Abstract
The study of strain localized waves of permanent form (solitary waves) is of theoretical and experimental interest because these waves may propagate and transfer energy over long distances along homogeneous free lateral surface elastic wave-guides. However, geometrical inhomogeneities of the waveguide, influence of an external medium or microstructure of the wave-guide material may result in an amplification of the strain wave causing the appearance of plasticity zones or micro cracks and eventually the breakdown of a wave-guide. This is of importance for an assessment of durability of elastic materials and structures, methods of nondestructive testing. Among the elastic wave-guides the cylindrical elastic rod is chosen since this real-life wave-guide admits an analytical description in a closed form. The theory is developed to account for longitudinal nonlinear strain waves in a rod with varying cross-sections, in a rod surrounded by a dissipative (active) external medium and in an elastic medium with microstructure. The governing equations obtained turn out nonintegrable, however, some exact traveling wave solutions are found. The asymptotic analysis reveals a possibility of a solitary wave selection when the initial KdV-like solitary wave transforms into the dissipative solitary wave with the amplitude and the velocity prescribed by the equation coefficients. Moreover, it was found that dissipation may be in balance with nonlinearity rather than with dispersion. As a result the kink-shaped strain wave propagates. Numerical simulations on the evolution of an initial arbitrary localized pulse confirm the predictions about solitary-wave selection done on the basis of the asymptotic solution. The asymptotic description of the amplification of the solitary wave in a narrowing rod is proven also in experiments.
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Porubov, A.V. (2002). Dissipative Nonlinear Strain Waves in Solids. In: Christov, C.I., Guran, A. (eds) Selected Topics in Nonlinear Wave Mechanics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0095-6_7
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DOI: https://doi.org/10.1007/978-1-4612-0095-6_7
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