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Citation:
　M. Salai Mathi Selvi,L. Rajendran,Marwan Abukhaled.Estimation of Rolling Motion of Ship in Random Beam Seas by Efficient Analytical and Numerical Approaches[J].Journal of Marine Science and Application,2021,(1):55-66.[doi:10.1007/s11804-020-00183-x]
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Estimation of Rolling Motion of Ship in Random Beam Seas by Efficient Analytical and Numerical Approaches

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Title:
Estimation of Rolling Motion of Ship in Random Beam Seas by Efficient Analytical and Numerical Approaches
Author(s):
M. Salai Mathi Selvi1;  L. Rajendran1;  Marwan Abukhaled2
Affilations:
Author(s):
M. Salai Mathi Selvi1;  L. Rajendran1;  Marwan Abukhaled2
1. Department of Mathematics, AMET (Deemed to be University), Chennai, Tamil Nadu, India;
2. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE
Keywords:
Nonlinear damping; Steady-state roll motion; Ultraspherical wavelets; Homotopy perturbation method; Analytical solution
分类号:
-
DOI:
10.1007/s11804-020-00183-x
Abstract:
A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation. Analytical expressions for the roll angle, velocity, acceleration, and damping and restoring moments are derived using a modified approach of homotopy perturbation method (HPM). Also, the operational matrix of derivatives of ultraspherical wavelets is used to obtain a numerical solution of the governing equation. Illustrative examples are provided to examine the applicability and accuracy of the proposed methods when compared with a highly accurate numerical scheme.

References:

