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 -