TY - JOUR

T1 - Harmonic wavelets based response evolutionary power spectrum determination of linear and nonlinear structural systems with singular matrices

AU - Pasparakis, G. D.

AU - Fragkoulis, V. C.

AU - Beer, M.

N1 - Funding Information: The authors gratefully acknowledge the support and funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 764547.

PY - 2021/2/15

Y1 - 2021/2/15

N2 - A new approximate analytical technique is proposed for determining the response evolutionary power spectrum (EPS) of stochastically excited structural multi-degree-of-freedom (MDOF) linear and nonlinear systems with singular matrices. Such systems can appear, indicatively, when a redundant coordinates modeling is adopted for forming the equations of motion of complex multi-body systems. For this case, it can be argued that this modeling approach facilitates the system's stochastic response analysis, since employment of redundant DOFs is associated with computational cost efficient solution frameworks, and potentially provides with enhanced modeling flexibility. In this context, aiming at the joint time–frequency response analysis of MDOF systems, recently developed wavelet-based solution frameworks, which generalize classic input–output relationships of random vibration, are adopted and further generalized in this paper to account for systems with singular matrices. Specifically, resorting to the theory of generalized inverses of singular matrices, as well as to the theory of harmonic wavelets, a Moore–Penrose generalized matrix inverse excitation-response relationship is derived herein for determining the response EPS of linear MDOF systems. Further, a recently developed harmonic-wavelet-based statistical linearization technique is also generalized to account for the case of nonlinear MDOF systems. The validity of the proposed technique is demonstrated by pertinent numerical examples.

AB - A new approximate analytical technique is proposed for determining the response evolutionary power spectrum (EPS) of stochastically excited structural multi-degree-of-freedom (MDOF) linear and nonlinear systems with singular matrices. Such systems can appear, indicatively, when a redundant coordinates modeling is adopted for forming the equations of motion of complex multi-body systems. For this case, it can be argued that this modeling approach facilitates the system's stochastic response analysis, since employment of redundant DOFs is associated with computational cost efficient solution frameworks, and potentially provides with enhanced modeling flexibility. In this context, aiming at the joint time–frequency response analysis of MDOF systems, recently developed wavelet-based solution frameworks, which generalize classic input–output relationships of random vibration, are adopted and further generalized in this paper to account for systems with singular matrices. Specifically, resorting to the theory of generalized inverses of singular matrices, as well as to the theory of harmonic wavelets, a Moore–Penrose generalized matrix inverse excitation-response relationship is derived herein for determining the response EPS of linear MDOF systems. Further, a recently developed harmonic-wavelet-based statistical linearization technique is also generalized to account for the case of nonlinear MDOF systems. The validity of the proposed technique is demonstrated by pertinent numerical examples.

KW - Evolutionary power spectrum

KW - Harmonic wavelet

KW - Moore–Penrose inverse

KW - Singular matrix

KW - Stochastic dynamics

KW - Time–frequency analysis

UR - http://www.scopus.com/inward/record.url?scp=85089956857&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2020.107203

DO - 10.1016/j.ymssp.2020.107203

M3 - Article

AN - SCOPUS:85089956857

VL - 149

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 107203

ER -