Details
| Original language | English |
|---|---|
| Article number | 108701 |
| Journal | Mechanical Systems and Signal Processing |
| Volume | 169 |
| Early online date | 28 Dec 2021 |
| Publication status | Published - 15 Apr 2022 |
Abstract
Novel wavelet-based input–output (excitation–response) relationships are developed referring to stochastically excited linear structural systems with singular parameter matrices. This is done by relying on the family of periodized generalized harmonic wavelets for expanding the excitation and response processes, and by resorting to the concept of Moore–Penrose matrix inverse for solving the resulting overdetermined linear system of algebraic equations to calculate the response wavelet coefficients. In this regard, system response statistics in the joint time–frequency domain, such as the response evolutionary power spectrum matrix, can be determined in a straightforward manner based on the herein derived input–output relationships. The developed technique can be construed as a generalization of earlier efforts in the literature to account for singular parameter matrices in the governing equations of motion. The reliability of the technique is demonstrated by comparing the analytical results with pertinent Monte Carlo simulation data. This is done in conjunction with various diverse numerical examples pertaining to energy harvesters with coupled electromechanical equations, oscillators subject to non-white excitations modeled via auxiliary filter equations and structural systems modeled by a set of dependent coordinates.
Keywords
- Energy harvesting, Evolutionary power spectrum, Joint time–frequency analysis, Moore–Penrose matrix inverse, Random vibration
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Mechanical Systems and Signal Processing, Vol. 169, 108701, 15.04.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Excitation–response relationships for linear structural systems with singular parameter matrices
T2 - A periodized harmonic wavelet perspective
AU - Pasparakis, G. D.
AU - Kougioumtzoglou, I. A.
AU - Fragkoulis, V. C.
AU - Kong, F.
AU - Beer, M.
N1 - Funding Information: The authors gratefully acknowledge the support from the European Union's Horizon 2020 research and innovation programme under the Marie Sk?odowska-Curie grant agreement No 764547, and from the German Research Foundation under Grant No. FR 4442/2-1.
PY - 2022/4/15
Y1 - 2022/4/15
N2 - Novel wavelet-based input–output (excitation–response) relationships are developed referring to stochastically excited linear structural systems with singular parameter matrices. This is done by relying on the family of periodized generalized harmonic wavelets for expanding the excitation and response processes, and by resorting to the concept of Moore–Penrose matrix inverse for solving the resulting overdetermined linear system of algebraic equations to calculate the response wavelet coefficients. In this regard, system response statistics in the joint time–frequency domain, such as the response evolutionary power spectrum matrix, can be determined in a straightforward manner based on the herein derived input–output relationships. The developed technique can be construed as a generalization of earlier efforts in the literature to account for singular parameter matrices in the governing equations of motion. The reliability of the technique is demonstrated by comparing the analytical results with pertinent Monte Carlo simulation data. This is done in conjunction with various diverse numerical examples pertaining to energy harvesters with coupled electromechanical equations, oscillators subject to non-white excitations modeled via auxiliary filter equations and structural systems modeled by a set of dependent coordinates.
AB - Novel wavelet-based input–output (excitation–response) relationships are developed referring to stochastically excited linear structural systems with singular parameter matrices. This is done by relying on the family of periodized generalized harmonic wavelets for expanding the excitation and response processes, and by resorting to the concept of Moore–Penrose matrix inverse for solving the resulting overdetermined linear system of algebraic equations to calculate the response wavelet coefficients. In this regard, system response statistics in the joint time–frequency domain, such as the response evolutionary power spectrum matrix, can be determined in a straightforward manner based on the herein derived input–output relationships. The developed technique can be construed as a generalization of earlier efforts in the literature to account for singular parameter matrices in the governing equations of motion. The reliability of the technique is demonstrated by comparing the analytical results with pertinent Monte Carlo simulation data. This is done in conjunction with various diverse numerical examples pertaining to energy harvesters with coupled electromechanical equations, oscillators subject to non-white excitations modeled via auxiliary filter equations and structural systems modeled by a set of dependent coordinates.
KW - Energy harvesting
KW - Evolutionary power spectrum
KW - Joint time–frequency analysis
KW - Moore–Penrose matrix inverse
KW - Random vibration
UR - http://www.scopus.com/inward/record.url?scp=85121855931&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2021.108701
DO - 10.1016/j.ymssp.2021.108701
M3 - Article
AN - SCOPUS:85121855931
VL - 169
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
M1 - 108701
ER -