Details
| Original language | English |
|---|---|
| Article number | 040150811 |
| Journal | Journal of engineering mechanics |
| Volume | 142 |
| Issue number | 2 |
| Publication status | Published - 1 Feb 2016 |
| Externally published | Yes |
Abstract
A framework is developed for determining the stochastic response of linear multi-degree-of-freedom (MDOF) structural systems with singular matrices. This system modeling can arise when using more than the minimum number of coordinates, and can be advantageous, for instance, in cases of complex multibody systems whose dynamics satisfy a number of constraints. In such cases the explicit formulation of the equations of motion can be a nontrivial task, whereas the introduction of additional/redundant degrees of freedom can facilitate the formulation of the equations of motion in a less labor-intensive manner. Relying on the generalized matrix inverse theory and on the Moore-Penrose (M-P) matrix inverse, standard concepts, relationships, and equations of the linear random vibration theory are extended and generalized herein to account for systems with singular matrices. Adopting a state-variable formulation, equations governing the system response mean vector and covariance matrix are formed and solved. Further, it is shown that a complex modal analysis treatment, unlike the standard system modeling case, does not lead to decoupling of the equations of motion. However, relying on a singular value decomposition of the system transition matrix significantly facilitates the efficient computation of the system response statistics. A linear structural system with singular matrices is considered as a numerical example for demonstrating the applicability of the methodology and for elucidating certain related numerical aspects.
Keywords
- Moore-Penrose inverse, Random vibration, Singular matrix, Structural dynamics
ASJC Scopus subject areas
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
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In: Journal of engineering mechanics, Vol. 142, No. 2, 040150811, 01.02.2016.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Linear Random Vibration of Structural Systems with Singular Matrices
AU - Fragkoulis, Vasileios C.
AU - Kougioumtzoglou, Ioannis A.
AU - Pantelous, Athanasios A.
N1 - Publisher Copyright: © 2015 American Society of Civil Engineers. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2016/2/1
Y1 - 2016/2/1
N2 - A framework is developed for determining the stochastic response of linear multi-degree-of-freedom (MDOF) structural systems with singular matrices. This system modeling can arise when using more than the minimum number of coordinates, and can be advantageous, for instance, in cases of complex multibody systems whose dynamics satisfy a number of constraints. In such cases the explicit formulation of the equations of motion can be a nontrivial task, whereas the introduction of additional/redundant degrees of freedom can facilitate the formulation of the equations of motion in a less labor-intensive manner. Relying on the generalized matrix inverse theory and on the Moore-Penrose (M-P) matrix inverse, standard concepts, relationships, and equations of the linear random vibration theory are extended and generalized herein to account for systems with singular matrices. Adopting a state-variable formulation, equations governing the system response mean vector and covariance matrix are formed and solved. Further, it is shown that a complex modal analysis treatment, unlike the standard system modeling case, does not lead to decoupling of the equations of motion. However, relying on a singular value decomposition of the system transition matrix significantly facilitates the efficient computation of the system response statistics. A linear structural system with singular matrices is considered as a numerical example for demonstrating the applicability of the methodology and for elucidating certain related numerical aspects.
AB - A framework is developed for determining the stochastic response of linear multi-degree-of-freedom (MDOF) structural systems with singular matrices. This system modeling can arise when using more than the minimum number of coordinates, and can be advantageous, for instance, in cases of complex multibody systems whose dynamics satisfy a number of constraints. In such cases the explicit formulation of the equations of motion can be a nontrivial task, whereas the introduction of additional/redundant degrees of freedom can facilitate the formulation of the equations of motion in a less labor-intensive manner. Relying on the generalized matrix inverse theory and on the Moore-Penrose (M-P) matrix inverse, standard concepts, relationships, and equations of the linear random vibration theory are extended and generalized herein to account for systems with singular matrices. Adopting a state-variable formulation, equations governing the system response mean vector and covariance matrix are formed and solved. Further, it is shown that a complex modal analysis treatment, unlike the standard system modeling case, does not lead to decoupling of the equations of motion. However, relying on a singular value decomposition of the system transition matrix significantly facilitates the efficient computation of the system response statistics. A linear structural system with singular matrices is considered as a numerical example for demonstrating the applicability of the methodology and for elucidating certain related numerical aspects.
KW - Moore-Penrose inverse
KW - Random vibration
KW - Singular matrix
KW - Structural dynamics
UR - http://www.scopus.com/inward/record.url?scp=84978484591&partnerID=8YFLogxK
U2 - 10.1061/(asce)em.1943-7889.0001000
DO - 10.1061/(asce)em.1943-7889.0001000
M3 - Article
AN - SCOPUS:84978484591
VL - 142
JO - Journal of engineering mechanics
JF - Journal of engineering mechanics
SN - 0733-9399
IS - 2
M1 - 040150811
ER -