Boundary Value Problems in Physics and Engineering By Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s

Boundary value problems

http://www.naoe.eng.osaka-u.ac.jp/naoe/naoe1/image/Reference01.pdf

Hydroelastic analysis of pontoon-type VLFS: a literature survey

Mathematical models for the prediction of the hydrodynamic pressure distribution and the force on a body entering liquid are investigated. Particular attention is paid to analytical models which are based on the velocity potential given by the classical Wagner theory. Formal use of the Wagner theory provides the loads on an entering body, which are higher than the measured ones. To improve the predictions, the higher order terms in the Bernoulli equation are taken into account within the generalized Wagner model and the Logvinovich model. It is shown that the Logvinovich model corresponds better to the experimental data than the generalized Wagner model. A rational derivation of the Logvinovich model is given in the paper for the two-dimensional case. The analytical models are tested against both numerical and experimental results.

Analytical models of water impact

https://cronfa.swan.ac.uk/Record/cronfa24898/Download/0024898-19022016141050.pdf

The mechanics of composite corrugated structures: A review with applications in morphing aircraft

Practical slamming problems for ships and ocean structures are briefly described. Theoretical status and future challenges for water entry on an initially calm free surface, wetdeck slamming, green water and sloshing are presented. It is emphasized that slamming should be considered in the framework of structural dynamics response and integrated with the global flow analysis around a ship or ocean structure or with violent fluid motion inside a tank. Two-phase flow can give important loading and needs to be better understood. Slamming on a VLFS with shallow draft is dealt with in detail.

Slamming in marine applications

The paper deals with the plane problem of the hydroelastic behaviour of floating plates under the influence of periodic surface water waves. Analysis of this problem is based on hydroelasticity, in which the coupled hydrodynamics and structural dynamics problems are solved simultaneously. The plate is modeled by an Euler beam. The method of numerical solution of the floating-beam problem is based on expansions of the hydrodynamic pressure and the beam deflection with respect to different basic functions. This makes it possible to simplify the treatment of the hydrodynamic part of the problem and at the same time to satisfy accurately the beam boundary conditions. Two approaches aimed to reduce the beam vibrations are described. In the first approach, an auxiliary floating plate is added to the main structure. The size of the auxiliary plate and its elastic characteristics can be chosen in such a way that deflections of the main structure for a given frequency of incident wave are reduced. Within the second approach the floating beam is connected to the sea bottom with a spring, the rigidity of which can be selected in such a way that deflections in the main part of the floating beam are very small. The effect of the vibration reduction is quite pronounced and can be utilized at the design stage.

Hydroelastic behaviour of compound floating plate in waves

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

A computational analysis of an elastic plate dropped against regular long waves is presented. The problem is considered within the linear potential-flow theory. The liquid flow is two-dimensional and the plate is modelled by an Euler beam. The analysis is based on the normal-mode method with hydroelastic behavior of the plate being of main interest. Different impact conditions are considered to study the dependence of the total energy of the plate–liquid system on impact geometry and plate properties. The contributions of kinetic and potential energies to the total energy are analyzed. It is shown that the kinetic part of the system energy is small at the instant of time when bending stresses in the beam approach their maximum values. Estimations of both the total energy and the maximum of bending stresses are presented. Most of the calculations are performed for the conditions of experiments carried out in MARINTEK. A range of the problem parameters is also considered, to reveal peculiarities of the unsteady interaction between a falling elastic plate and surface waves.

Regular wave impact onto an elastic plate

Linear progressive waves in a channel covered with ice sheet are studied. The channel is of rectangular cross section. The ice sheet is clamped to the walls of the channel. The thickness of the ice plate is constant. Deflections of the ice sheet are described by the linear elastic plate equation. The hydroelastic waves in the channel are combinations of waves propagating along the channel and sloshing waves. The problem is formulated with respect to the wave profiles across the channel. The problem is solved by the normal mode method for a channel of finite depth and by using the shallow water approximation for a channel of small depth. The dispersion relations of the hydroelastic waves and the characteristics of these waves are determined. It is shown that the shallow water approximation predicts well the dispersion relations for long waves. The dispersion relation for the wave, which does not oscillate across the channel, is well approximated by the corresponding dispersion relation of one-dimensional hydroelastic waves in an unbounded ice sheet. The wave profiles across the channel and the distributions of strains in the ice sheet are investigated. It is shown that the strains are maximum at the walls for long waves and at the centreline of the channel for short waves. The bending stresses across the channel are higher than the stresses along the channel for the conditions of the present study.

Tatyana Khabakhpasheva

Papers

Hydroelastic behaviour of compound floating plate in waves

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

Regular wave impact onto an elastic plate

Waves propagating along a channel with ice cover

The response of ice cover to a load moving along a frozen channel