Developments of numerical methods for linear and nonlinear fluid-solid interaction dynamics with applications

Jing Tang XING

doi:10.6052/1000-0992-15-038

Volume 46 Issue 1

May 2016

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Jing Tang XING. Developments of numerical methods for linear and nonlinear fluid-solid interaction dynamics with applications[J]. Advances in Mechanics, 2016, 46(1): 201602. doi: 10.6052/1000-0992-15-038

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Jing Tang XING. Developments of numerical methods for linear and nonlinear fluid-solid interaction dynamics with applications[J]. Advances in Mechanics, 2016, 46(1): 201602. doi: 10.6052/1000-0992-15-038

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Developments of numerical methods for linear and nonlinear fluid-solid interaction dynamics with applications

doi: 10.6052/1000-0992-15-038 cstr: 32046.14.1000-0992-15-038

Jing Tang XING

Fluid-Structure Interaction Research Group, Faculty of Engineering & the Environment, University of Southampton, Southampton SO17 1BJ, UK

Received Date: 2015-10-08
Rev Recd Date: 2015-11-17
Publish Date: 2016-05-20

Abstract

Abstract

This paper presents a review on some developments of numerical methods for linear and nonlinear fluid-solid interaction (FSI) problems with their applications in engineering. The discussion covers the four types of numerical methods: (1) mixed finite element (FE)-substructure-subdomain model to deal with linear FSI in a finite domain, such as sloshing, acoustic-structure interac-tions, pressure waves in fluids, earthquake responses of chemical vessels, dam-water couplings, etc.; (2) mixed FE-boundary element (BE) model to solve linear FSI with infinite domains, for example, very large floating structure (VLFS) subject to airplane landing impacts, ship dynamic response caused by cannon/missile fire im-pacts, etc.; (3) mixed FE-finite difference (FD)/volume (FV) model for nonlinear FSI problems with no separations between fluids and solids and breaking waves; (4) mixed FE-smooth particle (SP) method to simulate nonlinear FSI problems with F-S separations as well as breaking waves. The partitioned iteration approach is suggested in base of available fluid and solid codes to separately solve their gov-erning equations in a time step, and then through reaching its convergence in coupling iteration to forward until the problem solved. The selected application examples include air-liquid-shell three phases interactions, liquefield natural gas (LNG) ship-water sloshing; acoustic analysis of air-building interaction system excited by human foot impacts; transient dynamic response of an airplane-VLFS-water interaction system excited by airplane landing impacts; turbulence flow-body interactions; structure dropping down on the water surface with breaking waves, etc. The numerical results are compared with the available experiment or numeri-cal data to demonstrate the accuracy of the discussed approaches and their values for engineering applications. Based on FSI analysis, linear and nonlinear wave energy harvesting devices are listed to use the resonance in a linear system and the periodical solution in a nonlinear system, such as flutter, to effectively harvest wave energy. There are 231 references are given in the paper, which provides very useful resources for readers to further investigate their interesting approaches.

