Hyuck Chung

Dynamic, in situ measurement of sea-ice characteristic length

Abstract We present a method for measuring the characteristic length of sea ice based on fitting to a recently found solution for the flexural response of a floating ice sheet subject to localized periodic loading. Unlike previous techniques, the method enables localized measurements at single frequencies of geophysical interest, and since the measurements may be synchronously demodulated, gives excellent rejection of unwanted measurement signal (e.g. from ocean swell). The loading mechanism is described and we discuss how the effective characteristic length may be determined using a range of localized measurements. The method is used to determine the characteristic length of the sea ice in McMurdo Sound, Antarctica.

Reflection and transmission at the ocean/sea-ice boundary

Abstract The scattering of water waves by the edge of a semi-infinite ice sheet in a finite depth ocean is solved using the residue calculus technique. We consider both the case where the obliquely incident plane wave is from the open sea region and the complementary problem where the wave is incident from the ice-covered region. Exact solutions to these problems are obtained, equivalent to those that can be obtained if the Wiener–Hopf technique is used. Contrary to popular belief, the solutions are easy to evaluate numerically.

Fourier Series Solutions to the Vibration of Rectangular Lightweight Floor/Ceiling Structures

This article presents a mathematical model of lightweight timber floor/ceiling structures. The structures studied here consist of three basic components: upper plate, joist beams and ceiling. The shape of the whole structure is rectangular with the edges simply supported. Connections between the joist beams, the upper plate and the ceiling are considered. These connections take the form of lateral and vertical elastic coupling between the plates and beams. The configuration of the structure is made progressively more complex by adding more components such as cavity air and stiffening battens. The resulting solution formulae can be directly written into computer codes, which compute the vibration of the structure.

Vibration reduction in lightweight floor/ceiling systems with a sand-sawdust damping layer

This paper shows how to use a mathematical model to predict the vibration of lightweight timber-framed floor/ceiling systems (LTFSs) caused by mechanical excitation. The LTFS considered here is made up of an upper floor layer, a cavity space with timber joists and a ceiling. These components are joined by timber battens, ceiling furring channels and ceiling clips. The vibration in the structure is caused by a localized excitation on the top surface and the resulting vibration level of the ceiling surface will be analysed. The cavity space is filled with fibre infill for damping the sound transmitting through the cavity. A unique feature of the design and the model is the sand-sawdust mixture in the upper layer. The theoretical model and the experimental measurements show that the sand-sawdust dampens the vibration in the frequency range between 10 and 200 Hz. The damping by the sand-sawdust and the fibre infill are found by comparing the numerical simulations against the experimental measurements. We show that the simple linear frequency dependent loss factors can be used to predict the low-frequency vibrations of LTFSs.

Lightweight floor/ceiling systems with improved impact sound insulation

Contrary to common belief, a relatively simple and practical lightweight timber based floor/ceiling can have impact sound insulation superior to that of concrete slab based systems. This paper presents examples of such systems that include vibration isolation/damping features, such as rubber ceiling batten clips, glass fibre wool, and a sand-sawdust mixture layer. We give enough details to reproduce our experiments and build the proposed lightweight systems.

Mid-frequency vibrations of a double-leaf plate with random inhomogeneities

Predicting vibrations of composite structures such as double-leaf plates is difficult because of the large number of components and random inhomogeneities in the components. In the low and high frequency ranges, the components may be homogenized, and consequently the model of a structure becomes simple enough to be mathematically and computationally tractable. However the vibrations in the mid-frequency range cannot be predicted using such methods because the wavelengths are comparable to the size of the components and junctions between components. Simply adding more details, e.g., higher resolution in finite element mesh, will not result in more accurate predictions. In this paper a double-leaf plate is modeled using the Kirchhoff plate and Euler beam theories. The elastic moduli and junctions are allowed to be inhomogeneous over the plates and beams. These inhomogeneities are simulated as continuous smooth random functions rather than series of discrete random numbers. The random functions are incorpora...

Vibration of a rib‐reinforced floor/ceiling structures with irregularities

This paper describes mathematical modelling procedure of the rib‐reinforced floor/ceiling structures, which are made up of components with irregular shapes and physical parameters. Exact determination of the vibration of a composite structure becomes impossible beyond the low‐frequency range because one cannot determine all the necessary parameters of the components. Even if every possible parameter of the structure is known, the results from such deterministic model would not represent the real behaviour of the structure. Therefore, the prediction model in the mid‐ to high‐frequency range must include the effects of the irregularities. We show how the power spectra of the irregular features of each component can be included in the model. The model gives statistical estimates of the solutions, which can give appropriate mean and variance of the vibration of the structure for the given severity of the irregularities.

A variational approach to modeling the vibration of timber joist floors

We present a comprehensive variational model for the vibration of timber joist floors and a simple computer algorithm for finite, particularly rectangular, floors. We allow for floor constructions that are typical in the New Zealand context, consisting of edge‐supported timber joists with flooring material above, often a suspended ceiling below with absorptive material in the cavity, and a range of joint types such as gluing or nailing. The model and algorithm are structured in such a way that a component can easily be either added to, or removed from, the structure. Hence the configuration may be made progressively more complex from the simplest floor‐joists type to floor‐joists‐ceiling with cavity air and damper‐spring connectors.

Wave Reflection by a Sheet of Sea Ice

The effect of a thin sheet of sea ice, modelled as an elastic plate, on the propagation of surface gravity waves in the ocean has been the subject of extensive study. A classic problem is that of a plane wave obliquely incident from an open ocean of constant finite depth on an ice sheet in the form of a half-plane. This problem was solved using the Wiener-Hopf technique by Evans and Davies [3]. In their report Evans and Davies wrote of part of the solution process “Unfortunately, the determination of the constants... presents enormous computational difficulties...” and ever since their appears to have been a general feeling that the Weiner-Hopf solution to this problem is cumbersome and impractical.

Transmission loss across a rectangular partition or aperture

We give closed‐form solutions for sound propagation through a rectangular aperture, or plate, in a finite or infinite acoustically opaque barrier. This model is useful in descibing airborne excitation and reradiation through window openings or through floor/wall partitions that can be modeled in terms of bending stiffness and mass. While mode‐matching solutions are routinely available for these problems, we are not aware of any previous analytic solutions. The value of the closed‐form solution, other than the obvious ease of calculation, is in establishing scaling laws for the various regimes of structure‐borne and air‐borne sound. We derive the analytic solution using an extension of the Wiener–Hopf technique as applied to sound propagation in ducts with a partial rigid barrier.