Hydroelastic analysis of a rectangular plate subjected to slamming loads

Abstract

A hydroelastic analysis of a rectangular plate subjected to slamming loads is presented. An analytical model based on Wagner theory is used for calculations of transient slamming load on the ship plate. A thin isotropic plate theory is considered for determining the vibration of a rectangular plate excited by an external slamming force. The forced vibration of the plate is calculated by the modal expansion method. Analytical results of the transient response of a rectangular plate induced by slamming loads are compared with numerical calculations from finite element method. The theoretical slamming pressure based on Wagner model is applied on the finite element model of a plate. Good agreement is obtained between the analytical and numerical results for the structural deflection of a rectangular plate due to slamming pressure. The effects of plate dimension and wave profile on the structural vibration are discussed as well. The results show that a low impact velocity and a small wetted radial length of wave yield negligible effects of hydroelasticity.

Keywords

slamming load / hydroelastic analysis / vibration of plates / modal expansion method / finite element method

References

[1] Bereznitski A. Slamming: the role of hydroelasticity. International Shipbuilding Progress, 2001, 48: 333-351

[2] Bishop RED, Price WG. Hydroelasticity of ships, 1979, London: Cambridge University Press, 88-92

[3] Chuang SL. Slamming of rigid wedge-shaped bodies with various deadrise angles, 1966, Washington DC: Structural Mechanics Lab.

[4] Corak M, Parunov J, Guedes Soares C. Probabilistic load combination factors of wave and whipping bending moments. Journal of Ship Research, 2015, 59(1): 11-30

[5] Faltinsen OM. The effect of hydroelasticity on ship slamming. Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, 1997, 355(1724): 575-591

[6] Faltinsen OM. Water entry of a wedge by hydroelastic orthotropic plate theory. Journal of Ship Research, 1999, 43: 180-193

[7] Faltinsen OM. Hydroelastic slamming. Journal of Marine Science and Technology, 2000, 5(2): 49-65

[8] Faltinsen OM, Kvalsvold J, Aarsnes JV. Water impact on a horizontal elastic plate. Journal of Marine Science and Technology, 1997, 2(2): 87-100

[9] Hirdaris SE, Temarel P. Hydroelasticity of ships: recent advances and future trends. Journal of Engineering for the Maritime Environment, 2009, 223(3): 305-330

[10] Keane AJ, Temarel P, Wu XJ, Wu Y, Chalmers DW, Keane AJ, Nicholson K, Incecik A, Hylarides S, Beukelman W. Hydroelasticity of non-beamlike ships in waves. Philosophical Transactions: Physical Sciences and Engineering, 1991, 339-355

[11] Khabakhpasheva TI. Impact of a surface wave on an elastic hull. Fluid Dynamics, 2006, 41(3): 424-433

[12] Khabakhpasheva TI, Korobkin AA. Elastic wedge impact onto a liquid surface: Wagner’s solution and approximate models. Journal of Fluids and Structures, 2013, 36: 32-49

[13] Korobkin A, Gueret R, Malenica S. Hydroelastic coupling of beam finite element model with Wagner theory of water impact. Journal of Fluid and Structures, 2006, 22(4): 493-504

[14] Korobkin AA. Wave impact on the center of an Euler beam. Journal of Applied Mathematics and Technical Physics, 1998, 39(5): 770-781

[15] Kvalsvold J, Faltinsen OM. Hydroelastic modelling of wetdeck slamming on multihull vessels. Journal of Ship Research, 1995, 39: 225-239

[16] Lakitosh F, Ananthakrishnan P. Analysis of ship hull plate vibrations induced by wave and slamming loads. 31st International Conference on Ocean, Offshore and Arctic Engineering, 2012, 289-298

[17] Lloyd PM, Stansby PK. Slam forces and pressures on a flat plate due to impact on a wave crest. International Workshop on Water Waves and Floating Bodies, 1999, 92-94

[18] Lu CH, He YS, Wu GX. Coupled analysis of nonlinear interaction between fluid and structure during impact. Journal of Fluid and Structures, 2000, 14: 127-146

[19] Luo H, Zhao Z, Xie P, Wu H, Li X. Experimental and numerical investigation on hydroelastic impact of one free-drop wedge with aluminum stiffened panels. Proc. OCEANS 2014, 2014, 1-7

[20] Luo HB, Wang H, Guedes Soares C. Numerical and experimental study of hydrodynamic impact and elastic response for one free-drop wedge with stiffened panels. Ocean Engineering, 2012, 40: 1-14

