Journal of Theoretical
and Applied Mechanics

47, 4, pp. 761-778, Warsaw 2009

Analysis of the parameters of a spherical stress wave expanding in a linear isotropic elastic medium

Edward Włodarczyk, Mariusz Zielenkiewicz
The vast qualitative and quantitative analysis of the characteristics of a spherical stress wave expanding in a linear-elastic medium was made. The wave was generated by pressure $ p_0=\text{const }$ suddenly created in a spherical cavity of initial radius $ r_0$. From the analytical form of the solution to the problem it results that displacement and stresses decrease approximately in inverse proportion to the square and cube of the distance from cavity center. It was found that the cavity surface and successive spherical sections of the compressible medium move in the course of time with damped vibrating motion around their static positions. The remaining characteristics of the wave behave analogously. Material compressibility, represented by Poisson's ratio $ \nu$ in this paper, has the main influence on vibration damping. The increase of the parameter $ \nu$ over 0.4 causes an intense decrease of the damping, and in the limiting case $ \nu=0.5$, i.e. in the incompre ssible material the damping vanishes completely. The incompressible medium vibrates like a conservative mechanical system of one degree of freedom.
Keywords: expanding spherical stress wave; isotropic elastic medium; dynamic load