Eigen-matrix for the dynamic behavior of linear engineering structures

X. Ma; Z. Liang; G. C. Lee

Eigen-matrix for the dynamic behavior of linear engineering structures

X. Ma
, Z. Liang
, G. C. Lee

Department of Civil, Structural & Environmental Engineering

SUNY Buffalo

Research output: Contribution to journal › Conference article › peer-review

Abstract

The eigen-matrix, defined by A = PΛP^-1 (where P and Λ are the eigenvector and eigenvalue matrices of an MCK system, respectively), and its associated properties in describing the dynamic behaviors of linear elastic system are presented. The eigen-matrix is defined to satisfy the quadratic matrix equation of the form MA² + CA + K = 0 An analytic solution to this equation for the proportionally damped system is obtained. For non-proportionally damped system, A numerical algorithm is developed. The numerical algorithm is especially useful in the dynamic analysis of structures with large number of degrees of freedom.

Original language	English
Pages (from-to)	19-24
Number of pages	6
Journal	Proceedings of the International Modal Analysis Conference - IMAC
Volume	1
State	Published - 1991
Event	Proceedings of the 9th International Modal Analysis Conference Part 1 (of 2) - Florence, Italy Duration: Apr 15 1991 → Apr 18 1991

Cite this

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title = "Eigen-matrix for the dynamic behavior of linear engineering structures",

abstract = "The eigen-matrix, defined by A = PΛP-1 (where P and Λ are the eigenvector and eigenvalue matrices of an MCK system, respectively), and its associated properties in describing the dynamic behaviors of linear elastic system are presented. The eigen-matrix is defined to satisfy the quadratic matrix equation of the form MA2 + CA + K = 0 An analytic solution to this equation for the proportionally damped system is obtained. For non-proportionally damped system, A numerical algorithm is developed. The numerical algorithm is especially useful in the dynamic analysis of structures with large number of degrees of freedom.",

author = "X. Ma and Z. Liang and Lee, \{G. C.\}",

year = "1991",

language = "English",

volume = "1",

pages = "19--24",

journal = "Proceedings of the International Modal Analysis Conference - IMAC",

issn = "1046-6770",

publisher = "Society for Experimental Mechanics",

note = "Proceedings of the 9th International Modal Analysis Conference Part 1 (of 2) ; Conference date: 15-04-1991 Through 18-04-1991",

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TY - JOUR

T1 - Eigen-matrix for the dynamic behavior of linear engineering structures

AU - Ma, X.

AU - Liang, Z.

AU - Lee, G. C.

PY - 1991

Y1 - 1991

N2 - The eigen-matrix, defined by A = PΛP-1 (where P and Λ are the eigenvector and eigenvalue matrices of an MCK system, respectively), and its associated properties in describing the dynamic behaviors of linear elastic system are presented. The eigen-matrix is defined to satisfy the quadratic matrix equation of the form MA2 + CA + K = 0 An analytic solution to this equation for the proportionally damped system is obtained. For non-proportionally damped system, A numerical algorithm is developed. The numerical algorithm is especially useful in the dynamic analysis of structures with large number of degrees of freedom.

AB - The eigen-matrix, defined by A = PΛP-1 (where P and Λ are the eigenvector and eigenvalue matrices of an MCK system, respectively), and its associated properties in describing the dynamic behaviors of linear elastic system are presented. The eigen-matrix is defined to satisfy the quadratic matrix equation of the form MA2 + CA + K = 0 An analytic solution to this equation for the proportionally damped system is obtained. For non-proportionally damped system, A numerical algorithm is developed. The numerical algorithm is especially useful in the dynamic analysis of structures with large number of degrees of freedom.

UR - https://www.scopus.com/pages/publications/0025898361

M3 - Conference article

AN - SCOPUS:0025898361

SN - 1046-6770

VL - 1

SP - 19

EP - 24

JO - Proceedings of the International Modal Analysis Conference - IMAC

JF - Proceedings of the International Modal Analysis Conference - IMAC

T2 - Proceedings of the 9th International Modal Analysis Conference Part 1 (of 2)

Y2 - 15 April 1991 through 18 April 1991

ER -

Eigen-matrix for the dynamic behavior of linear engineering structures

Abstract

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