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References

[1]	Aluru N R. 1999. A reproducing kernel particle method for meshless analysis of microelectromechanical systems. Computational Mechanics, 23: 324-338.
[2]	Anderson J D. 1995. Computational Fluid Dynamics, the Basics with Applications. McGraw-Hill.
[3]	Antoci C, Gallati M, Sibilla S. 2007. Numerical simulation of fluid-structure interaction by SPH. Comput. Struct., 85: 879-890.
[4]	Ataie-Ashtiani B, Shobeyri G, Farhadi L. 2008. Modified incompressible SPH method for simulating free surface problems. Fluid Dynamics Research, 40: 637-661.
[5]	Attawy S W, Heinstein M W, Swegle J W. 1994. Coupling of smoothed particle hydrodynamics with the finite element method. Nuclear Engineering and Design, 150: 199-205.
[6]	Axisa F, Antunes J. 2007. Fluid Structure Interaction. Butterworth-Heinemann.
[7]	Basa M, Quinlan N J, Lastiwka M. 2009. Robustness and accuracy of SPH formulations for viscous flow.International Journal for Numerical Methods in Fluids, 60: 1127-1148.
[8]	Bathe K J. 1996. Finite Element Procedures in Engineering Analysis. Prentice-Hall.
[9]	Bathe K J, Nitikitpaiboon C, Wang X. 1995. A mixed displacement-based finite element formulation for acoustic fluid-structure interaction. Computers and Structures, 56: 225-237.
[10]	Bazilevs Y, Takizawa K, Tezduyar T E. 2013. Computational Fluid-Structure Interaction: Methods and Applications. Wiley.
[11]	Bedard R, Hagerman G, Previsic M, Siddiqui O, Thresher R, Ram B. 2005. Final summary report of offshore wave power feasibility demonstration project. EPRI Global WP 009-US Rev.
[12]	Belytschko T, Kennedy J M. 1978. Computer models for subassembly simulation. Nuclear Eng Des, 49: 17-38.
[13]	Belytschko T, Flanagan D P, Kennedy J M. 1982. Finite element methods with user-controlled meshes for fluid-structure interaction. Computer Methods in Applied Mechanics and Engineering, 33: 669-688.
[14]	Bishop R E D, Price W G. 1979. Hydroelasticity of Ships. Cambridge University Press, London.
[15]	Bishop R E D, Price W G, Wu Y. 1986. A general linear hydroelasticity theory of floating structures moving in a seaway. Phil. Trans. R. Soc. Lond. A, 316: 375-426.
[16]	Bisplinghoff R L, Ashley H, Halfman R L. 1957. Aeroelasticity. Addison-Wesley Publ. Comp. Inc. Mass.
[17]	Bisplinghoff R L, Ashley H. 1962. Principles of Aeroelasticity. John Wiley & Sons, Inc., New York.
[18]	Bisplinghoff R L. 1958. Aeroelasticity. Appl. Mech. Rev. 11: 99-103.
[19]	Bodnar T, Galdi G P, Necasova S. 2014. Fluid-Structure Interaction and Biomedical Applications. Springer. BOEING webpage www.boeing.com.
[20]	Bonet J, Lok T S L. 1999. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Computer Methods in Applied Mechanics and Engineering, 180: 97-115.
[21]	Bonet J, Kulasegaram S, Rodriguez-Paz M X, Profit M. 2004. Variational formulation for the smooth particle hydrodynamics (SPH) simulation of fluid and solid problems. Computer Methods in Applied Mechanics and Engineering, 193: 1245-1256.
[22]	Brebbia C A. 1980. The Boundary Element Method for Engineers. Pentech Press, London.
[23]	Brebbia C A, Rodriguez G R. 2013. Fluid Structure Interaction VII. WIT Press.
[24]	Bui H H, Sako K, Fukagawa R. 2007. Numerical simulation of soil-water interaction using smoothed particle hydrodynamcis (SPH) method. Journal of Terramechanics, 44: 339-346.
[25]	Cao Q, Wiercigroch M, Pavlovskaia E E, Grebogi C, Thompson J M T. 2006. Archetypal oscillator for smooth and discontinuous dynamics. Physical Review E , 74: 046218.
[26]	Cao Q, Wiercigroch M, Pavlovskaia E E, Grebogi C, Thompson J M T. 2008a. The limit case response of the archetypal oscillator for smooth and discontinuous dynamics. Int J. Non Mech, 43: 462-473.
[27]	Cao Q, Wiercigroch M, Pavlovskaia E E, Thompson J M T, Grebogi C. 2008b. Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics. Phil Trans R Soc A, 366: 635-652.
[28]	Capuzzo-Dolcetta R, Robert D L. 2000. A criterion for the choice of the interpolation kernel in smoothed particle hydrodynamics. Appl. Numer. Math., 34: 363-371.
[29]	Caughey D A. 2001. Implicit multigrid computation of unsteady flows past cylinders of square cross-section. Computers & Fluids, 30: 939-960.
[30]	Chan R K-C. 1975. A generalized arbitrary Lagrangian-Eulerian method for incompressible flows with sharp interfaces. Journal of Computational Physics, 17: 311-331.
[31]	Chen J K, Beraun J E, Carney T C. 1999. A corrective smoothed particle method for boundary value problems in heat conduction. International Journal for Numerical Methods in Engineering, 46: 231-252.
[32]	Chen J K, Beraun J E. 2000. A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems. Computer Methods in Applied Mechanics and Engineering, 190: 225-239.
[33]	Chen X. 2013. Fluid-structure Interaction Modelling Cell Deformation Airways. Lambert Academic Pub-lishing.
[34]	Colagrossi A, Antuono M, Touze D L. 2009. Theoretical considerations on the free-surface role in the smoothed-particle-hydrodynamics. Physical Revire E, 79: 056701.
[35]	Colagrossi A, Landrini M. 2003. Numerical simulation of interfacial flows by smoothed particle hydrody-namics. Journal of Computational Physics, 191: 448-475.
[36]	Courant R, Hilbert D. 1962. Methods of Mathematical Physics. Interscience, New York.
[37]	Craig R R, Bampton M C C. 1968. Coupling of substructures for dynamical analysis. AIAA. Jl, 6: 1313-1319.
