A two-dimensional acoustic waveguide of infinite extent described by two parallel lines contains an obstruction of fairly general shape which is symmetric about the centreline of the waveguide. It is proved that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction. Mathematically, this trapped mode is related to an eigenvalue of the Laplace operator in the waveguide. The proof makes use of an extension of the idea of the Rayleight quotient to characterize the lowest eigenvalue of a differential operator on an infinite domain.
The scattering of water waves by an array of N bottom-mounted vertical circular cylinders is solved exactly (under the assumption of linear water wave theory) using the method proposed by Spring & Monkmeyer in 1974. A major simplification to this theory has been found which makes the evaluation of quantities such as the forces on the cylinders much simpler. New formulae are given for the first and mean second-order forces together with one for the free-surface elevation in the vicinity of a particular cylinder. Comparisons are made between the exact results shown here and those generated using the approximate method of McIver & Evans (1984). The behaviour of the forces on the bodies in the long-wave limit is also examined for the special case of two cylinders with equal radii.
A theory is given for predicting the absorption of the power in an incident sinusoidal wave train by means of a damped, oscillating, partly or completely submerged body. General expressions for the efficiency of wave absorption when the body oscillates in one or, in some cases, two modes are given. It is shown that 100% efficiency is possible in some cases. Curves describing the variation of efficiency and amplitude of the body with wavenumber for various bodies are presented.
Some general results are derived for the efficiency of energy absorption of a system of uniform oscillatory surface pressure distributions. The results, which are based on classical linear water-wave theory, show the close analogies which exist with theories for systems of absorbing oscillatory rigid bodies and a number of new reciprocal relations for pressure distributions are suggested and proved. Some simple examples illustrating the general results are given and compared with the corresponding results for rigid bodies.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.