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PDF Solution to nonlinear ship roll motion excited by external Poisson white noise
ER GuoKang1; ZHU HaiTao2; IU VaiPan1; KOU KunPang1
Conference NameThe Third International Conference on Dynamics, Vibration and Control
Source Publicationproceedings of The Third International Conference on Dynamics, Vibration and Control
Conference Date12-14 May 2010
Conference PlaceHangzhou, China

The evaluation on ship roll motion in seas has attracted many researchers in the field of science and engineering in the case of either deterministic or random excitation because overlarge motion will be a potential and life on the ship. For the case of random excitation. most efforts have been devoted to the moments of responses under continuous Gaussian white noise excitation. The probability density function (PDF) has been less addressed and other types of excitation are scarcely investigated (i.e. diserete Poisson of response white noise. In this paper. the stationary PDF solution to nonlinear ship roll motion subjected to Poisson white noise is analyzed. Under such random excitation, the stochastic roll response of ship can be evaluated by a joint continuous Markov model. According to this model, the joint PDF solution for the roll displacement and velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. Subsequently, the exponential polynomial closure EPC) method is adopted to solve the generalized FPK equation. In the EPC method, the PDF solution is assumed to be an exponential function of polynomials in state variables. Special measure is taken such that the generalized FPK equation is satisfied in average sense of integration with the assumed PDF·The problem of determining unknown parameters of the approximate PDF finally results in solving simultancous nonlinear algebraic equations In order to evaluate the effectiveness of the EPC method. numerical analysis is conducted. The results show that the result obtained with the EPC method (n-2) is the same as the results given by the equivalent linearization (EQL) method and the EQL. resuit differs a lot from the simulation result, especially in the tail region. When the polynomial (n) increases to 4 or 6. the EPC method presents a good result compared with the simulation even in the tail of the PDF

KeywordProbability Density Function Ship Roll Motion Poisson White Noise Generalized Fpk Equation
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Document TypeConference paper
CollectionFaculty of Science and Technology
Affiliation1.Department of Civil and Environmental Engineering, University of Macau, Macao SAR, China
2.Department of Civil Engineering, Tianjin University / Key Laboratory of Coast Civil Structure Safety (Tianjin University), Ministry of Education, Tianjin 300072, China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
ER GuoKang,ZHU HaiTao,IU VaiPan,et al. PDF Solution to nonlinear ship roll motion excited by external Poisson white noise[C],2010.
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