827 research outputs found

    AM baseband telemetry systems. Volume 1 - Factors affecting a common pilot system

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    Coherent demodulation in single and double side bands with frequency modulation telemetry system

    Am-baseband Telemetry Systems. Volume 4 - Problems Relating to Am-baseband Systems

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    Distortion of amplitude modulated radio signals passing within passband of bandpass filter

    AM-baseband telemetry systems. Volume 5 - Summary

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    Demodulation process for AM baseband telemetry system

    Mathematical modelling of nonlinear waves in layered waveguides with delamination

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    The propagation of nonlinear bulk strain waves in layered elastic waveguides has many applications, particularly its potential use for non-destructive testing, where a small defect in the bonding between the layers of a waveguide can lead to a catastrophic failure of the structure. Experiments have shown that strain solitons can propagate for significantly longer distances than the waves used in current methods, and therefore they are of great interest. This thesis considers two problems. Firstly, we consider the scattering of nonlinear bulk strain waves in two types of waveguides: a perfectly bonded layered waveguide, and a layered waveguide with a soft bond between the layers, when the materials in the layers have similar properties. In each case we assume that there is a region where the bond is absent - a delamination. This behaviour is described by a system of uncoupled or coupled Boussinesq equations, with conditions on the interface between the sections of the bar. This is a complicated system of equations, and we develop a direct numerical method to solve these equations numerically. A weakly nonlinear solution is then constructed for the system of equations, describing the leading order reflected and transmitted strain waves. In the case of a layered elastic bar with a perfect bond we obtain Korteweg-de Vries equations, and in the case of a soft bond between the layers, where the properties of the layers are close, we obtain coupled Ostrovsky equations describing the propagation of the reflected and transmitted waves in each layer of the waveguide. In the delaminated regions of the bar, Korteweg-de Vries equations are derived in every case and therefore we make use of the Inverse Scattering Transform to provide theoretical predictions in this region. The modelling in each case is extended to the case of a finite delamination in the waveguide, and we study the effect of re-entering a bonded region on a strain wave. In each case considered we develop a measure of the delamination length in terms of the change in amplitude of the incident wave, and furthermore the structure of the wave provides further insight about the structure of the waveguide. Numerical simulations are developed using finite-difference techniques and pseudospectral methods, and these are detailed in the appendices. Finally, we consider the initial value problem for the Boussinesq equation with an Ostrovsky term, on a periodic domain. The initial condition for this equation does not necessary have zero mean on the interval. The mean value is subtracted from the function so that a weakly nonlinear solution to the problem can be constructed where all functions in this expansion have zero mean. This is necessary as the derived Ostrovsky equations have zero mean. The expansion is constructed in increasing powers of ϵ\sqrt{\epsilon} up to and including \O{\epsilon}, where ϵ\epsilon is a small amplitude parameter in the equation. We compare the results for a wide range of values of γ\gamma (the coefficient of the Ostrovsky term) and varying mean values for the initial condition, to confirm that the expansion is valid. A comparison of the errors shows that the constructed expansion is correct and the errors behave as predicted by the expansion. This was further confirmed for non-unity coefficients in the equation

    Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction

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    Coupled Boussinesq equations describe long weakly-nonlinear longitudinal strain waves in a bi-layer with a soft bonding between the layers (e.g. a soft adhesive). From the mathematical viewpoint, a particularly difficult case appears when the linear long-wave speeds in the layers are significantly different (high-contrast case). The traditional derivation of the uni-directional models leads to four uncoupled Ostrovsky equations, for the right- and left-propagating waves in each layer. However, the models impose a ``zero-mass constraint'' i.e. the initial conditions should necessarily have zero mean, restricting the applicability of that description. Here, we bypass the contradiction in this high-contrast case by constructing the solution for the deviation from the evolving mean value, using asymptotic multiple-scale expansions involving two pairs of fast characteristic variables and two slow-time variables. By construction, the Ostrovsky equations emerging within the scope of this derivation are solved for initial conditions with zero mean while initial conditions for the original system may have non-zero mean values. Asymptotic validity of the solution is carefully examined numerically. We apply the models to the description of counter-propagating waves generated by solitary wave initial conditions, or co-propagating waves generated by cnoidal wave initial conditions, as well as the resulting wave interactions, and contrast with the behaviour of the waves in bi-layers when the linear long-wave speeds in the layers are close (low-contrast case). One local (classical) and two non-local (generalised) conservation laws of the coupled Boussinesq equations for strains are derived, and these are used to control the accuracy of the numerical simulations.Comment: 25 pages, 11 figures; previously this version appeared as arXiv:2210.14107 which was submitted as a new work by acciden

    Simultaneous Pairs of Dual Integral Equations

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