Details
| Original language | English |
|---|---|
| Article number | 110009 |
| Journal | Mechanical Systems and Signal Processing |
| Volume | 188 |
| Early online date | 9 Dec 2022 |
| Publication status | Published - 1 Apr 2023 |
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.
Keywords
- Combined excitation, Energy harvester, Moore–Penrose matrix inverse, Statistical linearization, Stochastic dynamics
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. 188, 110009, 01.04.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Non-stationary response of nonlinear systems with singular parameter matrices subject to combined deterministic and stochastic excitation
AU - Ni, P.
AU - Fragkoulis, V. C.
AU - Kong, F.
AU - Mitseas, I. P.
AU - Beer, M.
N1 - Funding Information: The authors gratefully acknowledge the support by the German Research Foundation (Grant No. FR 4442/2-1 and No. BE 2570/7-1 with MI 2459/1-1 ), by the National Natural Science Foundation of China (Grant No. 52078399 ), and by the Hellenic Foundation for Research and Innovation (Grant No. 1261 ).
PY - 2023/4/1
Y1 - 2023/4/1
N2 - 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.
AB - 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.
KW - Combined excitation
KW - Energy harvester
KW - Moore–Penrose matrix inverse
KW - Statistical linearization
KW - Stochastic dynamics
UR - http://www.scopus.com/inward/record.url?scp=85143785895&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2022.110009
DO - 10.1016/j.ymssp.2022.110009
M3 - Article
AN - SCOPUS:85143785895
VL - 188
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
M1 - 110009
ER -