The interaction between a submerged evacuated cylindrical shell and an external shock wave is considered in the presence of a rigid wall. A semi-analytical model of the system is developed using the classical apparatus of mathematical physics. The detailed analysis of the interaction is carried out with the focus on the stress state, and it is demonstrated that the highest stress in the shell dramatically depends on the distance between the wall and source of the shock wave. In particular, it is shown that for certain locations of the wall, the peak structural stress is considerably higher than that observed for the stand-alone structure, with the difference reaching as much as 50% in some cases. It is also demonstrated that the magnitude of this difference dramatically depends on the distance between the source of the shock wave and the shell. The most and least dangerous locations of the wall are identified. A comparison between the present full model and the simplified one that was developed in our earlier work is carried out, and the possibility of using the latter as a reliable substitute for the former is discussed.

A two-dimensional problem of elastic wave propagation in a rectangular solid is considered. It is first approached using the classical apparatus of mathematical physics, with a fully analytical model produced as the result. The same system is then analysed numerically using two commercial finite element software packages, COMSOL and ANSYS APDL, with the focus on the bulk and guided wave propagation. The results produced by the numerical models are compared with those produced by the analytical one, and the superiority of the latter in terms of the computational costs is established, while a good overall quantitative agreement is observed. The proposed analytical model is therefore shown to be a very attractive choice as a benchmark for validation of fully-numerical models. A procedure for the inverse use of the model is established and tested as well.

This chapter outlines the semi-analytical methodology that was developed over the past decade and a half to model transient fluid-structure interaction phenomena for thin-walled structures submerged in and/or filled with fluid. The theoretical framework of the methodology based on the use of the classical apparatus of mathematical physics is exposed first. Then, a demonstration of some of the capabilities of the methodology is presented as it is applied to an industrially relevant fluid-structure interaction problem. Specifically, the response of a submerged cylindrical shell to a double-front shock wave is considered, with the emphasis on the existence of certain resonance-like phenomena which result in a considerable increase of the maximum stress induced in the structure by such a loading. The outcomes of the modeling using both the 2D and 3D versions of the methodology are presented, and the differences between the results produced by these two approaches, a lower-fidelity one and a higher-fidelity one, are highlighted.

Three-dimensional structural dynamics of a circular cylindrical shell submerged in fluid and subjected to two consecutive spherical shock waves is addressed using a semi-analytical model based on the classical apparatus of mathematical physics. It is established that for certain values of the delay between the first and second incident wavefronts, the highest stress observed in the system significantly (by up to 50%) exceeds the peak stress observed for the single-front loading of the same intensity. Although this result is quantitatively the same as the one reported for the simplified two-dimensional model of the system, it is demonstrated that there exist very substantial differences between the evolution of the peak stress predicted by the two models when the three-dimensionality of the incident shock waves is pronounced. It is thus established that the presented three-dimensional model is a far more reliable pre-design analysis tool for such loadings than its two-dimensional counterpart.

The field radiated by a transiently responding submerged cylindrical shell is addressed, with the focus on the pseudo-Rayleigh wave A0. The main objective of the study is to offer further insights into the experimentally observed issues with the observability of the A0 wave on certain types of thin shells. The presented analysis employs a semi-analytical methodology based on combining the use of classical methods of mathematical physics with a finite-difference approximation for the resulting structural modes. Two shell materials are considered, steel and duraluminum. The radiated hydrodynamic fields are explicitly imaged, and the A0 wave is analyzed. It is demonstrated that for the steel shell, the A0 wave is much more pronounced and has a much lower attenuation than for the same duraluminum shell, a result that is in agreement with the experimental studies. The shell material density is identified as the most likely primary cause of the observed differences in the radiation of the A0 wave.

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.

Analytical approach to modeling the interaction between submerged elastic structures and non- stationary loads has long been recognized as an attractive tool of engineering analysis, especially at the pre- design stage where it has been particularly valued for its high computational efficiency. At the same time, the approach has a number of limitations, the most regrettable one being its inability to handle geometries that are more complex than the basic ones such as a spherical or cylindrical geometry. We present an attempt to overcome this limitation while still preserving the much favored computational efficiency by introducing a hybrid methodology that combines the analytical and finiteelement approaches. We then validate the methodology using available experimental data and show that a good agreement with the experiments is observed.

