The probabilistic solution of stochastic oscillators with even nonlinearity under poisson excitation

• Authors: Siu-Siu Guo , Guo-Kang Er
• Languages of publication: EN

Abstracts

EN

The probabilistic solutions of nonlinear stochastic oscillators with even nonlinearity driven by Poisson white noise are investigated in this paper. The stationary probability density function (PDF) of the oscillator responses governed by the reduced Fokker-Planck-Kolmogorov equation is obtained with exponentialpolynomial closure (EPC) method. Different types of nonlinear oscillators are considered. Monte Carlo simulation is conducted to examine the effectiveness and accuracy of the EPC method in this case. It is found that the PDF solutions obtained with EPC agree well with those obtained with Monte Carlo simulation, especially in the tail regions of the PDFs of oscillator responses. Numerical analysis shows that the mean of displacement is nonzero and the PDF of displacement is nonsymmetric about its mean when there is even nonlinearity in displacement in the oscillator. Numerical analysis further shows that the mean of velocity always equals zero and the PDF of velocity is symmetrically distributed about its mean.

Keywords

EN

even nonlinearity; exponential-polynomial closure method; Fokker-Planck-Komogorov (FPK) equation; poisson white noise

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2012
• Volume: 10
• Issue: 3
• Pages: 702-707

Dates

published

1 - 6 - 2012

online

17 - 6 - 2012

Contributors

author

Siu-Siu Guo

• Faculty of Science and Technology, University of Macau, Macau SAR, China

author

Guo-Kang Er

• Faculty of Science and Technology, University of Macau, Macau SAR, China

References

• [1] T.T. Soong, Random Differential Equations in Science and Enginnering (Academic Press, New York, 1973)
• [2] H. Risken, T. Frank, Fokker-Planck Equation: Methods of Solution and Applications (Springer-Verlag, Berlin, 1989) http://dx.doi.org/10.1007/978-3-642-61544-3[Crossref]
• [3] K. Sobczyk, Stochastic Differential Equations with Application to Science and Engineering (Kluwer, Boston, 1991)
• [4] O. Schmitz, S.K. Hammpel, H. Eul, D. Schwingshackl, Adv. Radio. Sci. 5, 265 (2007) http://dx.doi.org/10.5194/ars-5-265-2007[Crossref]
• [5] A.K. Chaudhary, V.B. Bhatia, M.K. Das, R.K. Tavakol, J. Astrophys. Astr. 16, 45 (1995) http://dx.doi.org/10.1007/BF02702485[Crossref]
• [6] C.W.S. To, D.M. Li, Prob. Eng. Mech. 6, 184 (1991) http://dx.doi.org/10.1016/0266-8920(91)90009-S[Crossref]
• [7] L. Cveticanin, Publication de l’Institut Mathe. 85, 119 (2009) http://dx.doi.org/10.2298/PIM0999119C[Crossref]
• [8] R.A. Ibrahim, A. Soundararajan, Int. J. Non-Linear Mech. 20, 309 (1985) http://dx.doi.org/10.1016/0020-7462(85)90039-3[Crossref]
• [9] G. Schmidt, Z. Angew. Math. Mech. 60, 409 (1981) http://dx.doi.org/10.1002/zamm.19800600906[Crossref]
• [10] R.A. Ibrahim, A. Soundararajan, J. Sound Vib. 91, 119 (1983) http://dx.doi.org/10.1016/0022-460X(83)90455-8[Crossref]
• [11] J.B. Roberts, J. Sound Vib. 24, 23 (1972) http://dx.doi.org/10.1016/0022-460X(72)90119-8[Crossref]
• [12] R.C. Booton, IRE Trans. Circuit Theory 1, 9 (1954)
• [13] T.K. Caughey, ASME J. Appl. Mech. 26, 341 (1959)
• [14] G.Q. Cai, J. Sound Vib. 278, 889 (2004) http://dx.doi.org/10.1016/j.jsv.2003.10.030[Crossref]
• [15] L. Socha, Linearization Methods for Stochastic Dynamic Systems (Springer, Berlin, 2008)
• [16] G.Q. Cai, Y.K. Lin, Int. J. Non-Linear Mech. 27, 955 (1992) http://dx.doi.org/10.1016/0020-7462(92)90048-C[Crossref]
• [17] R. Iwankiewicz, S.R.K. Nielsen, J. Sound Vib. 156, 407 (1992) http://dx.doi.org/10.1016/0022-460X(92)90736-H[Crossref]
• [18] Z.Y. Su, J.M. Falzarano, Int. Ship. Prog. 58, 97 (2011)
• [19] H.U. Kölüğlu, S.R.K. Nielsen, R. Iwankiewicz, J. Sound Vib. 176, 19 (1994) http://dx.doi.org/10.1006/jsvi.1994.1356[Crossref]
• [20] H.U. Kölüğlu, S.R.K. Nielsen, R. Iwankiewicz, J. Eng. Mech. ASCE 121, 117 (1995) http://dx.doi.org/10.1061/(ASCE)0733-9399(1995)121:1(117)[Crossref]
• [21] S.F. Wojtkiewicz, E.A. Johnson, L.A. Bergman, M. Grigoriu, B.F. Spencer Jr., Comput. Methods Appl. Mech. Eng. 168, 73 (1999) http://dx.doi.org/10.1016/S0045-7825(98)00098-X[Crossref]
• [22] R.S. Langley, J. Sound Vib. 101(1), 41 (1985) http://dx.doi.org/10.1016/S0022-460X(85)80037-7[Crossref]
• [23] G.K. Er, S.S. Guo, In: G. Deodatis and P.D. Spanos (Ed.), International Conference of Computational Stochastic Mechanics, 13–16 June, 2010, Rhodes, Greece (Research Publishing Services, Singapore 2011) 230
• [24] G.K. Er, Nonlinear Dyn. 17, 285 (1998) http://dx.doi.org/10.1023/A:1008346204836[Crossref]
• [25] G.K. Er, ASME J. Appl. Mech. 67, 355 (2000) http://dx.doi.org/10.1115/1.1304842[Crossref]
• [26] G.K. Er, H.T. Zhu, V.P. Iu, K.P. Kou, AIAA J. 46, 2839 (2008) http://dx.doi.org/10.2514/1.36556[Crossref]
• [27] H.T. Zhu, G.K. Er, V.P. Iu, K.P. Kou, J. Sound Vib. 330, 2900 (2011) http://dx.doi.org/10.1016/j.jsv.2011.01.005[Crossref]
• [28] G.K. Er, Annalen der Physik 523, 247 (2011) http://dx.doi.org/10.1002/andp.201010465[Crossref]
• [29] G.K. Er, V.P. Iu, In: W.Q. Zhu, Y.K. Lin, G.Q. Cai (Ed.), IUTAM Symposium on Nonlinear Stochastic Dynamics and Control, 10–14 May, 2011, Hangzhou, China (Springer, 2011) IUTAM book series 29, 25

Identifiers

DOI

10.2478/s11534-012-0062-7