

Author

Ye, J Q ; Williams, F W . / Quadratic representation of a nonlinear dynamic stiffness matrix and related eigenvalue problems. In: Computer Methods in Applied Mechanics and Engineering. 1997 ; Vol. 146, No. 3-4. pp. 313-323.

Bibtex

@article{44adc6e43e774168bac2525a74771011,
title = "Quadratic representation of a nonlinear dynamic stiffness matrix and related eigenvalue problems",
abstract = "The approximate representation of an exact dynamic stiffness matrix K(rho) by a quadratic matrix formulation, A-rho B-rho(2)C, is studied theoretically in this paper. The matrix formulation is formed by expressing the elements of K(rho) as parabolic functions based on choosing three fixed values of the eigenparameter rho. The general bounding properties of the approximate eigenvalues provided by the quadratic matrix formulation are shown to exist, provided that the three fixed values are below the lowest pole of the nonlinear stiffness matrix and that the three coefficient matrices, A, B and C, are positive definite. It is shown theoretically in this paper that the approximate eigenvalues are either upper or lower bounds of the corresponding exact ones of the exact dynamic stiffness matrix.",
author = "Ye, {J Q} and Williams, {F W}",
year = "1997",
month = jul,
day = "15",
doi = "10.1016/S0045-7825(96)01239-X",
language = "English",
volume = "146",
pages = "313--323",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
number = "3-4",

}

RIS

TY - JOUR

T1 - Quadratic representation of a nonlinear dynamic stiffness matrix and related eigenvalue problems

AU - Ye, J Q

AU - Williams, F W

PY - 1997/7/15

Y1 - 1997/7/15

N2 - The approximate representation of an exact dynamic stiffness matrix K(rho) by a quadratic matrix formulation, A-rho B-rho(2)C, is studied theoretically in this paper. The matrix formulation is formed by expressing the elements of K(rho) as parabolic functions based on choosing three fixed values of the eigenparameter rho. The general bounding properties of the approximate eigenvalues provided by the quadratic matrix formulation are shown to exist, provided that the three fixed values are below the lowest pole of the nonlinear stiffness matrix and that the three coefficient matrices, A, B and C, are positive definite. It is shown theoretically in this paper that the approximate eigenvalues are either upper or lower bounds of the corresponding exact ones of the exact dynamic stiffness matrix.

AB - The approximate representation of an exact dynamic stiffness matrix K(rho) by a quadratic matrix formulation, A-rho B-rho(2)C, is studied theoretically in this paper. The matrix formulation is formed by expressing the elements of K(rho) as parabolic functions based on choosing three fixed values of the eigenparameter rho. The general bounding properties of the approximate eigenvalues provided by the quadratic matrix formulation are shown to exist, provided that the three fixed values are below the lowest pole of the nonlinear stiffness matrix and that the three coefficient matrices, A, B and C, are positive definite. It is shown theoretically in this paper that the approximate eigenvalues are either upper or lower bounds of the corresponding exact ones of the exact dynamic stiffness matrix.

U2 - 10.1016/S0045-7825(96)01239-X

DO - 10.1016/S0045-7825(96)01239-X

M3 - Journal article

VL - 146

SP - 313

EP - 323

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

IS - 3-4

ER -