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- W2890648049 abstract "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 $sqrt{epsilon}$ up to and including $O{epsilon}$, where $epsilon$ is a small amplitude parameter in the equation. We compare the results for a wide range of values of $gamma$ (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." @default.
- W2890648049 created "2018-09-27" @default.
- W2890648049 creator A5046454191 @default.
- W2890648049 date "2018-01-01" @default.
- W2890648049 modified "2023-09-26" @default.
- W2890648049 title "Mathematical modelling of nonlinear waves in layered waveguides with delamination" @default.
- W2890648049 cites W1490180844 @default.
- W2890648049 cites W1510530389 @default.
- W2890648049 cites W1536812575 @default.
- W2890648049 cites W1558122728 @default.
- W2890648049 cites W1561892995 @default.
- W2890648049 cites W1598578620 @default.
- W2890648049 cites W1632757846 @default.
- W2890648049 cites W1708785370 @default.
- W2890648049 cites W1718948689 @default.
- W2890648049 cites W1805381866 @default.
- W2890648049 cites W1830295866 @default.
- W2890648049 cites W193443676 @default.
- W2890648049 cites W1966241802 @default.
- W2890648049 cites W1967528517 @default.
- W2890648049 cites W1971523400 @default.
- W2890648049 cites W1971947347 @default.
- W2890648049 cites W1972109532 @default.
- W2890648049 cites W1979722387 @default.
- W2890648049 cites W1983031318 @default.
- W2890648049 cites W1983034410 @default.
- W2890648049 cites W1985822072 @default.
- W2890648049 cites W1986788497 @default.
- W2890648049 cites W1987198047 @default.
- W2890648049 cites W1994985671 @default.
- W2890648049 cites W2002790427 @default.
- W2890648049 cites W2002941250 @default.
- W2890648049 cites W2003364054 @default.
- W2890648049 cites W2005380085 @default.
- W2890648049 cites W2006718018 @default.
- W2890648049 cites W2009997011 @default.
- W2890648049 cites W2013109521 @default.
- W2890648049 cites W2013951928 @default.
- W2890648049 cites W2014868183 @default.
- W2890648049 cites W2019132011 @default.
- W2890648049 cites W2022377982 @default.
- W2890648049 cites W2022749327 @default.
- W2890648049 cites W2027595215 @default.
- W2890648049 cites W2029703793 @default.
- W2890648049 cites W2030669316 @default.
- W2890648049 cites W2032741615 @default.
- W2890648049 cites W2041060520 @default.
- W2890648049 cites W2047246798 @default.
- W2890648049 cites W2050080189 @default.
- W2890648049 cites W2050568622 @default.
- W2890648049 cites W2050639649 @default.
- W2890648049 cites W2051944838 @default.
- W2890648049 cites W2061171222 @default.
- W2890648049 cites W2062477930 @default.
- W2890648049 cites W2066766180 @default.
- W2890648049 cites W2070585813 @default.
- W2890648049 cites W2072116514 @default.
- W2890648049 cites W2080012289 @default.
- W2890648049 cites W2083386974 @default.
- W2890648049 cites W2086025231 @default.
- W2890648049 cites W2091946035 @default.
- W2890648049 cites W2095669631 @default.
- W2890648049 cites W2102182691 @default.
- W2890648049 cites W2118072606 @default.
- W2890648049 cites W2129821313 @default.
- W2890648049 cites W2137598555 @default.
- W2890648049 cites W2143167560 @default.
- W2890648049 cites W2146063576 @default.
- W2890648049 cites W2147425354 @default.
- W2890648049 cites W2150349419 @default.
- W2890648049 cites W2152015319 @default.
- W2890648049 cites W2152083780 @default.
- W2890648049 cites W2152112575 @default.
- W2890648049 cites W2165565696 @default.
- W2890648049 cites W2165957857 @default.
- W2890648049 cites W2167257763 @default.
- W2890648049 cites W2217752536 @default.
- W2890648049 cites W2296733954 @default.
- W2890648049 cites W2340178336 @default.
- W2890648049 cites W2464427297 @default.
- W2890648049 cites W2487796470 @default.
- W2890648049 cites W2576231464 @default.
- W2890648049 cites W2596004680 @default.
- W2890648049 cites W2619175936 @default.
- W2890648049 cites W2798379006 @default.
- W2890648049 cites W296150345 @default.
- W2890648049 cites W3038282287 @default.
- W2890648049 cites W31278 @default.
- W2890648049 cites W567765689 @default.
- W2890648049 cites W589218252 @default.
- W2890648049 cites W630319947 @default.
- W2890648049 cites W83201085 @default.
- W2890648049 cites W914192099 @default.
- W2890648049 cites W146849614 @default.
- W2890648049 cites W2055623556 @default.
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