Semi-analytical technique for isolating the pseudo-Rayleigh component of the field induced by a transiently responding submerged cylindrical shell

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Abstract

A semi-analytical technique is proposed for isolating the pseudo-Rayleigh (A0) component of the field radiated into the surrounding fluid by a submerged elastic cylindrical shell. The technique is based on the simultaneous use of two fluid–shell interaction models, one based on the Reissner–Mindlin shell theory, and the other on the Kirchhoff–Love shell theory, and is aimed at offering the possibility of analyzing the pseudo-Rayleigh component in its pure form, an approach that has certain rather important advantages over analyzing the component as a part of the overall radiated hydrodynamic pattern. The technique is applied to the analysis of the radiation by two elastic shells with parameters that are common in industry, and the high computational efficiency of the technique is demonstrated.

Introduction

Several distinct wave components of the radiated hydrodynamic field are known to exist when a submerged elastic shell is responding to a transient loading, namely the symmetric Lamb waves S0, the anti-symmetric Lamb, or pseudo-Rayleigh, waves A0, and the Scholte–Stoneley waves A, along with, of course, the scattered and incident waves (e.g. Ahyi et al., 1998, Derbesse et al., 2000, Sessarego et al., 1997, Iakovlev et al., 2013, Iakovlev et al., 2014 and references therein).

These individual components have been analyzed in considerable detail, usually as an integral part of the overall radiated field. Occasionally, however, one or more components were isolated and analyzed in their ‘pure’ form, as, for example, was done in Sessarego et al. (1997) for the S0 and A waves where such isolating allowed for obtaining pure resonance spectrums of the respective waves uncluttered by the other radiated components. The possibility of producing such resonance spectrums alone would be a more than sufficient justification of the need for reliable and efficient procedures allowing the radiated component isolation, but their use is by no means limited to producing resonance curves, and offers a range of other potential applications. At the same time, we are not aware of any purely theoretical technique that allows for such an isolation.

In the present study, we propose a methodology that allows for a numerical isolation of the pseudo-Rayleigh (A0) radiated component. The main idea of the methodology is based on our earlier work on cylindrical shells, in particular on the studies of the radiated fields produced by different shell models (Iakovlev, 2008a, Iakovlev, 2008b, Iakovlev et al., 2013, Iakovlev et al., 2014).

Namely, it was observed that various shell models produce results of rather widely varying accuracy. The simulations based on the Reissner–Mindlin shell model (Iakovlev et al., 2013, Iakovlev et al., 2014) were found to be most accurate, and were seen to adequately reproduce the S0 waves, the A0 waves, and the A waves. At the same time, the simulations based on the Kirchhoff–Love model with the bending stiffness taken into account (Iakovlev, 2008a, Iakovlev, 2008b, Iakovlev et al., 2013) produced a wave that was neither the S0 nor the A0 wave and that had certain characteristics of both of them; therefore, it was the least useful of the models considered. Finally, the simulations based on the Kirchhoff–Love model with bending stiffness neglected (Iakovlev, 2008a, Iakovlev, 2008b, Iakovlev et al., 2013) produced very accurate results for the S0 wave, but the A0 wave was not reproduced at all, thus the model was quite useful but only in those cases where the S0 wave alone was of interest.

In one of our recent projects, it became important to be able to isolate the A0 wave, and, in the light of the above findings, an idea was born to simultaneously use the numerical simulations based on both the Reissner–Mindlin and the Kirchhoff–Love no-bending models, subsequently subtracting the pressure produced by the latter from that produced by the former with the goal of obtaining the A0 wave in its ‘pure’ state. The idea has been implemented and was shown to work very well, and it is detailed in the remaining sections of the present study.

Section snippets

Mathematical model

The models that we are employing here have been introduced, discussed in much detail, and successfully validated in our earlier work (Iakovlev, 2008a, Iakovlev, 2008b, Iakovlev et al., 2013, Iakovlev et al., 2014), thus we include in the present study only a brief summary of the main features of the respective solutions.

To that end, we are considering an elastic circular cylindrical shell of radius r0 and thickness h0 submerged into an irrotational, inviscid, and linearly compressible fluid of

General considerations

We consider a steel shell of radius r0=1m and thickness h0=0.06 m, cs=5790 m/s, ρs=7900kg/m3, and ν=0.30, submerged into water, ρf=1000kg/m3 and cf=1470 m/s. The shell is subjected to a point-generated pressure pulse located at the distance of five radii of the shell from the shell axis, R0=5m, with the peak pressure in the front of 25 kPa and the exponential decay rate of 0.1314 ms.

For the sake of completeness, we first revisit the results that we have already reported in our earlier work (

Conclusions

Using two semi-analytical models of fluid–shell interactions (one based on the Reissner–Mindlin shell model and the other on the Kirchhoff–Love model), we introduced a purely theoretical technique that allows one to isolate the pseudo-Rayleigh, or A0, component of the shell-radiated field. We then applied the technique to two typical thin shells and produced the respective A0 time-histories at a point inside the fluid domain.

The proposed technique seems to be quite an attractive tool for the

Acknowledgments

The authors acknowledge the financial support of the Natural Sciences and Engineering Research Council (NSERC) of Canada. S. Iakovlev also acknowledges the financial support of the Killam Trusts at Dalhousie University.

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