|2015||Meylan MH, Bennetts LG, Cavaliere C, Alberello A, Toffoli A, 'Experimental and theoretical models of wave-induced flexure of a sea ice floe', Physics of Fluids, 27 (2015)|
An experimental model is used to validate a theoretical model of a sea ice floe's flexural motion, induced by ocean waves. A thin plastic plate models the ice floe in the experiments. Rigid and compliant plastics and two different thicknesses are tested. Regular incident waves are used, with wavelengths less than, equal to, and greater than the floe length, and steepnesses ranging from gently sloping to storm-like. Results show the models agree well, despite the overwash phenomenon occurring in the experiments, which the theoretical model neglects.
|2015||Meylan MH, Yiew LJ, Bennetts LG, French B, Thomas GA, 'Surge motion of an ice floe in waves: comparison of theoretical and experimental models', Annals of Glaciology, 56 155-159 (2015)|
|2014||Meylan MH, Fitzgerald CJ, 'The singularity expansion method and near-trapping of linear water waves', JOURNAL OF FLUID MECHANICS, 755 (2014) [C1]|
|2014||Kohout AL, Williams MJM, Dean SM, Meylan MH, 'Storm-induced sea-ice breakup and the implications for ice extent', NATURE, 509 604-+ (2014) [C1]|
|2014||Smith MJA, Meylan MH, Mcphedran RC, 'Density of states for platonic crystals and clusters', SIAM Journal on Applied Mathematics, 74 1551-1570 (2014) [C1]|
The density of states, which measures the density of the spectrum, is evaluated for a platonic crystal (periodically structured elastic plate) using the Green's function approach. Results are presented not only for the standard density of states, but also for the mutual, local, and spectral density of states. These other state functions provide a pathway to the standard density of states and characterize the radiative and other properties of the crystal. This is the first known examination of the density of states for a platonic crystal and extends the existing Green's function approach for photonic crystals to thin, elastic plates. As a motivating example the theory is applied to the problem of a square array of pins embedded in a thin plate. The density of states functions for an empty lattice (a uniform plate) are also presented in order to give a clear illustration of the steps in the derivation. Careful numerical calculations are given which reveal the complex behavior of the crystal, including intervals of suppressed density of states. These results are compared to calculations for a finite crystal with an interior source, and the behaviors of the finite and infinite systems are shown to be connected through the density of states.
|2014||Meylan MH, 'The time-dependent motion of a floating elastic or rigid body in two dimensions', APPLIED OCEAN RESEARCH, 46 54-61 (2014) [C1]|
|2014||Smith MJA, McPhedran RC, Meylan MH, 'Double dirac cones at k = 0 in pinned platonic crystals', Waves in Random and Complex Media, 24 35-54 (2014) [C1]|
In this paper, we compute the band structure for a pinned elastic plate which is constrained at the points of a hexagonal lattice. Existing work on platonic crystals has been restricted to square and rectangular array geometries, and an examination of other Bravais lattice geometries for platonic crystals has yet to be made. Such hexagonal arrays have been shown to support Dirac cone dispersion at the center of the Brillouin zone for phononic crystals, and we demonstrate the existence of double Dirac cones for the first time in platonic crystals here. In the vicinity of these Dirac points, there are several complex dispersion phenomena, including a multiple interference phenomenon between families of waves which correspond to free space transport and those which interact with the pins. An examination of the reflectance and transmittance for large finite gratings arranged in a hexagonal fashion is also made, where these effects can be visualized using plane waves. This is achieved via a recurrence relation approach for the reflection and transmission matrices, which is computationally stable compared to transfer matrix approaches.© 2013 Taylor and Francis.
|2014||Smith MJA, Meylan MH, McPhedran RC, Poulton CG, 'A short remark on the band structure of free-edge platonic crystals', Waves in Random and Complex Media, 24 421-430 (2014) [C1]|
A corrected version of the multipole solution for a thin plate perforated in a doubly periodic fashion is presented. It is assumed that free-edge boundary conditions are imposed at the edge of each cylindrical inclusion. The solution procedure given here exploits a well-known property of Bessel functions to obtain the solution directly, in contrast to the existing incorrect derivation. A series of band diagrams and an updated table of values are given for the resulting system (correcting known publications on the topic), which shows a spectral band at low frequency for the free-edge problem. This is in contrast to clamped-edge boundary conditions for the same biharmonic plate problem, which features a low-frequency band gap. The numerical solution procedure outlined here is also simplified relative to earlier publications, and exploits the spectral properties of complex-valued matrices to determine the band structure of the structured plate.
