TY - JOUR

T1 - Response Determination of Nonlinear Systems with Singular Matrices Subject to Combined Stochastic and Deterministic Excitations

AU - Ni, Peihua

AU - Fragkoulis, Vasileios C.

AU - Kong, Fan

AU - Mitseas, Ioannis P.

AU - Beer, Michael

N1 - Funding Information: 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.

PY - 2021/12

Y1 - 2021/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85111758218&partnerID=8YFLogxK

U2 - 10.1061/AJRUA6.0001167

DO - 10.1061/AJRUA6.0001167

M3 - Article

AN - SCOPUS:85111758218

VL - 7

JO - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering

JF - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering

SN - 2376-7642

IS - 4

M1 - 04021049

ER -