Non-stationary response of nonlinear systems with singular parameter matrices subject to combined deterministic and stochastic excitation

authored by: P. Ni, V. C. Fragkoulis, F. Kong, I. P. Mitseas, M. Beer
Abstract: A new technique is proposed for determining the response of multi-degree-of-freedom nonlinear systems with singular parameter matrices subject to combined deterministic and non-stationary stochastic excitation. Singular matrices in the governing equations of motion potentially account for the presence of constraints equations in the system. Further, they also appear when a redundant coordinates modeling is adopted to derive the equations of motion of complex multi-body systems. In this regard, the system response is decomposed into a deterministic and a stochastic component corresponding to the two components of the excitation. Then, two sets of differential equations are formulated and solved simultaneously to compute the system response. The first set pertains to the deterministic response component, whereas the second one pertains to the stochastic component of the response. The latter is derived by utilizing the generalized statistical linearization method for systems with singular matrices, while a formula for determining the time-dependent equivalent elements of the generalized statistical linearization methodology is also derived. The efficiency of the proposed technique is demonstrated by pertinent numerical examples. Specifically, a vibration energy harvesting device subject to combined deterministic and modulated white noise excitation and a structural nonlinear system with singular parameter matrices subject to combined deterministic and modulated white and colored noise excitations are considered.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): Hefei University of Technology
University of Leeds
National Technical University of Athens (NTUA)
University of Liverpool
Tongji University
Type: Article
Journal: Mechanical Systems and Signal Processing
Volume: 188
ISSN: 0888-3270
Publication date: 01.04.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Control and Systems Engineering, Signal Processing, Civil and Structural Engineering, Aerospace Engineering, Mechanical Engineering, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.ymssp.2022.110009 (Access: Closed)