Abstract
For the first time, the features of the evolution of the five kinds of nonlinear elastic waves with the initial profiles differing by the mathematical form—harmonic (cosinusoidal), Gauss, Whittaker, MacDonald, and Friedlander—are compared and commented on. A nonlinearity of elastic deformation is described by the Murnaghan five-constant model. The evolution of these waves is studied theoretically and numerically. The approximate methods of solving are utilized, and the first three approximations are used to compare the evolution. In the comparison, the main emphasis is on the similarities and differences of the studied waves. The main similarity for all the profiles is that they distort the form (evolute) during the motion of the wave due to the nonlinear interaction of the wave with itself. However, distortion occurs for each profile in its way. The comparison results are listed in the 16 positions, where the observed similarities and differences are concretized.
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Rushchitsky, J., Yurchuk, V. (2023). Comparison of Evolution of Five Types of Elastic Waves (Harmonic, Gauss, Whittaker, MacDonald, and Friedlander Initial Profiles). In: Guz, A.N., Altenbach, H., Bogdanov, V., Nazarenko, V.M. (eds) Advances in Mechanics. Advanced Structured Materials, vol 191. Springer, Cham. https://doi.org/10.1007/978-3-031-37313-8_25
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