A method for estimating depth-limited wave energy /

"November 1981."

Development of a method for numerical calculation of wave refraction /

"October 1964."

A method for calculating and plotting surface wave rays /

See addenda at end of item.

Back scattering of a plane electromagnetic wave from an infinite cylinder of plasma with small axial gradients and arbitrary radial gradients of electron density : normal incidence /

"Prepared under contract no. NOrd 18053."

North Atlantic coast wave statistics : hindcast by Bretschneider-Revised Sverdrup-Munk Method /

Mode of access: Internet.

North Atlantic coast wave statistics hindcast by the wave spectrum method /

Mode of access: Internet.

Wave velocity method of depth determination for non-uniform short crested wave systems by aerial photography /

Mode of access: Internet.

A treatise of plane trigonometry : to which is prefixed a summary view of the nature and use of logarithms : being the second part of a course of mathematics, adapted to the method of instruction in the American colleges /

Mode of access: Internet.

A treatise of plane trigonometry : to which is prefixed a summary view of the nature and use of logarithms : being the second part of a course of mathematics, adapted to the method of instruction in the American colleges /

With: A Practical application of The Principles of geometry to the mensuration of superficies and solids: being the third part of a Course of mathematics, ...

An elementary treatise on plane geometry, according to the method of rectilineal co-ordinates.

Mode of access: Internet.

Surface wave techniques for the study of engineering structures and materials

A wire drive pulse echo method of measuring the spectrum of solid bodies described. Using an 's' plane representation, a general analysis of the transient response of such solids has been carried out. This was used for the study of the stepped amplitude transient of high order modes of disks and for the case where there are two adjacent resonant frequencies. The techniques developed have been applied to the measurenent of the elasticities of refractory materials at high temperatures. In the experimental study of the high order in-plane resonances of thin disks it was found that the energy travelled at the edge of the disk and this initiated the work on one dimensional Rayleigh waves.Their properties were established for the straight edge condition by following an analysis similar to that of the two dimensional case. Experiments were then carried out on the velocity dispersion of various circuits including the disk and a hole in a large plate - the negative curvature condition.Theoretical analysis established the phase and group velocities for these cases and experimental tests on aluminium and glass gave good agreement with theory. At high frequencies all velocities approach that of the one dimensional Rayleigh waves. When applied to crack detection it was observed that a signal burst travelling round a disk showed an anomalous amplitude effect. In certain cases the signal which travelled the greater distance had the greater amplitude.An experiment was designed to investigate the phenanenon and it was established that the energy travelled in two nodes with different velocities.It was found by analysis that as well as the Rayleigh surface wave on the edge, a seoond node travelling at about the shear velocity was excited and the calculated results gave reasonable agreement with the experiments.

Solving Fractional Diffusion-Wave Equations Using a New Iterative Method

Mathematics Subject Classification: 26A33, 31B10

Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method

Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.

Time-domain simulation of wave-induced ship motions by a Rankine panel method

In this thesis, a numerical program has been developed to simulate the wave-induced ship motions in the time domain. Wave-body interactions have been studied for various ships and floating bodies through forced motion and free motion simulations in a wide range of wave frequencies. A three-dimensional Rankine panel method is applied to solve the boundary value problem for the wave-body interactions. The velocity potentials and normal velocities on the boundaries are obtained in the time domain by solving the mixed boundary integral equations in relation to the source and dipole distributions. The hydrodynamic forces are calculated by the integration of the instantaneous hydrodynamic pressures over the body surface. The equations of ship motion are solved simultaneously with the boundary value problem for each time step. The wave elevation is computed by applying the linear free surface conditions. A numerical damping zone is adopted to absorb the outgoing waves in order to satisfy the radiation condition for the truncated free surface. A numerical filter is applied on the free surface for the smoothing of the wave elevation. Good convergence has been reached for both forced motion simulations and free motion simulations. The computed added-mass and damping coefficients, wave exciting forces, and motion responses for ships and floating bodies are in good agreement with the numerical results from other programs and experimental data.