Response Determination of Nonlinear Systems with Singular Matrices Subject to Combined Stochastic and Deterministic Excitations
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 4
Abstract
A new technique is proposed for determining the response of multi-degree-of-freedom nonlinear systems with singular parameter matrices subject to combined stochastic and deterministic excitations. Singular matrices in the governing equations of motion potentially account for the presence of constraint equations in the system. They also appear when a redundant coordinates modeling is adopted to derive the equations of motion of complex multibody systems. Since the system is subject to both stochastic and deterministic excitations, its response also has two components, namely a deterministic and a stochastic component. Therefore, using the harmonic balance method to treat the deterministic component leads to an overdetermined system of equations to be solved for computing the associated coefficients. Then the generalized statistical linearization method for deriving the stochastic response of nonlinear systems with singular matrices, in conjunction with an averaging treatment, are utilized to determine the stochastic component of the response. The validity of the proposed technique is demonstrated by pertinent numerical examples.
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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 and funding from the German Research Foundation under Grants No. BE 2570/7-1 and MI 2459/1-1, and from the European Union’s Horizon 2020 RISE 2016 programme under Grant agreement No. 730888.
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ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 4 • December 2021
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© 2021 American Society of Civil Engineers.
History
Received: Oct 23, 2020
Accepted: Apr 29, 2021
Published online: Jul 31, 2021
Published in print: Dec 1, 2021
Discussion open until: Dec 31, 2021
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