[38]	Craig R R, Chang C J. 1977. On the use of attachment modes in substructure coupling for dynamical analysis//AIAA/ASME 18th Struc. Dyn. & Matls. Conf., San Diego, Paper 77-405.
[39]	Crespo A J C, Gomez-Gesteira M, Dalrymple R A. 2007. Boundary conditions generated by dynamic paticles in SPH methods. CMC, 5: 173-184.
[40]	Crolet J M, Ohayon R. 1994. Computational Methods for Fluid-Structure Interaction. Taylor & Francis,London.
[41]	Cummins S J, Rudman M. 1999. An SPH projection method. J. Comput. Phys., 152: 584-607.
[42]	Dalrymple R A, Knio O. 2010. SPH Modelling of Water Waves//Hans H, Magnus L eds. ASCE: Conference Proceedings Sweden, 80.
[43]	Dahl J, Hover F, Triantafyllou M, Oakley O. 2010. Dual resonance in vortes-induced vibrations ar subcritical and supercritical reynolds numbers. Journal of Fluid Mechanics, 643: 395-424.
[44]	Department of the Navy. 2003. Environmental Assessment, Proposed Wave Energy Technology Project. M. Corps Base Hawaii, Hawaii.
[45]	Dervieux A. 2003. Fluid-Structure Interaction. Kogan Page Limited, London.
[46]	Dominguez J M, Crespo A J C, Gomez-Gesteria M, Marongiu J C. 2010. Neighbour lists in smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids, 67: 2026-2042.
[47]	Donea J. 1980. Finite element analysis of transient dynamic fluid-structure interaction//Donea J. ed. Ad-vanced Structural Dynamics, Chapter 8, 255-290, Applied Science.
[48]	Donea J. 1983. An arbitrary Lagrangian-Eulerian finite element method//Belytschko T, Hughes T J R eds. Computational Methods for Transient Analysis, Chapter 10, 473-516, Elsevier.
[49]	Donea J, Fasoli-Stella P, Giuliani S. 1977. Lagrangian-Eulerian finite element techniques for transient fluid-structure interaction problems. Paper B1/2//Transactions of 4th SMIRT Conference, San Francisco, 15-19 August 1977.
[50]	Donea J, Giuliani S, Halleux J P. 1982. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Computer Methods in Applied Mechanics and Engineering, 33: 689-723.
[51]	Durao D F G, Heitor M V, Pereira J C F. 1988. Measurements of turbulent and periodic flows around a square cross-section cylinder. Experiments in Fluids, 6: 298-304.
[52]	Ellero M, Serrano M, Espanol P. 2007. Incompressible smoothed particle hydrodynamics. J. Comput. Phys., 226: 1731-1752.
[53]	Endo H, Yago K. 1998. Time history response of a large floating structure subjected to dynamic load. J. Soc. Naval Arch. Japan, 186: 369-376.
[54]	Falnes J. 2002. Ocean Waves and Oscillating Systems, Linear Interactions Including Wave-Energy Extrac-tion. Cam. Univ. Press, London.
[55]	Floryan J M, Rasmussen H. 1989. Numerical methods for viscous flows with moving boundaries. Applied Mechanics Reviews, 42: 323-341.
[56]	Franke R, Rodi W. 1991. Calculation of vortex shedding past a square cylinder with various turbulence models//Proceedings of the Eighth Symposium on Turbulent Shear Flows, pp. 20.1.1-20.1.6, Tech. Univ. of Munich.
[57]	Freitas C J, Runnels S R. 1999. Simulation of fluid-structure interaction using patched-overset grids. J. F. & Structures, 13: 191-207.
[58]	Fung Y C. 1955. An Introduction to the Theory of Aeroelasticity. John Wiley & Sons, Inc., New York.
[59]	Galdi G P, Rannacher R. 2010. Fundamental Trends in Fluid-Structure Interaction. World Scientific.
[60]	Gingold R A, Monaghan J J. 1977. Smoothed particle hydrodynamics: Theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181: 375-389.
[61]	Grenier N, Antuono M, Colagrossi A, Touze D L, Alessandrini B. 2009. An hamiltonian interface SPH formulation for multi-fluid and free surface flows. Journal of Computational Physics, 228: 8380-8393.
[62]	Grenier N, Touze D L. 2008. An improved SPH method for multi-phase simulations//Proceedings of the 8nd International Conference on Hydrodynamics, 11.
[63]	Hirsch C. 1988. Numerical Computation of Internal and External Flows, Volume 1: Fundamentals of Numerical Discretization. John Wiley & Sons.
[64]	Hirsch C. 1990. Numerical Computation of Internal and External Flows, Volume 2: Computational Methods for Inviscid and Viscous Flows. John Wiley & Sons.
[65]	Hirt C W, Amsden A A, Cook J L. 1974. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics, 14: 227-253.
[66]	Horton B, Sieber J, Thompson J M T, Wiercigroch M. 2011. Dynamics of the nearly parametric pendulum. Int J. Non Mech, 46: 436-442.
[67]	Hosseini S M, Manzari M T, Hannani S K. 2007. A fully explicit three-step SPH algorithm for simulation of non-newtonian fluid flow. International Journal for Numerical Methods for Heat & Fluid Flow, 17: 715-735.
[68]	Hou S N. 1969. Review of modal synthesis techniques and a new approach. Shock and Vib. Bull., 40: 25-29.
[69]	Howe M S. 1998. Acoustics of Fluid-Structure Interactions. Cambridge University Press.
[70]	Hu X Y, Adams N A. 2006. A multi-phase SPH method for macroscopic and mesoscopic flows. Journal of Computational Physics, 213: 844-861.
[71]	Hu X Y, Adams N A. 2007. An incompressible multi-phase SPH method. J. Comput. Phys., 227: 264-278.
[72]	Hughes T J R, Liu W K, Zimmermann T K. 1981. Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Computer Methods in Applied Mechanics and Engineering, 29: 329-349.
[73]	Hunn B A. 1955. A method of calculating normal modes of an aircraft. Quart. Jl. Mech. Appl. Math., 8: 38-58.
[74]	Hurty W C. 1960. Vibration of structural systems by component mode synthesis. Proc. ASCE. J. E. M. Div., 8: 51-69.
[75]	Hurty W C. 1965. Dynamic analysis of structural systems using component modes. AIAA. Jl., 3: 678-685.
[76]	Ibrahim R A. 2005. Liquid Sloshing Dynamics, Theory and Applications. Cambridge University Press, London.
