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A theoretical model based on linear potential flow theory and an eigenfunction matching method is developed to analyse the hydroelastic interaction between water waves and multiple circular floating porous elastic plates. The water domain is divided into the interior and exterior regions, representing the domain beneath each plate and the rest, which extends towards infinity horizontally, respectively. Spatial potentials in these two regions can be expressed as a series expansion of eigenfunctions. Three different types of edge conditions are considered. The unknown coefficients in the potential expressions can be determined by satisfying the continuity conditions for pressure and velocity at the interface of the two regions, together with the requirements for the motion/force at the edge of the plates. Apart from the straightforward method to evaluate the exact power dissipated by the array of porous elastic plates, an indirect method based on Green's theorem is determined. The indirect method expresses the wave-power dissipation in terms of Kochin functions. It is found that wave-power dissipation of an array of circular porous elastic plates can be enhanced by the constructive hydrodynamic interaction between the plates, and there is a profound potential of porous elastic plates for wave-power extraction. The results can be applied to a range of floating structures but have special application in modelling energy loss in flexible ice floes and wave-power extraction by flexible plate wave-energy converters.

The convergence of two numerical methods for solving linear water wave scattering problems, namely the eigenfunction matching method (EMM) and the singularity-respecting Galerkin approximation (SRGA), is examined. To do so, the methods are applied to two simple problems, namely scattering by a partially submerged vertical barrier and scattering in a parallel walled channel with a step change in width. These problems contain corner singularities in the velocity potential of order −1/2 and −1/3, respectively, which the SRGA accounts for but EMMs do not. The results presented to compare the methods show that SRGA solutions are consistently more accurate than EMM solutions for the same amount of computing time. The results also show that the EMM solution for the channel problem is more accurate than the EMM solution for the vertical barrier problem due to the weaker singularity. Nevertheless, the EMM for the barrier is shown to still converge beyond three decimal places if a sufficiently large matrix is used—slower computation may be a worthwhile trade-off in certain situations because the EMM is usually considered to be more straightforward to implement. Our results serve as a practical guide for researchers selecting between the numerical methods.

A method is presented to calculate the vibrations of an ice shelf floating in shallow water under different boundary conditions. One condition is that there is no flux, which reduces all calculations and the other is that there is no pressure at the seaward end of the ice shelf. The effect of these boundary conditions is investigated in detail, and the modes of vibration are also determined. Motion simulations of the system are presented for the potential velocity of the water and the vertical displacement of the ice shelf. These are found through a numerical method, which reduces all calculations to matrix multiplication. The underlying motion is shown to be very complex and difficult to interpret from single-point response measurements. The motion of more realistic ice shelves can be expected to be even more complicated.

This work presents an investigation of ice shelf vibration using a model based on shallow water approximation. The study focused on the effect of changes in the draft on the vibration of the ice shelf and presents both time-domain and frequency-domain results. The model used a radiation condition for energy propagation into the ice shelf. Furthermore, an energy balance relation was derived to investigate the energy flow within the system. Results show that changes in the draft can significantly impact the ice shelf’s vibration and that the energy flow within the system is affected by the geometry of the ice shelf. Results are presented for the interaction of wave packets in the time domain with the ice shelf. These show that energy is reflected and transmitted by the ice shelf and that the motion of the wave packets is very different in the ice shelf than in the open water. Overall, this study provides insight into the dynamics of ice shelf vibration and highlights the importance of considering changes in the draft and using the time domain when modelling these phenomena.

This work investigates the interaction between water waves and multiple ice shelf fragments in front of a semi-infinite ice sheet. The hydrodynamics are modelled using shallow water wave theory and the ice shelf vibration is modelled using Euler–Bernoulli beam theory. The ensuing multiple scattering problem is solved in the frequency domain using the transfer matrix method. The appropriate conservation of energy identity is derived in order to validate our numerical calculations. The transient scattering problem for incident wave packets is constructed from the frequency domain solutions. By incorporating multiple scattering, this paper extends previous models that have only considered a continuous semi-infinite ice shelf. This paper serves as a fundamental step towards developing a comprehensive model to simulate the breakup of ice shelves.

