Fluid-filled Shell Research Articles

A comparison of different nonlinear shell theories for rotating fluid‐filled structures

AbstractRotating fluid‐filled shell structures can be used for different applications in technique. Because of spin‐softening as well as stress‐stiffening it is essential to consider geometrical non‐linearities. Additionally, shear deformation is getting important in case of thick shells. At this point different theories from KIRCHHOFF‐LOVE (no shear deformation) and MINDLIN‐REISSNER (first order shear deformation) are compared with each other.For both theories the nonlinear kinematics are shown and therewith the HAMILTON's principle is evaluated to receive the equations of motion. The solution of the corresponding eigenvalue problem is done with a global RITZ approach on the one hand, on the other hand with local FE‐discretization. Different results of rotating and non‐rotating cylindrical shells with respect to their eigenfrequencies are presented and compared. Furthermore, experimental data is used for validation.

Investigation of a noninvasive method for monitoring intracranial pressure using sheep skulls

It has been previously demonstrated that resonance frequencies of fluid-filled shells of simple geometry are shifted in proportion to fluid pressure [J.Acoust. Soc. Am. 131, EL506 (2012)]. We investigate the applicability of this approach for measuring changes of intracranial pressure in ovine skulls. A catheter inserted through the foramen magnum of a complete sheep’s head enables the control of hydrostatic pressure, which is measured independently using a pressure transducer inserted into the parenchyma through a drilled hole in the skull. The vibrational response is measured using a small modal impact hammer to gently tap the skull with small accelerometers mounted at different locations on skull. Acceleration normalized by impact force is computed in the frequency domain, averaged over multiple taps. Significant peaks in the response spectrum are identified and associated with vibrational modes observed using a laser Doppler vibrometer. The consistency with which peaks shift in frequency in proportion to ICP is reported. The effect of tap location and accelerometer placement is also explored.

Effects of Internal Fluid on the Dynamic Behaviors of Double Cylindrical Shells Subjected to Underwater Explosion

Abstract Fluid-filled double cylindrical shells were widely used in the marine engineering field and their blast resistance was considerably concerned. In this paper, the dynamic behaviors of fluid-filled double cylindrical shells subjected to underwater explosion were studied through a combination of experimental and numerical methods. First, a series of comparative underwater explosion tests were carried out on the scaled empty and fluid-filled double cylindrical shells. Then, more detailed numerical simulations were developed to give more results, and the model was verified by comparing with the data gathered from tests. Based on the experimental and numerical results, the effects of internal fluid on the shock wave propagation process, deformation modes, dynamic response, and energy characteristics of structures were analyzed. It is shown that the internal fluid is helpful to resist the structural deformation of outer shell and significantly decreased the axial strains of inner shell. Meanwhile, the dynamic response of the inner shell of fluid-filled shells was more violent. Besides, the internal and kinetic energy of outer shell decreased markedly. Above results would provide a reference for the protection of fluid-filled structures.

Free vibration of partially fluid-filled or fluid-surrounded composite shells using the dynamic stiffness method

In this paper, the dynamic stiffness method (DSM) is developed for the vibration analysis of laminated cylindrical and conical shells, which are partially filled or surrounded by quiescent fluid. The Reissner and Naghdi’s thin shell theory and incompressible fluid equations are employed on the structures and fluid, respectively, so as to characterize the fluid–structure coupling model. Shell elements with/without fluid loadings are derived and assembled by using the dynamic stiffness method. Numerical examples of the free vibration analysis for both empty and fluid-filled shells are validated against previous studies. Remarkable advantages regarding computational efficiency and accuracy of the DSM, especially in high-frequency domain, are presented through response curves compared with finite element calculations. As for partially fluid-filled or fluid-surrounded laminated shells, parametric studies are made to find the effects of material properties, fluid heights and semi-vertex angles on the dynamic characteristics.

Comprehensive vibrational dynamics of half-open fluid-filled shells.

Fluid-filled shells are near-ubiquitous in natural and engineered structures-a familiar example is that of glass harps comprising partially filled wineglasses or glass bowls, whose acoustic properties are readily noticeable. Existing theories modelling the mechanical properties of such systems under vibrational load either vastly simplify shell geometry and oscillatory modal shapes to admit analytical solutions or rely on finite-element black-box computations for general cases, the former yielding poor accuracy and the latter offering limited tractability and physical insight. In the present study, we derive a theoretical framework encompassing elastic shell deformation with structural and viscous dissipation, accommodating arbitrary axisymmetric shell geometries and fluid levels; reductions to closed-form solutions under specific assumptions are shown to be possible. The theory is extensively verified against a range of geometries, fluid levels and fluid viscosities in experiments; an extension of the model encompassing additional solid objects within the fluid-filled shell is also considered and verified. The presented theoretical advance in describing vibrational response is relevant in performance evaluation for engineered structures and quality validation in manufacturing.