The shock response of a submerged system consisting of two co-axial cylindrical shells coupled with the fluid filling the inter-shell space is considered. The shock–structure interaction is modeled using a semi-analytical methodology based on the use of the classical apparatus of mathematical physics. Both the fluid and structural dynamics of the interaction is addressed, with special attention paid to the interplay between the two. It is demonstrated that the wave effects due to multiple reflections of the pressure waves travelling in the inter-shell fluid to a large degree determine the structural dynamics of the system, but have a more pronounced effect on the outer shell than on the inner one. It is also established that the effect of changing the thickness of the outer shell on the stress–strain state of the inner shell is incomparably more pronounced than vice versa. The investigation culminates with the results of a parametric study of the overall peak stress in the system, an example of utilizing the approach developed based on the introduced model and aiming at facilitating structural optimization of industrial systems at the pre-design stage in the context of shock resistance.

We introduce a hybrid analytical-numerical approach to modeling the acoustic field radiated by a submerged structure of a cylindrical outer shape but without any limitations on the geometrical and/or physical complexity of the internal composition. The approach relies on the FEM methodology in modeling the structural dynamics but utilizes the analytical response-functions-based ideology for the fluid domain, providing the advantage of being able to handle complex geometries that are outside of the capabilities of the traditional analytical or semi-analytical approaches, but at the same time possessing the computational efficiency that is higher than common FEM fluid-structure interaction codes. The capabilities of the approach are demonstrated on a typical configuration of industrial interest

A submerged fluid-filled cylindrical shell subjected to a sequence of two shock waves originated at the same source is considered. It is demonstrated that, unlike in the case of a submerged evacuated shell, there exists a certain critical range of the values of the delay between the incident wavefronts where both the peak compressive and the peak tensile stress observed in the structure are significantly (60% or more) higher than the respective stresses in the same system subjected to a single-front loading. It is further demonstrated that the highest and the lowest hydrodynamic pressure attained in the system is also dramatically affected for certain values of the delay between the incident wavefronts, with the maximum double-front pressure being more than 30% higher than its single-front counterpart. The practical relevance of the findings is discussed in the context of the pre-design analysis of industrial systems subjected to shock loading.

We consider the acoustic field radiated by a system of two submerged co-axial cylindrical shells with fluid filling the inter-shell space. We propose a semi-analytical solution to the problem, and then use it to simulate the interaction of the system with an external acoustic pulse. We demonstrate that the acoustic field radiated by the two-shell system is to a large degree dominated by the multiple reflections of the waves propagating in the inter-shell volume off the surfaces of the shells, and that the effect of the inner shell is strongly manifested in the structure of the acoustic pattern observed in the outer fluid domain

A circular cylindrical shell loaded by one or two fluids and responding to an external shock wave is analyzed in the context of the possible inception of shock-induced cavitation. Several scenarios of fluid contact are considered including a submerged evacuated shell and a submerged fluid-filled shell for three different combinations of the parameters of the internal and external fluids. A semi-analytical shell-shock interaction model is employed in order to predict the regions of the fluids where cavitation is likely to occur, and the respective cavitation development is hypothesized about. The most interesting and practically important finding is that when fluid is present both inside and outside the shell, there exist conditions when cavitation is expected to occur in both the internal and external fluid, resulting in a particularly complex and violent structural re-loading occurring upon the collapse of the respective cavitation regions. The inception of cavitation in the internal fluid alone and in the external fluid alone is also possible. The findings are summarized in a manner that is suitable for use at the pre-design stage as a guide for preliminary assessment of the possibility of shock-induced cavitation in fluid-interacting industrial systems.

We consider the interaction between a sequence of two shock waves and a cylindrical shell submerged into and filled with fluid. The focus of our study is on determining the effect that such a two-front loading has on the extremities of the stress state and the peak hydrodynamic pressure observed in the system, with the ultimate goal of providing the practitioner with the information that could be used at the pre-design stage in determining the most and least dangerous loading conditions for fluid-contacting industrial structures subjected to shock loading.

A submerged fluid-filled cylindrical shell containing a rigid co-axial core and subjected to an external shock wave is considered, and the fluid dynamics of such interaction is analyzed for the most general scenario of two different fluids. It is demonstrated that the phenomenology of the interaction in this case is fundamentally different from the case when the fluids are identical. In the latter case, all the most important wave propagation, reflection and focusing phenomena in the internal fluid that are observed for the shell without a core are also present when a core is placed inside the fluid, unless the core directly occupies the region of the fluid where the phenomena occur. When the fluids are different, however, it is possible that some phenomena are not observed even when the core does not occupy the respective region of the fluid. Due to the very high pressure that is often associated with the phenomena in question, this observation is of considerable practical significance in that it suggests the possibility of a very significant reduction of the peak pressure in the system by means of placing an additional structure inside the primary shell. The observations made are quantified using a number of pressure time-histories aimed at facilitating the pre-design analysis of shock-subjected fluid-interacting structures.