In this study, a numerical simulation of fluid flow through railway ballast in the time domain is presented, providing a model for unsteady-state flow. It is demonstrated that the position of the free surface with respect to time can also be used to solve the steady flow case. The effect of ballast fouling is included in the model to capture the realistic behavior of railway ballast, which is critical to understanding the impact of flooding. A thorough comparison with a range of previous studies, including theoretical and experimental approaches, is made, and very close agreement is obtained. The significant impact of ballast fouling on fluid flow and its potential consequences for railway infrastructure are highlighted by the simulation. Valuable insights into the behavior of water flow through porous media and its relevance to railway ballast management are offered by this study.

The flooding of railway ballasts can cause extensive damage. This process has been the subject of several experimental investigations. In the present work, a relatively easy to implement approach to modelling this fluid flow is presented. It is shown that good agreement with the experimental results is obtained. The fluid flow is modelled by Darcy’s law, which we extend to the free fluid flowing above the ballast. The main complexity is in determining the free surface position, which is accomplished using an iterative procedure. The equations are solved using the finite element method. The method is illustrated by careful numerical calculations that are carefully compared with the experimental results reported in the literature. The method is then extended to realistic railway ballast, including the effects of ballast fouling. It is shown that when the flow begins to overtop the ballast, the free surface shifts to greatly increase the chance of ballast scouring.

Transition zones in railway systems, where properties of the track foundation change abruptly, are known to increase dynamic loads, track deterioration, and passenger discomfort. As such, it is of particular importance to study railway transition zones with abrupt changes in foundation properties to minimize these railway problems. This paper presents a closed‐form solution for the long‐term deformation of an Euler‐Bernoulli beam on an elastic foundation with multiple abrupt changes in foundation stiffness and under multiple applied stationary point loads. The solutions are obtained by dividing the beam into segments and applying the method of undetermined coefficients. This exact analytical solution constitutes an improvement upon an approximate solution, which is presented in the literature as a recent method for modeling rail infrastructure at transition zones. A limitation of the approximate solution is its inability to account for the changed behavior of the beam close to a transition zone. The closed‐form solution overcomes this limitation and can be used to assess the suitability of the approximate solution. This paper presents a closed‐form solution for long‐term deformation of the Euler‐Bernoulli beam on an elastic foundation with multiple abrupt changes in foundation stiffness and under multiple applied stationary point loads. It provides correction and analysis of an existing approximate solution. Obtained results contribute to the understanding of track deformations where ground properties change.

The motion of a flexible elastic plate under wave action is simulated, and the well–known phenomena of overwash is investigated. The fluid motion is modelled by smoothed particle hydrodynamics, a mesh-free solution method which, while computationally demanding, is flexible and able to simulate complex fluid flows. The freely floating plate is modelled using linear thin plate elasticity plus the nonlinear rigid body motions. This assumption limits the elastic plate motion to be small but is valid for many cases both in geophysics and in the laboratory. The principal conclusion is that the inclusion of flexural motion causes significantly less overwash than that which occurs for a rigid plate.

In this paper, a concept of a floating elastic wave energy converter consisting of a disk-shaped elastic plate is proposed. The floating plate is moored to the seabed through a series of power take-off (PTO) units. A theoretical model based on the linear potential flow theory and eigenfunction matching method is developed to study the hydroelastic characteristics and evaluate wave power absorption of the device. The PTO system is simulated as a discrete PTO, and moreover, it is also modelled as a continuum PTO to represent the case when the PTO system is composed of a large number of PTO units. The continuum PTO approximation is tested against the discrete PTO simulation for accuracy. Two methods are proposed to predict the wave power absorption of the device. After running convergence analysis and model validation, the present model is employed to do a multiparameter impact analysis. The device adopting a continuum PTO system is found to capture wave power efficiently in an extensive range of wave frequencies. For the continuum PTO system, it is theoretically possible to adopt optimised PTO damper and stiffness/mass to guarantee the absorption of 100 % of the energy flux available in one circular component of the plane incident wave.