Characteristics of wave propagation, vibration transmission and acoustic emission in fluid-filled coaxial periodic shells

The wave propagation, vibration transmission and acoustic emission characteristics in the two coaxial shells containing fluid are studied. A finite element method (FEM) is utilized to conduct the investigation. Elastic band gaps (BGs) are generated in this coaxial shell system with either light or heavy fluid loading if the cylindrical shell walls are design to be periodic structure. For light fluid loading, BGs of the fluid-filled coaxial shell system are almost the same as those for the inner and outer shells in vacuum. Because the coupling effect of the annular light fluid is so weak that it can be neglected; thus, the inner and outer shell may behave independently. In terms of heavy fluid loading, the confined annular fluid region acts as an effective energy transmission medium that links the two shell motion together. The “hydrodynamic” mass induced by the annular-fluid can be far larger than its actual mass when the annular gap is sufficient narrow. As a result, the fluid inertial loading on the other shell can be quite enormous, rendering the central frequencies of BGs for the coaxial periodic shell system notably decreased. The BG formation mechanism may be attributed to (i) phenomenon of interference of waves reflected by these repeated “periodicity cells”, (ii) cut-off frequencies and (iii) hybrid vibration motion modes of different shell sections, according to various circumferential modes and frequency ranges. The acoustic pressure in the narrow annular region is extremely high, if the filling fluid is dense. However, when the harmonic frequency is located at the BG, the acoustic pressure becomes weaker and weaker along the axial direction of the shell; in contrast, if frequency is in the wave pass bands, the acoustic pressure levels will remain as strong as at the front end of the shell throughout the shell.

Method of discrete singularities in problems of filler vibrations in fuel tanks under overloads and at low gravity

The paper is about free vibration problems in fuel tanks with different levels of fillers both under overloads and low gravity. The fuel tanks are considered as rigid shells of revolution. The liquid, contained in the tanks, is supposed to be an ideal and incompressible one, and its flow, induced by external excitations, is irrotational. The problem of free axisymmetric harmonic oscillations of the fluid-filled rigid compound shell is considered. The mixed boundary value problem is formulated, and boundary conditions are received on the boundaries of the fluid domain. The non-penetration conditions is formulated on the rigid shell boundaries, and on the free liquid surface there are kinematic and dynamic boundary conditions. The flow fluctuations are described by using the velocity potential that for ideal and incompressible liquids satisfies the Laplace equation. For its solution, the integral representation is in use. But there are two unknown functions, the velocity potential and the function describing the shape and position of the free surface during time. The transformation of the boundary conditions leads to eliminating one of these unknown functions. So, the system of boundary singular integral equations is obtained to determine the velocity potential. The discrete singularity method and the boundary element method are applied for its numerical solution. The problem of determining own modes and frequencies is solved by using the techniques, where the surface tension effects are neglected. Then these modes are considered as basic functions to determine the modes and frequencies of the liquid taking into account the surface tension. Thus, in this work the method is developed which takes into account the surface tension effect on the frequency of fluid fluctuations in the rigid tank under low gravity conditions. The surface of the interaction between liquid media and gas is considered as a thin membrane, whose thickness is neglected. The fluid pressure on this surface is determined by the Laplace-Young equation. The developed method is useful for the investigation of free and forced fluid oscillations in rigid compound shells with arbitrary meridians.

Numerical simulation of the high-speed collision of the ball and the spherical fluid-filled shell

Effectiveness of a honeycomb shield assembled of gas-filled containments is discussed. A numerical tool is developed aimed at investigating hypervelocity impact of a spherical projectile on thin-walled metallic containment filled in with gas or fluid. Variation of gas density inside the containment essentially affects perforation scenario and successive fragmentation of the projectile, while variation of gas properties – adiabatic index – does not affect fragmentation, but has a strong influence on shock wave generated by fragments in the containment.