[77]	JAMSTEC. 2006. Wave Energy Research and Development at JAMSTEC, Offshore Floating Wave Energy Device, Mighty Whale.
[78]	Javed A. 2015. Investigation on meshfree particle methods for fluid-structure interaction problems. [PhD
[79]	Thesis], Faculty of Engineering & Environments, University of Southampton, Southampton, UK.
[80]	Javed A, Djidjeli K, Xing J T. 2013a. Adaptive shape parameter (ASP) technique for local radial basis functions (RBFs) and their application for solution of Navier-Strokes equations. International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering, 7: 771-780.
[81]	Javed A, Djidjeli K, Xing J T, Cox S J. 2013b. A hybrid mesh free local RBF-Cartesian FD scheme for incompressible flow around solid bodies. International Journal of Mathematical, Computational, Natural and Physical Engineering, 7: 957-966.
[82]	Javed A, Djidjeli K, Xing J T. 2014a. Shape adaptive RBF-FD implicit scheme for incompressible viscous Navier-Stokes equations. Computer & Fluids, 89: 38-52.
[83]	Javed A, Djidjeli K, Xing J T. 2014b. An ALE based hybrid meshfree local RBF-Cartesian FD scheme for incompressible flow around moving boundaries. AIAA Aviation, American Institute of Aeronautics and Astronautics. doi: 10.2514/6.2014-2312.
[84]	Jiang F, Oliveira M S A, Sousa A C M. 2007. Mesoscale SPH modeling of fluid flow in isotropic porous media. Computer Physics Communications, 176: 471-480.
[85]	Jin J. 2007. A mixed mode function-boundary element method for very large floating structure-water Interaction systems excited by airplane landing impacts. [PhD Thesis], School of Engineering Sciences, University of Southampton, Southampton, UK.
[86]	Jin J, Xing J T. 2007. Transient dynamic analysis of a floating beam-water interaction system excited by the impact of a landing beam. Journal of Sound & Vibration, 303: 371-390.
[87]	Jin J, Xing J T. 2009. A convergence study on mixed mode function-boundary element method for aircraft- VLFS-water interaction system subject to aircraft landing impacts//Proceedings of the ASME 28th In-ternational Conference on Offshore Mechanics and Arctic Engineering-OMAE2009, 31 May-5 June, 2009, Honolulu, Hawaii.
[88]	Johnson G R. 1994. Linking of Lagrangian particle methods to standard finite element methods for high velocity impact computations. Nuclear Engineering and Design, 150: 265-274.
[89]	Johnson G R., Stryk R A, Beissel S R. 1996a. SPH for high velocity impact computations. Computer Methods in Applied Mechanics and Engineering, 139: 347-373.
[90]	Johnson G R, Stryk R A, Beissel S R. 1996b. Interface effects for SPH impact computations. Structures under shock and impact, IV: 285-294.
[91]	Johnson G R, Beissel S R. 1996c. Normalized smoothing functions for SPH impact computations. Interna-tional Journal for Numerical Methods in Engineering, 39: 2725-2541.
[92]	Jun S, Liu W K, Belytschko T. 1998. Explicit reproducing kernel particle methods for large deformation problems. International Journal for Numerical Methods in Engineering, 41: 137-166.
[93]	Khodabakhshi G. 2011. Computational Modelling Fluid-porous Solid Interaction Systems. LAMBERT Academic Publ.
[94]	Khabakhpasheva T I, Korobkin A A. 2003. Approximate models of elastic wedge impact//18th Int. Work. Water Waves & Floating Bodies, Le Croisic, France.
[95]	Khabakhpasheva T I, Korobkin A A. 2013. Elastic wedge impact onto a liquid surface: Wagner's solution and approximate models. Journal of Fluids and Structures, 36: 32-49.
[96]	Kock E, Olson L. 1991. Fluid-solid interaction analysis by the finite element method-a variational approach. Int. Jl. Numer. Methods Eng., 31: 463-491.
[97]	Koobus B, Farhat C, Tran H. 2000. Computation of unsteady viscous flows around moving bodies using the k-" turbulence model on unstructured dynamic grids. Com Meth Appl Mech & Eng, 190: 1441-1466.
[98]	Lee E S, Moulinec C, Xu R, Violeau D, Laurence D, Stansby P. 2008. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. J. Comput. Phys., 227: 8417-8436.
[99]	Lee E S, Violeau D, Issa R. 2010. Application of weakly compressible and truly incompressible SPH to 3-d water collapse in waterworks. Journal of Hydraulic Research, 48: 50-60.
[100]	Lencia S, Pavlovskaiab E, Regac G, Wiercigroch M. 2008. Rotating solutions and stability of parametric pendulum by perturbation method. Journal of Sound & Vibration, 310: 243-259.
[101]	Libersky L D, Petschek A G. 1991. Smoothed particle hydrodynamics with strength of materials//Trease H, Fritts J, Crowley W eds. Proceeding of The Next Free Lagrange Confrence, pp. 248-257, Springer Berlin.
[102]	Litaka G, Borowieca M, Wiercigroch M. 2008. Phase locking and rotational motion of a parametric pendulum in noisy and chaotic conditions. Dynamical Systems, 23: 259-265.
[103]	Litaka G, Wiercigroch M, Horton B, Xu X. 2010. Transient chaotic behaviour versus periodic motion of a parametric pendulum by recurrence plots. ZAMM. Z. Angew. Math. Mech., 90: 33-41.
[104]	Liu G R. 2003. Mesh free methods: Moving beyond the finite element method. Chemical Rubber Boca Raton, FL.
[105]	Liu G R, Liu M B. 2003a. Smoothed Particle Hydrodynamics. World Scientific Publishing Co. Pte. Ltd.
[106]	Liu M B, Liu G R, Lam K Y. 2003b. Constructing smoothing functions in smoothed particle hydrodynamics with applications. Journal of Computational and Applied Mathematics, 155: 263-284.
