Impact of a surfacewave on an elastic hull

Abstract

In order to model a ship hull's response to the impact of surface waves, the two-dimensional problem of wave impact on an elastic beam whose ends are connected by springs with a rigid structure uniformly submerged in a fluid is considered. The fluid is assumed to be ideal and incompressible and its flow symmetric; the lateral bending of the beam is described by the Euler equation. The fluid flow and the size of the wetted region are determined simultaneously with the calculation of the the beam deflection within the framework of the Wagner approach which takes into account the reshaping of the free surface of the fluid on interacting with a body. The stresses and strains arising in the beam and at its ends during impact are found. The numerical algorithm developed makes it possible to analyze the elastic effects in fluid impacts on thin-walled structures of finite length. Moreover, as the stiffness of the connecting springs tends to zero, the solution of this problem describes the impact of an elastic beam with free ends on a weakly curved fluid surface.

Elastic wedge impact onto a liquid surface: Wagner's solution and approximate models

“…The methods used in this study come from the analysis of elastic plate impact onto the crest of a surface wave (see Korobkin, 1998;Khabakhpasheva, 1998, 2006;Khabakhpasheva, 2006). It was shown that the numerical results obtained by these methods agree well with the results of the experiments and calculations by Faltinsen et al (1997).…”

“…For a homogeneous Euler beam such integrals were evaluated analytically. For a simply supported Euler beam it was done by Korobkin (1998) and for a beam attached by two linear springs at its ends to the main structure it was done by Khabakhpasheva (2006). These analytical formulas made it possible to obtain accurate solutions of beam impact problems using many modes.…”

“…In this case we havẽ The modesc k ðxÞ and the corresponding added-mass matrixSðcÞ for a homogeneous elastic plate attached by springs at its ends to the main structure are more complicated and are not reproduced here. They can be found in Khabakhpasheva (2006). The described method of computing the added-mass matrix S(c) and the forcing vector f !…”

Local slamming impact of sandwich composite hulls

“…However, high complexities of the slamming phenomena require continuous research to improve upon and optimize hull's design. In this context, issues of hydroelastic effect during the slamming impact on structural deformations have drawn considerable attention, see e.g., Bereznitski (2001), Faltinsen (1999), Khabakhpasheva (2005), Korobkin (1995), Kvålsvold and Faltinsen (1995), and Scolan (2004).…”

Hydroelastic effects during the fast lifting of a disc from a water surface

“…The problem formulated by equations (4.1)-(4.9) is coupled, the hydrodynamic loads and the disc displacement should be determined at the same time. The problem is solved by the normal mode method (Khabakhpasheva & Korobkin 1998;Korobkin 2000;Khabakhpasheva 2006;Khabakhpasheva et al 2013). Within this method the disc displacement is sought in the form w(r, t) = h(t) + ∞ n=1 a n (t)W n (r), (4.10) wherer = r/R is the non-dimensional radial coordinate,r < 1, a n (t) are the principal coordinates of the elastic deflections of the disc, which are to be determined, and h(t) is the rigid-body displacement of the disc.…”