Development of a child head analytical dynamic model considering cranial nonuniform thickness and curvature – Applying to children aged 0–1 years old

Background and objectiveAlthough analytical models have been used to quickly predict head response under impact condition, the existing models generally took the head as regular shell with uniform thickness which cannot account for the actual head geometry with varied cranial thickness and curvature at different locations. The objective of this study is to develop and validate an analytical model incorporating actual cranial thickness and curvature for child aged 0–1YO and investigate their effects on child head dynamic responses at different head locations. MethodsTo develop the new analytical model, the child head was simplified into an irregular fluid-filled shell with non-uniform thickness and the cranial thickness and curvature at different locations were automatically obtained from CT scans using a procedure developed in this study. The implicit equation of maximum impact force was derived as a function of elastic modulus, thickness and radius of curvature of cranium. ResultsThe proposed analytical model are compared with cadaver test data of children aged 0–1 years old and it is shown to be accurate in predicting head injury metrics. According to this model, obvious difference in injury metrics were observed among subjects with the same age, but different cranial thickness and curvature; and the injury metrics at forehead location are significant higher than those at other locations due to large thickness it owns. ConclusionsThe proposed model shows good biofidelity and can be used in quickly predicting the dynamics response at any location of head for child younger than 1 YO.

Bi-orthogonality relations for fluid-filled elastic cylindrical shells: Theory, generalisations and application to construct tailored Green's matrices

The paper addresses the classical problem of time-harmonic forced vibrations of a fluid-filled cylindrical shell considered as a multi-modal waveguide carrying infinitely many waves. The forced vibration problem is solved using tailored Green's matrices formulated in terms of eigenfunction expansions. The formulation of Green's matrix is based on special (bi-)orthogonality relations between the eigenfunctions, which are derived here for the fluid-filled shell. Further, the relations are generalised to any multi-modal symmetric waveguide. Using the orthogonality relations the transcendental equation system is converted into algebraic modal equations that can be solved analytically. Upon formulation of Green's matrices the solution space is studied in terms of completeness and convergence (uniformity and rate). Special features and findings exposed only through this modal decomposition method are elaborated and the physical interpretation of the bi-orthogonality relation is discussed in relation to the total energy flow which leads to derivation of simplified equations for the energy flow components.

A numerical method for double-plated structure completely filled with liquid subjected to underwater explosion

The double-plated structure is extensively applied to the surface ships and submarines. Between the two plates there always exists liquid such as water or oil. When it is exposed to the attack by underwater weapon, the shock wave firstly hits the outer plates, and then it is transmitted into the internal liquid, subsequently to the inner plates. The mechanism in this process is so complex that has been a troublesome problem for a long time. In this paper, a numerical method is developed to solve this problem. The second-order doubly asymptotic approximations (DAA) is used to analyze the external fluid-structure interaction (FSI) effect for the outer fluid field with the outer plates, and cavitating acoustic finite element (CAFE) is used to model the internal FSI effect. Results obtained by this approach show good agreement with results of the excitation problem of 3D fluid-filled shell by a plane step wave. Last, two experiments are implemented to validate the method. From the comparative results, it shows that the simulation results coincide well with tests.

Vibro-acoustics of infinite and finite elastic fluid-filled cylindrical shells

The classical model of an elastic fluid-filled cylindrical shell is used for analysis of its vibrations. The model is based on thin shell theory, standard linear acoustics and the heavy fluid-loading coupling concept. First, several important features of performance of a fluid-filled shell not yet fully explored in literature e.g. the difference between kinematic/forcing excitations, acoustic source type identification (monopole/dipole) and energy transfer between fluid and shell are studied. Then the discussion is extended to finite fluid-filled shells by application of the Boundary Integral Equations Method (BIEM). Two techniques for solving the equations deduced from the BIEM are discussed and investigated with respect to convergence, respectively, Boundary Elements (BE) and modal expansion. Successively, the implementation of the BIEM is validated against numerical and experimental results for the simplified case of an empty shell. Finally, impedance boundary conditions for a fluid-filled shell in an assembled piping system and computations of its resonances and forced response using the BIEM are discussed.

Designing Synthetic Microcapsules That Undergo Biomimetic Communication and Autonomous Motion.