The radiation by a submerged fluid-filled cylindrical shell in response to a transient external pressure pulse is considered, and a semi-analytical model based on the Reissner–Mindlin shell theory is employed to simulate the interaction numerically. Two types of radiated waves that have been previously seen in experimental images for a submerged evacuated cylindrical shell are observed in both the external and internal fluids, the symmetric Lamb waves S0 and the antisymmetric Lamb (or pseudo-Rayleigh) waves A0. The third type of radiated waves is also observed that has not been explicitly imaged either experimentally or numerically for a submerged evacuated cylindrical shell, and it is demonstrated that these waves are the Scholte–Stoneley waves A. The effect that the complex structure of the radiated field has on the wave phenomena in the internal fluid is analyzed for shells of several different thicknesses, and the results of this analysis are summarized in the form of diagrams suitable for the use at the pre-design stage.

A submerged evacuated circular cylindrical shell subjected to a sequence of two external shock waves generated at the same source is considered. A semi-analytical model combining the classical methods of mathematical physics with the finite-difference methodology is developed and employed to simulate the interaction. Both the hydrodynamic and structural aspects of the problem are considered, and it is demonstrated that varying the delay between the first and second wavefronts has a very significant effect on the stress–strain state of the structure. In particular, it is shown that for certain values of the delay, the constructive superposition of the elastic waves travelling around the shell results in a ‘resonance-like’ increase of the structural stress in certain regions. The respective stress can be so high that it sometimes exceeds the overall maximum stress observed in the same structure but subjected to a single-front shock wave with the same parameters, in some cases by as much as 50%. A detailed parametric analysis of the observed phenomenon is carried out, and an easy-to-use diagram summarizing the finding is proposed to aim the pre-design analysis of engineering structures.

We present a semi-analytical approach, based on the Reissner-Mindlin shell theory, for the numerical analysis of the interaction between elastic circular cylindrical shell structures and external acoustic pulses or weak shock waves. We discuss the advantages and limitations of the approach over alternative methodologies and provide numerical results for the case of a submerged fluid-filled shell.

We consider a submerged fluid-filled cylindrical shell subjected to an external acoustic pulse and analyze the structure of the field radiated by the shell into the fluids, both external and internal. We first propose a computationally efficient semi-analytical model of the interaction based on the Reissner-Mindlin shell theory combining some of the classical methods of mathematical physics with the finite-difference methodology, and then use the model to simulate the interaction. We demonstrate that the model accurately reproduces the wave structure of the radiated fields seen in the experiments for submerged evacuated shells, namely, both the symmetric Lamb waves S0 and the pseudo-Rayleigh waves A0. It is further observed that the internal and external wave patterns associated with the A0 waves exhibit the same alternation of the equiphase lines as the one seen in the experiments for a plate loaded by the fluid on both sides, a result that seems to be particularly relevant in the context of very limited number of experimental images of the radiated field for shells loaded by fluid from both inside and outside. Not less interestingly, we also demonstrate that the Scholte-Stoneley, or A, wave is also reproduced by the model, and we offer some insights into the non-observability of this wave for certain types of cylindrical shells reported in earlier experimental studies.

We introduce a robust and computationally efficient methodology for numerical simulation of shock-structure interaction. The methodology is based on the use of some of the classical methods of mathematical physics, with the subsequent coupling between the fluid dynamics and structural parts using the finite-difference methodology. In order to demonstrate the versatility of the approach, we apply it to two rather different practically important problems of the interaction between shock waves and submerged cylindrical structures, aiming at providing insights that would be useful to engineers at the pre-design stage.We first consider a submerged cylindrical shell subjected to two consecutive shock waves, and analyze the effect of such loading in the context of both hydrodynamic fields and the structural stresses it induces. The most important result of this analysis is the observation, for certain values of the distance between the wavefronts, of a very significant increase of the maximum stress observed in the structure.Then, we consider a submerged cylindrical shell subjected to a single shock wave, but employ a more advanced shell theory than the one traditionally used, namely, the Reissner-Mindlin theory instead of the Kirchhoff-Love one. We demonstrate that such an advancement of the model not only leads to a very significant improvement of the accuracy of the respective simulations, but also allows for modeling relatively thick shells.

Accurate modeling of the structure of the acoustic field radiated by a submerged cylinderical shell responding to an external pulse is presented. A thin evacuated elastic circular cylindrical shell submerged into fluid is considered and it is modeled using the Reissner-Mindlin theory of shells. A steel shell is considered with the thickness of 0.03 m and the radius of 1 m, submerged into water. The fluids and the shell are coupled through the dynamic boundary condition on the interface. The results show that simulations of the stress state of the shell based on RM model take only 13% longer than those based on the KL model. Simulated time-histories of the acoustic pressure were evaluated at several points of the fluid to the available experimental time-histories for similar systems, and a very good match for the the waves is observed.