Abstract
Both time- and frequency-domain solution techniques are developed for determining the response of linear multi-degree-of-freedom systems exhibiting singular parameter matrices and endowed with derivative terms of noninteger orders modeled as rational numbers. This is done based on the Moore-Penrose matrix inverse theory, in conjunction with a state variable formulation and with a complex modal analysis treatment. It is worth noting that, for the class of systems considered herein, this treatment also yields decoupled governing equations, thus facilitating further their numerical solution. Next, a generalization of the standard frequency-domain input-output (excitation-response) relationship is derived based on an appropriately defined frequency response function. This spectral relationship is further extended to account also for stochastic excitation vector processes described by power spectral density matrices. Two illustrative examples are considered for demonstrating the validity of the herein developed technique and of the derived input-output relationships.
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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.
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Published In
Journal of Engineering Mechanics
Volume 147 • Issue 6 • June 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Oct 5, 2020
Accepted: Feb 2, 2021
Published online: Mar 27, 2021
Published in print: Jun 1, 2021
Discussion open until: Aug 27, 2021
ASCE Technical Topics:
- Analysis (by type)
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Frequency analysis
- Hydraulic engineering
- Hydraulic structures
- Linear functions
- Mathematical functions
- Mathematics
- Matrix (mathematics)
- Mooring
- Motion (dynamics)
- Parameters (statistics)
- Ports and harbors
- Power spectral density
- Probability
- Solid mechanics
- Statistical analysis (by type)
- Statistics
- Stochastic processes
- Vibration
- Water and water resources
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