Radial Vibrations of a Thick-Walled Spherical Reservoir Forced by an Internal Surge-Pressure in a Compressible Elastic Medium

The authors investigated radial vibrations of a metal thick-walled spherical reservoir forced by an internal surge-pressure. The reservoir is located in a compressible elastic medium. In this paper, the medium’s compressibility is represented by the Poisson’s ratio ν. Analytical closed-form formulae determining the dynamic state of mechanical parameters in the reservoir wall have been derived. These formulae were obtained for the surge pressure p(t) = p₀ = const. From analysis of these formulae it follows that the Poisson’s ratio ν, substantially influences variations of the parameters of reservoir wall in space and time. All parameters intensively decrease in space along with an increase of the Lagrangian coordinate r. On the contrary, these parameters oscillate versus time around their static values. These oscillations decay in the course of time. We can mark out two ranges of parameter ν values in which vibrations of the parameters are “damped” (there is no energy loss due to internal friction, energy is transferred from reservoir to further layers of the medium) at a different rate. Thus, Poisson’s ratio in the range below about 0.4 causes intensive decay of parameter oscillations and reduces reservoir dynamics to static state in no time. On the other hand, in the range 0.4 < ν < 0.5, the “damping” of parameter vibrations of the reservoir wall is very low. In the limiting case when ν = 0.5 (incompressible medium) “damping” vanishes and the parameters harmonically oscillate around their static values. In the range 0.4 < ν < 0.5, insignificant increase of Poisson’s ratio causes a considerable increase of the parameter vibration amplitude and decrease of vibration “damping”.