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Radial vibrations of a thick-walled spherical reservoir forced by an internal surge-pressure in a compressible elastic medium

Włodarczyk E., Fikus B.

Engineering Transactions

2015

Vol. 63, iss. 3

251--272

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 closedform 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”.

Radialne drgania grubościennego kulistego zbiornika w ośrodku liniowo-sprężystym obciążonego wewnętrznym ciśnieniem produktów wybuchu. Cz. 1, Rozważania teoretyczne

Włodarczyk E., Fikus B.

Biuletyn Wojskowej Akademii Technicznej

2013

Vol. 62, nr 3

157-170

Rozwiązano analitycznie problem drgań grubościennego zbiornika kulistego umieszczonego w ośrodku liniowo-sprężystym, wymuszonych wewnętrznym ciśnieniem produktów wybuchu. Określono wpływ dywergentnego transportu energii przez ekspandującą falę naprężeń od zbiornika do otaczającego ośrodka. Redukując grubość ścianki zbiornika do zera (β = 1), uzyskano jako przypadek szczególny rozwiązanie problemu ekspansji kulistej fali naprężeń w ośrodku sprężystym. Prezentowane rozwiązanie ma walory poznawcze i aplikacyjne. Między innymi pozwala oszacować tłumienie amplitudy drgań zbiornika, wywołanych na przykład awaryjnym wybuchem, przez otaczający go ściśliwy ośrodek.

The problem of radial vibrations of a thick-walled spherical reservoir, loaded with internal pressure of explosion products has been solved here in analytical, closed form. The reservoir is insertem inside an isotropic linear elastic medium. The influence of divergent transport of the energy by expanding stress wave from the reservoir to the surrounding medium is considered. The solution of the problem of the expanding spherical stress wave in linear elastic medium has been obtained here, as a particular case, by reducing the thickness of the reservoir wall to zero value (β = 1). The presented solution Has cognitive and applicable values. For example, it makes possible evaluation of damping of a vibration amplitude of the reservoir wall by surrounding medium during damage explosion.