Joint Statistics of Natural Frequencies Corresponding to Structural Systems with Singular Random Parameter Matrices
Publication: Journal of Engineering Mechanics
Volume 148, Issue 3
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.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors gratefully acknowledge the support from the German Research Foundation under Grant No. FR 4442/2-1.
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Journal of Engineering Mechanics
Volume 148 • Issue 3 • March 2022
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© 2022 American Society of Civil Engineers.
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Received: Feb 26, 2021
Accepted: Nov 3, 2021
Published online: Jan 3, 2022
Published in print: Mar 1, 2022
Discussion open until: Jun 3, 2022
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