|2014||Meylan MH, Bennetts LG, Kohout AL, 'In-situ measurements and analysis of ocean waves in the Antarctic marginal ice zone', Geophysical Research Letters, 41 5046-5051 (2014) [C1]|
|2013||Smith MJA, Meylan MH, McPhedran RC, 'Flexural wave filtering and platonic polarisers in thin elastic plates', Quarterly Journal of Mechanics and Applied Mathematics, 66 437-463 (2013) [C1]|
|2012||Meylan MH, Tomic M, 'Complex resonances and the approximation of wave forcing for floating elastic bodies', Applied Ocean Research, 36 51-59 (2012) [C1]|
|2012||Smith MJA, McPhedran RC, Poulton CG, Meylan MH, 'Negative refraction and dispersion phenomena in platonic clusters', Waves in Random and Complex Media, 22 435-458 (2012) [C1]|
|2007||Kohout AL, Meylan MH, Sakai S, Hanai K, Leman P, Brossard D, 'Linear water wave propagation through multiple floating elastic plates of variable properties', JOURNAL OF FLUIDS AND STRUCTURES, 23 649-663 (2007)|
|2007||Wang CD, Meylan MH, Porter R, 'The linear-wave response of a periodic array of floating elastic plates', JOURNAL OF ENGINEERING MATHEMATICS, 57 23-40 (2007)|
|2007||Peter MA, Meylan MH, 'Water-wave scattering by a semi-infinite periodic array of arbitrary bodies', JOURNAL OF FLUID MECHANICS, 575 473-494 (2007)|
|2007||Hazard C, Meylan MH, 'Spectral theory for an elastic thin plate floating on water of finite depth', SIAM JOURNAL ON APPLIED MATHEMATICS, 68 629-647 (2007)|
|2006||Peter MA, Meylan MH, Linton CM, 'Water-wave scattering by a periodic array of arbitrary bodies', JOURNAL OF FLUID MECHANICS, 548 237-256 (2006)|
|2006||Meylan MH, 'A semi-analytic solution to the time-dependent half-space linear Boltzmann equation', TRANSPORT THEORY AND STATISTICAL PHYSICS, 35 187-227 (2006)|
|2006||Grotmaack R, Meylan MH, 'Wave forcing of small floating bodies', JOURNAL OF WATERWAY PORT COASTAL AND OCEAN ENGINEERING-ASCE, 132 192-198 (2006)|
|2006||Meylan MH, Masson D, 'A linear Boltzmann equation to model wave scattering in the marginal ice zone', OCEAN MODELLING, 11 417-427 (2006)|
|2004||Peter MA, Meylan MH, 'Infinite-depth interaction theory for arbitrary floating bodies applied to wave forcing of ice floes', JOURNAL OF FLUID MECHANICS, 500 145-167 (2004)|
|2004||Peter MA, Meylan MH, 'The eigenfunction expansion of the infinite depth free surface Green function in three dimensions', WAVE MOTION, 40 1-11 (2004)|
|2004||Wang CD, Meylan MH, 'A higher-order-coupled boundary element and finite element method for the wave forcing of a floating elastic plate', Journal of Fluids and Structures, 19 557-572 (2004)|
We present a higher-order method to calculate the motion of a floating, shallow draft, elastic plate of arbitrary geometry subject to linear wave forcing at a single frequency. The solution is found by coupling the boundary element and finite element methods. We use the same nodes, basis functions, and maintain the same order in both methods. Two equations are derived that relate the displacement of the plate and the velocity potential under the plate. The first equation is derived from the elastic plate equation. The discrete version of this equation is very similar to the standard finite element method elastic plate equation except that the potential of the water is included in a consistent manner. The second equation is based on the boundary integral equation which relates the displacement of the plate and the potential using the free-surface Green function. The discrete version of this equation, which is consistent with the order of the basis functions, includes a Green matrix that is analogous to the mass and stiffness matrices of the classical finite element method for an elastic plate. The two equations are solved simultaneously to give the potential and displacement. Results are presented showing that the method agrees with previous results and its performance is analysed. © 2004 Elsevier Ltd. All rights reserved.
|2002||Meylan MH, 'Spectral solution of time-dependent shallow water hydroelasticity', JOURNAL OF FLUID MECHANICS, 454 387-402 (2002)|
|2002||Wang CD, Meylan MH, 'The linear wave response of a floating thin plate on water of variable depth', APPLIED OCEAN RESEARCH, 24 163-174 (2002)|
|2002||Meylan MH, 'Wave response of an ice floe of arbitrary geometry', Journal of Geophysical Research: Oceans, 107 (2002)|
A fully three-dimensional model for the motion and bending of a solitary ice floe due to wave forcing is presented. This allows the scattering and wave-induced force for a realistic ice floe to be calculated. These are required to model wave scattering and wave-induced ice drift in the marginal ice zone. The ice floe is modeled as a thin plate, and its motion is expanded in the thin plate modes of vibration. The modes are substituted into the integral equation for the water. This gives a linear system of equations for the coefficients used to expand the ice floe motion. Solutions are presented for the ice floe displacement, the scattered energy, and the time-averaged force for a range of ice floe geometries and wave periods. It is found that ice floe stiffness is the most important factor in determining ice floe motion, scattering, and force. However, above a critical value of stiffness the floe geometry also influences the scattering and force.
|2001||Meylan MH, 'A variational equation for the wave forcing of floating thin plates', APPLIED OCEAN RESEARCH, 23 195-206 (2001)|