[107]	Liu W K, Ma D C. 1982. Computer implementation aspects for fluid-structure interaction problems. Com-puter Methods in Applied Mechanics and Engineering, 31: 129-148.
[108]	Liu W K, Uras R A. 1988. Variational approach to fluid-structure interaction with sloshing. N. E. Des., 106: 69-85.
[109]	Liu W K, Jun S, Zhang Y F. 1995a. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids, 20: 1081-1106.
[110]	Liu W K, Jun S, Li S, Adee J, Belytschko T. 1995b. Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering, 38: 1655-1679.
[111]	Lobovský L, Vimmr J. 2007. Smoothed particle hydrodynamics and finite volume modelling of incompress-ible fluid flow. Mathematics and Computers in Simulation, 76: 124-131.
[112]	Lucy L B. 1977. Numerical approach to testing the fission hypothesis. Astronomical Journal, 82: 1013-1024.
[113]	MacNeal R H. 1977. A hybrid method of component mode synthesis. Comp. Strs, 1: 581-601.
[114]	Magnus W, Oberhettinger F. 1949. Formulas and Theorems for the Special Functions of Mathematical Physics. Chelsea Publishing Co., New York.
[115]	Monaghan J J. 1982. Why particle methods work. SIAM J. on Scientific and Statistical Computing, 3: 422-433.
[116]	Monaghan J J. 1987. SPH meets the Shocks of Noh. Monash University Paper.
[117]	Monaghan J J. 1988. An introduction to SPH. Computer Physics Communications, 48: 89-96.
[118]	Monaghan J J. 1989. On the problem of penetration in particle methods. Journal of Comp. Physics, 82: 1-15.
[119]	Monaghan J J. 1992. Smoothed particle hydrodynamics. Annual Review of Astr. and Astrophysics, 30: 543-574.
[120]	Monaghan J J. 1994. Simulating free surface flows with SPH. J. Comput. Phys., 110: 399-406.
[121]	Monaghan J J. 1996. Gravity currents and solitary waves. Physica D: Nonlinear Phenomena, 98: 523-533.
[122]	Monaghan J J. 2002. SPH compressible turbulence. Monthly Notices of the Royal Astro Society, 335: 843-852.
[123]	Monaghan J J, Gingold R A. 1983. Shock simulation by the particle method SPH. Journal of Computational Physics, 52: 374-389.
[124]	Monaghan J J, Lattanzio J C. 1985a. A refined particle method for astrophysical problems. Astro & Astrophy, 149: 135-143.
[125]	Monaghan J J, Poinracic J. 1985b. Artificial viscosity for particle methods. Applied Numerical Math., 1: 187-194.
[126]	Monaghan J J, Kocharyan A. 1995c. SPH simulation of multi-phase flow. Com Phys Comms, 87: 225-235.
[127]	Monaghan J J, Kos A. 1999. Solitary waves on a cretan beach. Journal of Waterway, Port, Coastal, and Ocean Engineering, 125: 145-155.
[128]	Morand H J P, Ohayon R. 1995. Fluid Structure Interaction. John Wiley and Sons, Chichester.
[129]	Morris J P, Fox P J, Zhu Y. 1997. Modeling low reynolds number incompressible flows using SPH. Journal of Computational Physics, 136: 214-226.
[130]	Nandakumar K, Wiercigroch M, Chatterjee A. 2012. Optimum energy extraction from rotational motion in a parametrically excited pendulum. Mechanics Research Communications, 43: 7-14.
[131]	Newman J N. 1977. Marine Hydrodynamics. MIT press.
[132]	Newman J N. 1978. The theory of ship motions. Advances in Applied Mechanics, 18: 221-283.
[133]	Newman J N. 1994. Wave effects on deformable bodies. J. Appl. Ocean Res., 16: 47-59.
[134]	Nitikitpaiboon C, Bathe K J. 1993. An arbitrary Lagrangian-Eulerian velocity potential formulation for fluid-structure interaction. Computers and Structures, 47: 871-891.
[135]	Noh W F. 1964. A time-dependent, two-space dimensional, coupled Eulerian-Lagrangian code//Alder et al. eds. Methods in Computational Physics, vol. 3, pp. 117, Academic Press.
[136]	Ocean Power Delivery Ltd. 2006. World's First Wave Farm-Shipping of First Machine to Portugal. Press Release.
[137]	Ocean Power Technologies. 2006. Making Waves in Power. http://www.oceanwavetechnologies.com.
[138]	Oger G, Doring M, Alessandrini B, Ferrant P. 2006. Two-dimensional SPH simmulations of wedge water entries. Journal of Computational Physics, 213: 803-822.
[139]	Panahi K K. ed. 1997. Advances in Analytical, Experimental and Computational Technologies in Fluids, Structures, Transients and Natural Hazards. PVP-Vol. 355, ASME, New York.
[140]	Panciroli R. 2003. Hydroelastic impacts of deformable wedges. Solid Mechanics and its Applications, 192: 1-45.
[141]	Panciroli R, Abrate S, Minak G, Zucchelli A. 2012. Hydroelasticity in water-entry problems: comparison between experimental and SPH results. Composite Structures, 94: 532-539.
[142]	Païdoussis M P. 2013. Fluid-Structure Interactions: Slender Structures and Axial Flow. Academic Press.
[143]	Païdoussis M P, Price S J, Langre E D. 2011. Fluid-Structure Interactions: Cross-Flow-Induced Instabilities. Cambridge University, Cambridge.
[144]	Pavlovskaia E, Horton B, Wiercigroch M, Lenci S, Rega G. 2012. Approximate rotational solutions of pendulum under combined vertical and horizontal excitation. International Journal of Bifurcation and Chaos, 22: 1250100.
[145]	Pozorski J, Wawrenczuk A. 2002. SPH computation of incompressible viscous flows. J. T. Appl Mech, 40: 917.
[146]	Pracht W E. 1975. Calculating three-dimensional fluid flows at all speeds with an Eulerian-Lagrangian computing mesh. Journal of Computational Physics, 17: 132-159.
[147]	Quinlan N J, Basa M, Lastiwka M. 2006. Truncation error in mesh-free particle methods. International Journal for Numerical Methods in Engineering, 66: 2064-2085.
[148]	Rabczuk T, Xiao S P, Sauer M. 2006. Coupling of meshfree methods with finite elements: Basic concepts and test results. Communications in Numerical Methods in Engineering, 22: 1031-1065.
