Abstract
In this paper, wave propagation in a deformed elastic material is investigated theoretically. The material is assumed to be one-dimensional and inhomogeneous and to have a nonlinear stress–strain relation. The amplitude is assumed to be small with respect to the wavelength, and the wavelength is assumed to be small with respect to distances over which wave quantities, the predeformed state, and the inhomogeneity are subject to considerable change. Order of magnitude estimations are made via the equation of motion. By equating first-order terms, the propagation velocity is determined. Likewise, by equating second-order terms, a differential equation which governs the variation of amplitude is obtained. The waveform becomes flatter or steeper according to the material, the predeformed state and the waveform.
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