Details
| Original language | English |
|---|---|
| Journal | Journal of engineering mechanics |
| Volume | 148 |
| Issue number | 3 |
| Early online date | 3 Jan 2022 |
| Publication status | Published - Mar 2022 |
Abstract
An asymptotic approximation methodology for solving standard random eigenvalue problems is generalized herein to account for structural systems with singular random parameter matrices. In this regard, resorting to the concept of the Moore-Penrose matrix inverse and generalizing expressions for the rate of change of the eigenvalues, novel closed-form expressions are derived for the joint moments of the system natural frequencies. Two indicative examples pertaining to multiple-degree-of-freedom structural systems are considered for demonstrating the reliability of the methodology. Comparisons with pertinent Monte Carlo simulation data are included as well.
Keywords
- Moore-Penrose inverse, Random eigenvalue problem, Random vibration, Singular matrix
ASJC Scopus subject areas
- Engineering(all)
- Mechanical Engineering
- Engineering(all)
- Mechanics of Materials
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In: Journal of engineering mechanics, Vol. 148, No. 3, 03.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Joint Statistics of Natural Frequencies Corresponding to Structural Systems with Singular Random Parameter Matrices
AU - Fragkoulis, Vasileios C.
AU - Kougioumtzoglou, Ioannis A.
AU - Pantelous, Athanasios A.
AU - Beer, Michael
N1 - Funding Information: The authors gratefully acknowledge the support from the German Research Foundation under Grant No. FR 4442/2-1.
PY - 2022/3
Y1 - 2022/3
N2 - An asymptotic approximation methodology for solving standard random eigenvalue problems is generalized herein to account for structural systems with singular random parameter matrices. In this regard, resorting to the concept of the Moore-Penrose matrix inverse and generalizing expressions for the rate of change of the eigenvalues, novel closed-form expressions are derived for the joint moments of the system natural frequencies. Two indicative examples pertaining to multiple-degree-of-freedom structural systems are considered for demonstrating the reliability of the methodology. Comparisons with pertinent Monte Carlo simulation data are included as well.
AB - An asymptotic approximation methodology for solving standard random eigenvalue problems is generalized herein to account for structural systems with singular random parameter matrices. In this regard, resorting to the concept of the Moore-Penrose matrix inverse and generalizing expressions for the rate of change of the eigenvalues, novel closed-form expressions are derived for the joint moments of the system natural frequencies. Two indicative examples pertaining to multiple-degree-of-freedom structural systems are considered for demonstrating the reliability of the methodology. Comparisons with pertinent Monte Carlo simulation data are included as well.
KW - Moore-Penrose inverse
KW - Random eigenvalue problem
KW - Random vibration
KW - Singular matrix
UR - http://www.scopus.com/inward/record.url?scp=85121858264&partnerID=8YFLogxK
U2 - 10.1061/(ASCE)EM.1943-7889.0002081
DO - 10.1061/(ASCE)EM.1943-7889.0002081
M3 - Article
AN - SCOPUS:85121858264
VL - 148
JO - Journal of engineering mechanics
JF - Journal of engineering mechanics
SN - 0733-9399
IS - 3
ER -