[149]	Rafiee A, Thiagarajan K P. 2008. Fluid-structure interaction imulation using an incompressible SPH method//ASME 27th International Conference on Offshore Mechanics and Arctic Engineering, 485-496.
[150]	Rafiee A, Thiagarajan K P. 2009. An SPH projection method for simulating fluid-hypoelastic structure interaction. Computer Methods in Applied Mechanics and Engineering, 198: 2785-2795.
[151]	Ramaswamy B, Kawahara M. 1987. Arbitrary Lagrangian-Eulerian finite element method for unsteady, convective, incompressible viscous free surface fluid flows. Int. Journal for Numerical Methods in Fluids, 7: 1053-1075.
[152]	Randles P W, Libersky L D. 1996. Smoothed particle hydrodynamics: Some recent improvements and applications. Computer Methods in Applied Mechanics and Engineering, 139: 375-408.
[153]	Rellich F. 1943. Uber das asymptotische verhalten der losungen von Δu + λu = 0 in unendlichen gebieten.Jahr. D. Math Verein, 53: 57-65.
[154]	Rhinefrank K. 2005. Wave energy research development and demonstration at Oregon State Univer-sity//Energy Ocean 2005, Washington.
[155]	Ritchie B W, Thomas P A. 2001. Multiphase smoothed-particle hydrodynamics. Mon. Not. R. Astron. Soc, 323: 743-756.
[156]	Schussler M, Schmitt D. 1981. Comments on smoothed particle hydrodynamics. Astro. Astrophys., 97: 373-379.
[157]	Shao S. 2009. Incompressible SPH simulation of water entry of a free-falling object. International Journal for Numerical Methods in Fluids, 59: 91-115.
[158]	Shao S, Edmond Y M L. 2003. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Advances in Water Resources, 26: 787-800.
[159]	Sommerfeld A. 1912. Die greensche funktionen der schwingungsgleichung. Jahr. D. Math Verein, 21: 309-353.
[160]	Somerfield A. 1949. Partial Differential Equations in Physics. Academic Press, New York.
[161]	Souli M, Benson D J. 2010. Arbitrary Lagrangian Eulerian and Fluid-Structure Interaction: Numerical
[162]	Simulation. Wiley.
[163]	Stellingwerf R F, Wingate C. 1994. Impact modelling with SPH. Memorie della societa astro italiana, 65: 1117.
[164]	Sun F. 2013. Investigations of smoothed particle hydrodynamics method for nonlinear fluid-rigid body interaction dynamics. [PhD Thesis]. FEE, University of Southampton, UK.
[165]	Sun F, Tan M, Xing J T. 2011. Investigations of boundary treatments in incompressible smoothed particle hydrodynamics for fluid-structural interactions. Paper number 303-241//The 2nd International Confer-ence of Fluid Mechanics and Heat & Mass Transfer, Corfu, Greece, 14-17 July 2011, Recent Research in Mechanics, 92-97.
[166]	Sun F, Tan M, Xing J T. 2012. Air-water two phase flow simulation using smoothed particle hydrodynam-ics//David Le Touze D L, Grenier N, Barcarolo D A eds. 2nd International Conference on Violent Flows, pp.58-63, Nantes, France.
[167]	Sun F, Tan M, Xing J T. 2013. Application of incompressible smoothed particle hydrodynamics method for 3D fluid solid interaction problem//Liu G, Zabala D eds. Recent Researches in Mechanical Engineering, pp144-149, Milan: WSEAS Press, ISSN: 2227-4596, ISBN: 978-1-61804-153-1.
[168]	Sun Z, Djidjeli K, Xing J T, Cheng F, Javed A. 2014. Some modifications of MPS method for incompressible free surface flow//O~nate E, Oliver J and Huerta A eds. 11th World Congress On Computational Me-chanics (WCCM XI), 5th European Conference on Computational Mechanics (ECCM V), 6th European conference on computational fluid dynamics (ECFD VI).
[169]	Sun Z, Djidjeli K, Xing J T, Cheng F. 2015a. Coupling MPS and modal superposition method for flexible wedge dropping simulation. ISOPE 2015, 21-26 June, 2015, Hawaii, USA, Paper ID: TPC-1208.
[170]	Sun Z, Djidjeli K, Xing J T, Cheng F. 2015b. Modified MPS method for the 2D fluid structure interaction problem with free surface. Computer & Fluids, 122: 47-65.
[171]	Swegle J W, Hicks D L, Attaway S W. 1995. Smoothed particle hydrodynamics stability analysis. J. Comput. Phys., 116: 123-134.
[172]	Tan M, Xiong Y P, Xing J T, Toyoda M. 2006. A numerical investigation of natural characteristics of a partially filled tank using a substructure method//Proceedings of Hydroelasticity' 2006: Hydroelasticity in Marine Technology, pp.181-190, National Defence Industry Press, Beijing.
[173]	Thorpe T W. 1999. A brief review of wave energy. ETSU Report R-122, presented for UKDTI.
[174]	Trulio J G. 1966. Theory and structure of the AFTON codes, Report ASWL-TR-66-19, Air Force W. Laboratory.
[175]	Unruh, J.F. 1979. A finite-element sub-volume technique for structure-borne interior noise prediction//5th Aero. Acous. Conf. Seattle, WA, AIAA 79-585.
[176]	U.S. Department of the Interior. 2006. Technology White Paper on Wave Energy Potential on the U.S.
[177]	Outer Continental Shelf. Minerals Management Service, Renewable Energy and Alternate Use Program.
[178]	Wang X S. 2008. Fundamentals of Fluid-solid Interactions: Analytical and Computational Approaches. Elsevier.
[179]	Ward P, Desai R, Kebede W, Ecer A. 1988. A variational finite-element formulation for 3-dimensional incompressible flows//Morton K W, Baines M T eds. Num. Meth. Fluid Dyn. III, 46: 403-409, Oxford
[180]	UniversityWave Dragon, Technology. 2005. http: //www/wavedragon.net.
[181]	Wave Plane Production A/S=WPP A/S. 2006. http: //www.waveplane.com.
[182]	Wróblewski P, Marius Z K, Krzysztof B. 2007. SPH-A comparison of neighbor search methods based on constant number of neighbours and constant cut-off radius. Task Quarterly, 11: 273-283.