[21] Maki KJ, Lee D, Troesch A, Vlahopoulos N. Hydroelastic impact of a wedge-shaped body. Ocean Engineering, 2011, 38: 621-629

[22] Meirovitch L. Principles and techniques of vibrations. Englewood Cliffs. Prentice Hall, Inc., Vol., 1997, 1: 451-454

[23] Nichols BD, Hirt CW, Hotchkiss RS. SOLA-VOF: A solution algorithm for transient fluid flow with multiple free boundaries, 1980

[24] Okada S, Sumi Y. On the water impact and elastic response of a flat plate at small impact angles. Journal of Marine Science and Technology, 2000, 5(1): 31-39

[25] Panciroli R, Abrate S, Minak G, Zucchelli A. Hydroelasticity in water-entry problems: Comparison between experimental and SPH results. Composite Structures, 2012, 94(2): 532-539

[26] Peseux B, Gornet L, Donguy B. Hydrodynamic impact: numerical and experimental investigations. Journal of Fluids and Structure, 2005, 21(3): 277-303

[27] Phan TS, Temarel P. Hydroelastic responses of pontoon and semi-submersible types of very large floating structure in regular head waves. Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering, 2002, 753-763

[28] Price WG, Wu YS. Structural responses of a SWATH of multi-hulled vessel traveling in waves. International Conference on SWATH ships and advanced multi-hulled vessels, 1985

[29] Qin Z, Batra RC. Local slamming impact of sandwich composite hulls. International Journal of Solids and Structures, 2009, 46: 2011-2035

[30] Rajendran S, Guedes Soares C. Numerical investigation of the vertical response of a containership in large amplitude waves. Ocean Engineering, 2016, 123: 440-451

[31] Rajendran S, Fonseca N, Guedes Soares C. A numerical investigation of the flexible vertical response of an Ultra Large Containership in high seas compared with experiments. Ocean Engineering, 2016, 122: 293-310

[32] Santos FM, Temarel PA, Guedes Soares C. On the limitations of two and three-dimensional linear hydroelasticity analyses applied to a fast patrol boat. Journal of Engineering for the Maritime Environment, 2009, 223(3): 457-478

[33] Scolan YM. Hydroelastic behaviour of a conical shell impacting on a quiescent-free surface of an incompressible liquid. Journal of Sound and Vibration, 2004, 277(1/2): 163-203

[34] Senjanovic I, Catipovic I, Tomasevic S. Coupled flexural and torsional vibrations of ship-like girders. Thin-Walled Structures, 2007, 45: 1002-1021

[35] Senjanovic I, Malenica S, Tomasevic S. Investigation of ship hydroelasticity. Ocean Engineering, 2008, 35: 523-535

[36] Shams A, Porfiri M. Treatment of hydroelastic impact of flexible wedges. Journal of Fluid and Structures, 2015, 57: 229-246

[37] Stenius I, Rosn A, Kuttenkeuler J. Explicit FE-modelling of hydroelasticity in panel-water impacts. International Shipbuilding Progress, 2007, 54(2/3): 111-127

[38] Van Nuffel D, Vepa KS, De Baere I, Lava P, Kersemans M, Degrieck J, De Rouck J, Van Paepegem W. A comparison between the experimental and theoretical impact pressures acting on a horizontal quasi-rigid cylinder during vertical water entry. Ocean Engineering, 2014, 77: 42-54

[39] Wang S. Hydroelastic response of ship Structural Components subjected to slamming loads, 2016, 201-227

[40] Wang S, Guedes Soares C. Guedes Soares C, Lopez Pena F. Numerical study on hydroelastic water entry of a wedge. Developments in Maritime Transportation and Exploitation of Sea Resources, 2014, 199-208

[41] Wang S, Guedes Soares C. Numerical study on the water impact of 3D bodies by explicit finite element method. Ocean Engineering, 2014, 78: 73-88

[42] Wang S, Karmakar D, Guedes Soares C. Guedes Soares C, Santos TA. Hydroelastic impact due to longitudinal compression on transient vibration of a horizontal elastic plate. Maritime Technology and Engineering, 2015, 1073-1079

[43] Wang S, Karmakar D, Guedes Soares C. Hydroelastic impact of a horizontal floating plate with forward speed. Journal of Fluids and Structures, 2016, 60: 97-113