Note on Weak and Short Waves in One-Dimensional Inhomogeneous Nonlinear Elastic Materials

Abstract

The method of geometrical optics has been applied to the analysis of weak and short waves in one-dimensional deformed elastic materials [Tokuoka, J. Acoust. Soc. Am. 69, 66-69 (1981)]. Since the conditions on the amplitude of the wave required for the order estimation may be violated after a time interval, in general, the obtained result holds only for a small time interval. This note improves the above result, and obtains a partial differential equation of a parabolic type for the displacement which remains valid for a longer time interval. The difference of the distortion of the waveform according to the original and the improved equations is discussed briefly for an example.