[183]	Xiao Q, Zhu Q. 2014. A review on flow energy harvesters based on flapping foils. Journal of Fluids & Structures, 46: 174-191.
[184]	Xing J T. 1981. Variational principles for elastodynamics and study upon the theory of mode synthesis methods. [Master Thesis]. Dept. of Engineering Mechanics, Qinghua University, Beijing, China (in Chinese).
[185]	Xing J T. 1984. Some theoretical and computational aspects of finite element method and substructure-subdomain technique for dynamic analysis of the coupled fluid-solid interaction problems-variational prin-ciples elastodynamics and linear theory of micropolar elasticity with their applications to dynamic analysis. [PhD Thesis], Department of Engineering Mechanics, Qinghua University, Beijing, China (in Chinese).
[186]	Xing J T. 1986a. A study on finite element method and substructure-subdomain technique for dynamic analysis of coupled fluid-solid interaction problems. Acta Mechanica Solida Sinica, 4: 329-337.
[187]	Xing J T. 1986b. Mode synthesis method with displacement compatibility for dynamic analysis of fluid-solid interaction problems. Acta Aeronautica et Astronautica Sinica, 7: 148-156.
[188]	Xing J T, 1988. Two variational formulations for dynamics analysis of coupled fluid-solid interaction prob-lems with linearised free surface wave considered. Acta Aero Astro Sin, 9: A568-571.
[189]	Xing J T. 1992a/1995a. Theoretical Manual of Fluid-Structure Interaction Analysis Program-FSIAP. Chi-nese version, BUAA (1992); English version (1995), SES, University of Southampton.
[190]	Xing J T. 1992b/1995b. User Manual Fluid-Structure Interaction Analysis Program-FSIAP. Chinese version, BUAA (1992), English version (1995), SES, University of Southampton.
[191]	Xing J T. 2007. Natural vibration of two-dimensional slender structure-water interaction systems subject to Sommerfeld radiation condition. Journal of Sound and Vibration, 308: 67-79.
[192]	Xing J T. 2008. An investigation into natural vibrations of fluid-structure interaction systems subject to Sommerfeld radiation condition. Acta Mech Sin, 24: 69-82.
[193]	Xing J T. 2015. Energy Flow Theory of Nonlinear Dynamical Systems with Applications. Springer, Berlin.
[194]	Xing J T, Jin J. 2004. A mixed mode function-boundary element method for the transient impact analysis of an aircraft landing on a floating structure//Harald K, Eike L eds. Proc. 9th Int. Symposium on
[195]	Practical Design of Ships and Other Floating Structures, Luebeck-Travemuende, Germany, 819-826.
[196]	Xing J T, Jin, J. 2005a. A dynamic analysis of an integrated aircraft-floating structure-water interaction sys-tem excited by the impact of an aircraft landing. International Journal of Offshore & Polar Engineering, 15: 1-7.
[197]	Xing J T, Jin J. 2005b. A dynamic analysis of an integrated aircraft-floating structure-water interaction system excited by the impact of an aircraft landing//Proc. 15th Int. Offshore Polar Eng. Conf., Seoul, 1: 182-189.
[198]	Xing J T, Price W G. 1991. A mixed finite element method for the dynamic analysis of coupled fluid-solid interaction problems. Proc R Soc Lond A, 433: 235-255.
[199]	Xing J T, PriceWG, Du Q H. 1996 Mixed finite element substructure-subdomain methods for the dynamical analysis of coupled fluid-solid interaction problems. Phil Trans R Soc Lond A, 354: 259-295.
[200]	Xing J T, Price W G. 1997. Variational principles of nonlinear fluid-solid interaction systems. Phil. Trans. R. Soc. Lond. A, 335: 1063-1095.
[201]	Xing J T, Price W G. 1998. A variational solution method applied to a nonlinear water-structure interaction system//Wen B C ed. Proceedings of the International Conference on Vibration Engineering, vol.1, 219-224, August 6-8, 1998, Dalian, China, Northeastern University Press.
[202]	Xing J T, Price W G. 2000. The theory of non-linear elastic ship-water interaction dynamics. Journal of Sound & Vibration, 230: 877-914.
[203]	Xing J T, Price W G, Chen Y G. 2002. A numerical simulation of nonlinear fluid-rigid structure interaction problems//Proceedings of the ASME International Mechanical Engineering Congress & Exposition, Vol-ume 3 (7.CD-ROM), Session AMD-12A, Paper IMECE2002-32534, November 17-22, 2002, New Orleans,USA.
[204]	Xing J T, Price W G, Chen Y G. 2003. A mixed finite element -finite difference method for nonlinear fluid-structure interaction dynamics, Part I: rigid structure-fluid interaction. Proc. Royal Soc A, 459: 2399-2430.
[205]	Xing J T, Price W G, Chen Y G. 2005. A numerical method for simulating nonlinear fluid-rigid structure interaction problems. Acta Mechanica Solida Sinica, 18: 95-109.
[206]	Xing J T, Zheng Z C. 1983. A study upon mode synthesis methods based on variational principles for elastodynamics. Acta Mechanica Solida Sinica, 2: 250-257.
[207]	Xing J T, Zhou S, Cui E J. 1997a. A general survey of the fluid-solid interaction mechanics. Advances in Mechanics, 27: 19-38 (in Chinese).
[208]	Xing J T, Xiong Y P, Tan M. 2009. Developments of a mixed finite element substructure-subdomain method for fluid-structure interaction dynamics with applications in maritime engineering. Proc IMechE Part M: J Engineering for the Maritime Environment, 223: 399-418.
[209]	Xing J T, Price W G, Wang A. 1997b. Transient analysis of the ship-water interaction system excited by a pressure water wave. Marine Structures, 10: 305-321.
[210]	Xing J T, Xiong Y P, Tan M. 2007a. The natural vibration characteristics of a water-shell tank interaction system//Advancements in Marine Structures. Proceedings of Marstruct 2007, 1st International Confer-ence on Marine Structures, pp.305-312, Glasgow, UK, 12-14 March 2007, Taylor and Francis, London.