Abualrub T, Abukhaled M (2015) Wavelets approach for optimal boundary control of cellular uptake in tissue engineering. Int J Comp Math 92(7):1402–1412. https://doi.org/10.1080/00207160.2014.941826
Abualrub T, Abukhaled M, Jamal B (2018) Wavelets approach for the optimal control of vibrating plates by piezoelectric patches. J Vibr Cont 24(6):1101 –1108. https://doi.org/10.1177/1077546316657781
Abukhaled M (2013) Variational iteration method for nonlinear singular two-point boundary value problems arising in human physiology. J Math:ID:720134. https://doi.org/10.1155/2013/720134
Abukhaled M (2017) Green’s function iterative approach for solving strongly nonlinear oscillators. J Comp Nonlinear Dyn 12(5):051021. https://doi.org/10.1115/1.4036813
Agarwal D (2015) A study on the feasibility of using fractional differential equations for roll damping models. Master thesis, Virginia Polytechnic Institute and State University. http://hdl.handle.net/10919/52959
Aloisio G, Felice F (2006) PIV analysis around the bilge keel of a ship model in a free roll decay. In: XIV Congresso Nazionale AI VE. LA., Rome, Italy
Bassler CC, Carneal JB, Atsavapranee P (2007) Experimental investigation of hydrodynamic coefficients of a wavepiercing tumble home hull form. In: Proceeding of the 26th International Conference on Offshore Mechanics and Arctic Engineering, San Diego, USA
Cardo A, Francescutto A, Nabergoj R (1981) Ultraharmonics and subharmonics in the rolling motion of a ship: steadystate solution.Int Ship building Progress 28:234–251
Cardo A, Francescutto A, Nabergoj R (1984) Nonlinear rolling response in a regular sea. Int Shipbuild Prog 31(360):204–206. https://doi.org/10.3233/ISP-1984-3136002
Chen CL, Liu YC (1998) Solution of two-point boundary-value problems using the differential transformation method. J Optimization Theory Appl 99:23–35
Comini G, Del Guidice S, Lewis RW, Zienkiewicz OC (1970) Finite element solution of non-linear heat conduction problems with special reference to phase change. Num Meth Engg 8:613–624
Demirel H, Alarcin F (2016) LMI-based H2 and H1 state-feedback controller design for fin stabilizer of nonlinear roll motion of a fishing boat. Brodogradnja: Teorija i praksa brodogradnje i pomorske tehnike 67(4):91–107. https://doi.org/10.21278/brod67407
Demirel H, Dogrul A, Sezen S, Alarcin F (2017) Backstepping control of nonlinear roll motion for a trawler with fin stabilizer. Transactions of the Royal Institution of Naval Architects Part A: International Journal of Maritime Engineering, Part A2 159, pp. 205-212. doi:10.3940/rina.ijme.2017.a2.420
Doha EH, Abd-Elhameed WM, Youssri YH (2016) New ultraspherical wavelets collocation method for solving 2nth order initial and boundary value problems. J Egyp Math Soc 24:319–327. https://doi.org/10.1016/j.joems.2015.05.002
Froude W (1861) On the rolling of ships. Transactions of the Institution of Naval Architects 2, 1861, 180–229.
He JH (1999) Homotopy perturbation technique. Comp Meth Appl Mech Engg 178(4):257–262. https://doi.org/10.1016/S0045-7825(99)00018-3
Himeno Y (1981) Prediction of ship roll damping-a state of the art. DTIC Document, Ann Arbor.
Huang BG, Zou ZJ, Ding WW (2018) Online prediction of ship roll motion based on a coarse and fine tuning fixed grid wavelet network. Ocean Eng160:425–437. https://doi.org/10.1016/j.oceaneng.2018.04.065
Ikeda Y, Ali B, Yoshida H (2004) A roll damping prediction method for a FPSO with steady drift motion. Proceeding of the 14th International Conference on Offshore and Polar Engineering Conference, Toulon, France 676–681.
Jang TS (2011) Non-parametric simultaneous identification of both the nonlinear damping and restoring characteristics of nonlinear systems whose dampings depend on velocity alone. Mech Syst Signal Process 25(4):1159–1173. https://doi.org/10.1016/j.ymssp.2010.11.002
Jang TS (2013) A method for simultaneous identification of the full nonlinear damping and the phase shift and amplitude of the external harmonic excitation in a forced nonlinear oscillator. Comput Struct 120:77–85. https://doi.org/10.1016/j.compstruc.2013.02.008
Jang TS, Choi HS, Han SL (2009) A new method for detecting non-linear damping and restoring forces in non-linear oscillation systems from transient data. Int J Non-Linear Mech 44(7):801–808. https://doi.org/10.1016/j.ijnonlinmec.2009.05.001
Kato H (1965) Effects of bilge keels on the rolling of ships. J. Soc. Nav.Archit. Jpn. 117:93–101
Khuri SA, Abukhaled M (2017) A semi-analytical solution of amperometric enzymatic reactions based on Green’s functions and fixed point iterative schemes. J Electroanalytical Chem 792:66–71.https://doi.org/10.1016/j.jelechem.2017.03.015
Kianejad SS, Enshaei H, Du_y J, Ansarifard N (2019) Prediction of a ship roll added mass moment of inertia using numerical simulation.Ocean Eng 173:77–89. https://doi.org/10.1016/j.oceaneng.2018.12.049
Lavrov A, Rodrigues JM, Gadelho JFM, GuedesSoares C (2017) Calculation of hydrodynamic coe_cients of ship sections in roll motion using Navier-Stokes equations. Ocean Eng 133:36–46. https://doi.org/10.1016/j.oceaneng.2017.01.027
Liao S (1997) Homotopy analysis method: a new analytical technique for nonlinear problems. Commun Nonlinear Sci Numer Simul 2(2):95–100. https://doi.org/10.1016/S1007-5704(97)90047-2
Liao S (2004) On the homotopy analysis method for nonlinear problems. Appl Math Comput 47(2):499–513. https://doi.org/10.1016/S0096-3003(02)00790-7
Liao SJ, Chwang AT (1998) Application of homotopy analysis method in nonlinar oscillations. J Appl Mech 65(4):914–922. https://doi.org/10.1115/1.2791935
Lihua L, Peng Z, Songtao Z, Ming J, Jia Y (2018) Simulation analysis of fin stabilizer on ship roll control during turning motion. Ocean Eng 164:733–748. https://doi.org/10.1016/j.oceaneng.2018.07.015
Lu J (2007) Variational iteration method for solving a nonlinear system of second-order boundary value problems. Comp Math Appl 54:1133–1138. https://doi.org/10.1016/j.camwa.2006.12.060
Oliveira AC, Fernandes AC (2012) An empirical nonlinear model to estimate FPSO with extended bilge keel roll linear equivalent damping in extreme seas. In: Proceeding of the 31st International Conference on Ocean, Offshore and Arctic Engineering, (OMAE). Paper OMAE2012-83360, Rio de Janeiro, Brazil.
Oliveira AC, Fernandes AC (2014) The nonlinear roll damping of a FPSO hull. J Off shore Mech Arct Eng 136:1–10. https://doi.org/10.1115/1.4025870
Rainville ED (1960) Special functions. The Macmillan Co., New York, 1960. MR 0107725.
Razzaghi M, Yousef S (2002) Legendre wavelets method for constrained optimal control problems. Math Met Appl Sci 25:529–539. https://doi.org/10.1002/mma.299
Sadek I, Abualrub T, Abukhaled M (2007) A computational method for solving optimal control of a system of parallel beams using Legendre wavelets. Math Comp Modell 45:1253–1264. https://doi.org/10.1016/j.mcm.2006.10.008
Salai Mathi Selvi M, Hariharan G (2016) Wavelet based analytical algorithm for solving steady-state concentration in immobilized isomerase of packed bed reactor model. J Memb Biol. 249(4):559–586
Salai Mathi Selvi M, Hariharan G (2017) An improved method based on Legendre computational matrix method for time dependent Michaelis-Menten enzymatic reaction model arising in mathematical chemistry. Proc Jangjeon Mathe Soc. 20(3):483–503. https://doi.org/10.17777/pjms2017.20.3.483
Salai Mathi Selvi M, Hariharan G, Kannan K (2017) A reliable spectral, method to reaction-diffusion equations in entrapped-cell photobioreaction packed with gel grnules using chebyshev wavelets. J Memb Biol 250:663–670
Tanaka N (1961) A study on the bilge keels. J Soc Nav Archit Jpn 109:205–212
Tavassoli Kajani M, Hadi Vencheh A (2004) Solving linear integrodifferential equation with Legendre wavelets Int. J Comput Math 81(6):719–726. https://doi.org/10.1080/00207160310001650044
Yeung RW, Cermelli C, Liao SW (1997) Vorticity fields due to rolling bodies in a free surface - experiment and theory. Proceeding of the 21st symposium on naval hydrodynamics Trondheim Norway.
Zheng X, Wei Z (2016) Estimates of approximation error by Legendre wavelet. Appl Math 7:694–700. https://doi.org/10.4236/am.2016.77063
Salomi RJ, Sylvia SV, Rajendran L, Abukhaled M, (2020) Electric potential and surface oxygen ion density for planar, spherical and cylindrical metal oxide grains. Sensors and Actuators B: Chemical 321: 128576. https://doi.org/10.1016/j.snb.2020.128576

Memo

Memo:
Received date:2019-11-18;Accepted date:2020-05-12。
Foundation item:The authors are thankful to Shri J. Ramachandran, Chancellor, Col. Dr. G. Thiruvasagam, Vice-Chancellor, Academy of Maritime Education and Training (AMET), Deemed to be University, Chennai, for their support.
Corresponding author:Marwan Abukhaled, mabukhaed@aus.edu
Last Update: 2021-06-10