Higher order matrix differential equations with singular coefficient matrices

V. C. Fragkoulis; I. A. Kougioumtzoglou; A. A. Pantelous; A. Pirrotta

doi:10.1063/1.4912578

Higher order matrix differential equations with singular coefficient matrices

V. C. Fragkoulis
, I. A. Kougioumtzoglou
, A. A. Pantelous
, A. Pirrotta

Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review

Abstract

In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.

Original language	English
Title of host publication	Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
Editors	Theodore E. Simos, Theodore E. Simos, Charalambos Tsitouras, Theodore E. Simos
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735412873
DOIs	https://doi.org/10.1063/1.4912578
Publication status	Published - 10 Mar 2015
Externally published	Yes
Event	ICNAAM 2014, 12th International Conference on Numerical Analysis and Applied Mathematics - Rhodes, Greece Duration: 22 Sept 2014 → 28 Sept 2014 Conference number: 12

Publication series

Name	AIP Conference Proceedings
Volume	1648
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	ICNAAM 2014, 12th International Conference on Numerical Analysis and Applied Mathematics
Abbreviated title	ICNAAM 2014
Country/Territory	Greece
City	Rhodes
Period	22 Sept 2014 → 28 Sept 2014

Keywords

Higher order matrix equations
Multi-degree-of-freedom dynamical system
Random vibration theory
Singular matrices

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1063/1.4912578

Cite this

Fragkoulis, V. C., Kougioumtzoglou, I. A., Pantelous, A. A., & Pirrotta, A. (2015). Higher order matrix differential equations with singular coefficient matrices. In T. E. Simos, T. E. Simos, C. Tsitouras, & T. E. Simos (Eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 Article 340002 (AIP Conference Proceedings; Vol. 1648). American Institute of Physics Inc.. https://doi.org/10.1063/1.4912578

Fragkoulis, V. C. ; Kougioumtzoglou, I. A. ; Pantelous, A. A. et al. / Higher order matrix differential equations with singular coefficient matrices. Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. editor / Theodore E. Simos ; Theodore E. Simos ; Charalambos Tsitouras ; Theodore E. Simos. American Institute of Physics Inc., 2015. (AIP Conference Proceedings).

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title = "Higher order matrix differential equations with singular coefficient matrices",

abstract = "In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.",

keywords = "Higher order matrix equations, Multi-degree-of-freedom dynamical system, Random vibration theory, Singular matrices",

author = "Fragkoulis, \{V. C.\} and Kougioumtzoglou, \{I. A.\} and Pantelous, \{A. A.\} and A. Pirrotta",

note = "Publisher Copyright: {\textcopyright} 2015 AIP Publishing LLC. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.; ICNAAM 2014, 12th International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2014 ; Conference date: 22-09-2014 Through 28-09-2014",

year = "2015",

month = mar,

day = "10",

doi = "10.1063/1.4912578",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Simos, \{Theodore E.\} and Simos, \{Theodore E.\} and Charalambos Tsitouras and Simos, \{Theodore E.\}",

booktitle = "Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014",

address = "United States",

}

Fragkoulis, VC, Kougioumtzoglou, IA, Pantelous, AA & Pirrotta, A 2015, Higher order matrix differential equations with singular coefficient matrices. in TE Simos, TE Simos, C Tsitouras & TE Simos (eds), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014., 340002, AIP Conference Proceedings, vol. 1648, American Institute of Physics Inc., ICNAAM 2014, 12th International Conference on Numerical Analysis and Applied Mathematics, Rhodes, Greece, 22 Sept 2014. https://doi.org/10.1063/1.4912578

Higher order matrix differential equations with singular coefficient matrices. / Fragkoulis, V. C.; Kougioumtzoglou, I. A.; Pantelous, A. A. et al.
Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. ed. / Theodore E. Simos; Theodore E. Simos; Charalambos Tsitouras; Theodore E. Simos. American Institute of Physics Inc., 2015. 340002 (AIP Conference Proceedings; Vol. 1648).

Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review

TY - GEN

T1 - Higher order matrix differential equations with singular coefficient matrices

AU - Fragkoulis, V. C.

AU - Kougioumtzoglou, I. A.

AU - Pantelous, A. A.

AU - Pirrotta, A.

N1 - Conference code: 12

PY - 2015/3/10

Y1 - 2015/3/10

N2 - In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.

AB - In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.

KW - Higher order matrix equations

KW - Multi-degree-of-freedom dynamical system

KW - Random vibration theory

KW - Singular matrices

UR - https://www.scopus.com/pages/publications/84939650211

U2 - 10.1063/1.4912578

DO - 10.1063/1.4912578

M3 - Conference contribution

AN - SCOPUS:84939650211

T3 - AIP Conference Proceedings

BT - Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014

A2 - Simos, Theodore E.

A2 - Tsitouras, Charalambos

A2 - Simos, Theodore E.

PB - American Institute of Physics Inc.

T2 - ICNAAM 2014, 12th International Conference on Numerical Analysis and Applied Mathematics

Y2 - 22 September 2014 through 28 September 2014

ER -

Fragkoulis VC, Kougioumtzoglou IA, Pantelous AA, Pirrotta A. Higher order matrix differential equations with singular coefficient matrices. In Simos TE, Simos TE, Tsitouras C, Simos TE, editors, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. American Institute of Physics Inc. 2015. 340002. (AIP Conference Proceedings). doi: 10.1063/1.4912578

Higher order matrix differential equations with singular coefficient matrices

Abstract

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Keywords

ASJC Scopus subject areas

Access to Document

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