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- W2081935903 abstract "Abstract This series of papers is concerned with the three asymptotic limits of Fu and Devenish, Q. J. Mech. Appl. Math. , 1995, 49 , 65–80. When an incompressible elastic half-space is subjected to an all-round pressure, the Rayleigh waves become standing waves when p =±2 and degenerate into body waves when p =−1 , where p is the pressure scaled by the shear modulus. Part I of this series is concerned with the limit if p →2. The time scale over which surface waves in a neighbourhood of this limit evolve is O(ϵ 1 2 ) and is valid for p over the range p −2=O(ϵ) , where ϵ is a small parameter characterising the wave amplitude. The virtual work method of Fu and Devenish is used to derive the evolution equations which are then solved numerically subject to the condition that initially only the fundamental mode has non-zero amplitude whilst all the modes have zero initial velocity. Three qualitatively different cases are examined: the neutral case corresponding to p =2 , the subcritically near-neutral case corresponding to p and the supercritically near-neutral case corresponding to p >2 . For these three cases, linear theory predicts zero growth, linear growth and exponential growth, respectively. It is found that the main effect of nonlinearity is to generate higher harmonics from the fundamental mode whilst the back action of these harmonics on the fundamental mode can be neglected. Generation of higher harmonics always leads to the formation of shocks. Variation of p affects the shock formation time and the final amplitude of the wave at the time of shock formation. The shock formation time is found to be a monotonically decreasing function of p in a small neighbourhood of p =2 ." @default.
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- W2081935903 date "1997-12-01" @default.
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- W2081935903 title "The nonlinear evolution of near-neutral and near-body wave modes in a pre-stressed incompressible elastic half-space. Part II: Lower branch near-neutral modes" @default.
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- W2081935903 doi "https://doi.org/10.1016/s0020-7225(97)00018-9" @default.
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