[211]	Xing J T, Xiong Y P, Tan M. 2007b.The dynamic analysis of a building structure-acoustic volume interaction system excited by human footfall impacts//Proceedings of Fourteenth International Congress on Sound and Vibration, Cairns, Australia, 9-12 July 2007, Paper number 147, IIAV, Cairns.
[212]	Xing J T, Xiong Y P. 2008a. Numerical simulations of a building-acoustic volume interaction system excited by multiple human footfall impacts//Proceedings of 2008 ASME Pressure Vessels and Piping Division Conference, Chicago, Illinois, July 27-31, 2008, PVP2008-61813, pp.1-10, ASME, New York.
[213]	Xing J T, Xiong Y P. 2008b. Mixed finite element method and applications to dynamic analysis of fluid-structure interaction systems subject to earthquake, explosion and impact loads//Proceedings of ISMA 2008 International Conference on Noise and Vibration Engineering, Leuven, Belgium, September 15-17, 2008, Paper ID-562, pp.1-15, Katholieke Universiteit, Leuven.
[214]	Xing J T, Xiong Y P, Tan M, An H. 2009a. A numerical investigation of a wave energy harness device-water interaction system subject to the wave maker excitation in a towing tank//Proceedings of the 28th International Conference on Ocean, Offshore and Arctic Engineering, (OMAE2009), New York, USA, ASME, 1-10.
[215]	Xing J T, Xiong Y P, Wiercigroch M, Cao Q. 2011. Mathematical modelling of an integrated converter for wave energy harvesting//ENOC 2011, 24-29 July 2011, Rome, Italy.
[216]	Xiong Y P, Xing J T, Tan, M. 2006a. Transient dynamic responses of an internal liquid-LNG tank-sea water interaction system excited by waves and earthquake loads//Proceedings of the 14th International Congress on Sound and Vibration, Cairns, Australia, 9-12, July 2006, Paper number 566, pp.1-8 (IIAV, Cairns).
[217]	Xiong Y P, Xing J T, Price W G. 2006b. The interactive dynamic behaviour of an air-liquid-elastic spherical tank system//Proceedings of 2006 ASME Pressure Vessels and Piping Division Conference, Vancouver, BC, Canada, July 23-27, 2006, PVP2006-ICPVT11-93922, pp.1-8, ASME, New York.
[218]	Xiong Y P, Xing J T. 2007. Natural dynamic characteristics of an integrated liquid-LNG tank-water inter-action system//Advancements in Marine Structures//Proceedings of Marstruct 2007, 1st International Conference on Marine Structures, Glasgow, UK, 12-14 March 2007, pp.313-321, Taylor and Francis, Lon-don.
[219]	Xiong Y P, Xing J T. 2008a. Dynamic analysis and design of LNG tanks considering fluid structure in-teractions//Proceedings of 27th International Conference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal, June 15-20, 2008, OMAE2008-57937, pp. 1-8 ASME, New York.
[220]	Xiong Y P, Xing J T. 2008b. Transient dynamic responses of an integrated air-liquid-elastic tank interaction system subject to earthquake excitations//2008 ASME Pressure Vessels and Piping Division Conference- PVP2008, Chicago, Illinois, July 27-31, 2008, PVP2008-61815, pp.1-10, ASME, New York.
[221]	Xu X, Pavlovskaia1 E, Wiercigroch M, Romeo F, Lenci S. 2007. Dynamic Interactions between Parametric Pendulum and Electro-Dynamical Shaker. ZAMM Z. Angew Math Mech, 87: 172-186.
[222]	Xu X, Wiercigroch M, Cartel M P. 2005. Rotating orbits of a parametrically-excited pendulum. Chaos, S. and Fractals, 23: 1537-1548.
[223]	Yang J, Xiong Y P, Xing J T. 2011. Investigations on a nonlinear energy harvesting system consisting of a flapping foil and an electro-magnetic generator using power flow analysis. Paper number DETC2011-48445//Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Com-puters and Information in Engineering Conference IDETC/CIE 2011, August 29-31, 2011, Washington, DC, USA.
[224]	Young J, Lai J, Platzer M F. 2014a. A review of progress and challenges in flapping foil power generation. Progress in Aerospace Sciences, 67: 2-28.
[225]	Young J, Lai J, Platzer M F. 2014b. Addendum to a review of progress and challenges in flapping foil power generation. Progress in Aerospace Sciences, 67: 1.
[226]	Zhang G M, Batra R C. 2004. Modified smoothed particle hydrodynamics method and its application to transient problems. Computational Mechanics, 34: 137-146.
[227]	Zhang X, Lu M, Wang J. 1997. Research progress in arbitrary Lagrangian-Eulerian method (In Chinese). Chinese Journal of Computational Mechanics, 17: 91-102.
[228]	Zhao R, Faltinsen O, Aarsnes J. 1997. Water entry of arbitrary two-dimensional sections with and without flow separation.//21st Symposium on Naval Hydrodynamics. Trondheim, Norway, National Academy Press, Washington, DC, USA, 408-423.
[229]	Zhuo C, Wang D, Shen S, Xing J T. 2013. Nonlinear low-frequency gravity waves in a water-filled cylindrical vessel subjected to high-frequency excitations. Proc. R. Soc. Lond. A, 469: 20120536.
[230]	Zhou D, Tu J. 2012. Two degrees of freedom flow-induced vibrations on a cylinder//7th Int. Colloq. Bluff Body Aerodyn. Appl. BBAA7, International Association for Wind Engineering, AIAA.
[231]	Zienkiewicz O C, Bettess P. 1978. Fluid-structure dynamic interaction and wave forces, an introduction to numerical treatment. International Journal for Numerical Methods in Engineering, 13: 1-16.
[232]	Zienkiewicz O C, Taylor R L. 1989. The Finite Element Method. 4th ed., Vol.1. McGraw-Hill.
[233]	Zienkiewicz O C, Taylor R L. 1991. The Finite Element Method. 4th ed., Vol.2. McGraw-Hill.