A fully elastic model for studying submerged circular cylindrical shells subjected to a weak shock wave

Abstract

The transient dynamics of evacuated and fluid-filled circular elastic shells, submerged in an infinite fluid medium and subjected to an external weak shock wave, is considered in this paper. This circular shell/acoustic medium interaction problem has already been tackled with simplified thin shell models, based on the Love-Kirchhoff hypotheses for the structural dynamics. In this case, the resulting radiated pressure field displays some discrepancies related to the A0/S0 waves when compared to the experimental data available in the literature for the evacuated case. These drawbacks are overcome here by the use of an isotropic elastic model for the structural dynamics and an inviscid acoustic flow for the fluid dynamics, in a two-dimensional framework. The approach is based on the methods of Laplace transform in time, Fourier series expansions and separation of variables in space. For the fluid-filled case, the transient thick shell-weak shock wave interaction problem is explored and the radiated acoustic field described.

Non-stationary radiation by a cylindrical shell: Numerical modeling using the Reissner–Mindlin theory

“…The obtained results were in excellent agreement with the experimental data and, like in Voinovich et al (2001), all field components seen in the experiments were accurately reproduced, thus making the work of Leblond et al (2009) the other most accurate numerical study we are aware of. Similarly to Voinovich et al (2001), the success of the elasto-dynamic Nomenclature c f sound speed in the fluid,ĉ f ¼ 1 c s sound speed in the shell material,ĉ s ¼ c s c À1 f E s Young modulus of the shell material,…”

“…Iakovlev, 2006Iakovlev, , 2007Iakovlev, , 2008aIakovlev, , 2009Iakovlev et al, 2010Iakovlev et al, , 2011Leblond et al, 2009).…”

“…The latter is far more attractive for practical implementation, and an approach based on the numerical inversion algorithm proposed by Dubner and Abate (1968) was attempted in our earlier work (Iakovlev, 2006) where its unquestionable inferiority to the finite-difference approach adopted here was demonstrated. A different numerical-inversion-based approached was used in a very similar context by Leblond et al (2009) in order to obtain the displacement harmonics, and it was shown to be far more computationally efficient than the one we used for comparison in Iakovlev (2006). However, the present finite-difference approach has been found to considerably outperform even that methodology: the full run for one set of the system's parameters and 150 harmonics with h¼0.001 takes 23 and 25 s for the Kirchhoff-Love and Reissner-Mindlin models, respectively, on a PC with an AMD Athlon Dual Core 2.41 GHz processor, thus making the methodology developed here a very attractive choice for investigations where extensive parametric studies are intended.…”

“…In an attempt to eliminate the mentioned inconsistencies, a complete elasto-dynamic model was considered by Leblond et al (2009) who treated the shell as an elastic body, but retained the semi-analytical ideology of Iakovlev (2008a,b). The obtained results were in excellent agreement with the experimental data and, like in Voinovich et al (2001), all field components seen in the experiments were accurately reproduced, thus making the work of Leblond et al (2009) the other most accurate numerical study we are aware of.…”