Inspired by the collective behavior of slime molds and amoebas, we designed synthetic cell-like objects that move and self-organize in response to self-generated chemical gradients, thereby exhibiting autochemotaxis. Using computational modeling, we specifically focused on microcapsules that encompass a permeable shell and are localized on an adhesive surface in solution. Lacking any internal machinery, these spherical, fluid-filled shells might resemble the earliest protocells. Our microcapsules do, however, encase particles that can diffuse through the outer shell and into the surrounding fluid. The released particles play two important, physically realizable roles: (1) they affect the permeability of neighboring capsules and (2) they generate adhesion gradients on the underlying surface. Due to feedback mechanisms provided by the released particles, the self-generated adhesion gradients, and hydrodynamic interactions, the capsules undergo collective, self-sustained motion and even exhibit antlike tracking behavior. With the introduction of a chemically patterned stripe on the surface, a triad of capsules can be driven to pick up four-capsule cargo, transport this cargo, and drop off this payload at a designated site. We also modeled a system where the released particles give rise to a particular cycle of negative feedback loops (mimicking the "repressilator" network), which regulates the production of chemicals within the capsules and hence their release into the solution. By altering the system parameters, three capsules could be controllably driven to self-organize into a stable, close-packed triad that would either translate as a group or remain stationary. Moreover, the stationary triads could be made to switch off after assembly and thus produce minimal quantities of chemicals. Taken together, our models allow us to design a rich variety of self-propelled structures that achieve complex, cooperative behavior through fundamental physicochemical phenomena. The studies can also shed light on factors that enable individual protocells to communicate and self-assemble into larger communities.

On the possibility of shock-induced cavitation in submerged cylindrical shell systems

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.

Numerical Simulation and Experimental Study on Fluid-Filled Hemispherical Shell under Impact

The dynamic response of fluid-filled hemispherical shell in mass impact is studied by experiment using DHR9401. Combining the time history of impact force with experimental observation of the deformation process, it can be seen that the dynamic response can be divided into four stages: the flattening around the impact point, the forming and expanding outward of shell plastic hinge, the plastic edge region flatten by the punch, and elastic recovery. The experimental results show that: Because the shell filled with liquid, the local impact load that the shell suffered is translated into area load and loads on the inner shell uniformly, so that it has a high carrying capacity. Numerical simulation is used to study the time history of energy absorption of different shell structures. The result shows that the crashworthiness of sandwich fluid-filled shell is improved greatly. Under the certain impact energy, deformation of its inner shell is very small, which can provide effective security space.

Wave propagation in a fluid-filled shell excited by a dipole source

Wave propagation in a fluid filled cylindrical shell excited by a dipole source is investigated for the design of a new kind of calibration pit for dipole acoustic logging tools. Based on classical elasticity wave equations, phase and group velocity dispersion curves of each mode, excitation spectra and mode contributions to wave field in the shell are presented. The dispersion curves show that the lowest mode exists in the entire frequency range with the phase velocity smaller than shear wave velocity of the shell, higher-order modes have cutoff frequencies, below the cutoff frequencies these modes are non-propagating. Analysis on mode excitation spectra and their contributions suggest that the lowest mode has potential to be used in calibrating the velocity measurement accuracy of dipole acoustic logging tools quantitatively, provided that the contributions of this mode to the wave field dominating the first arrivals gathered by a specific dipole acoustic logging tool. [Work supported by National Natural Sciences of China, Grant No. 11134011.]

Development of a computational model to predict cranial resonance shifts due to changes in intracranial pressure

A possible method for noninvasively monitoring changes in intracranial pressure is to measure changes in skull resonance frequencies. Recent measurements of the vibrational response of a spherical aluminum shell clearly demonstrate that resonance frequencies shift higher as the internal pressure is increased [Piacsek et al, J. Acous. Soc. Am, 131, EL506-510 (2012)]. The frequency shift is approximately linear with the applied pressure, regardless of whether the shell is filled with air or water, and circumferential modes exhibit larger resonance shift than longitudinal modes. A computational model of a fluid-filled thin shell subject to acoustic stimulation was developed using the COMSOL multi-physics software to investigate the role of shell material and geometry in resonance shifts. The model predicts frequency shifts comparable to those observed in the spherical aluminum shell. Preliminary computational results for a spherical shell made of bone-like material, as well as for asymmetric and nonuniform shells, will be presented.

Asymptotic expansions for the coupled wavenumbers in an infinite orthotropic flexible fluid-filled cylindrical shell

Analytical expressions are found for the coupled wavenumbers in flexible, fluid-filled, circular cylindrical orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders. The Donnell-Mushtari shell theory is used to model the shell and the effect of the fluid is introduced through the fluid-loading parameter μ. The orthotropic problem is posed as a perturbation on the corresponding isotropic problem by defining a suitable orthotropy parameter ε, which is a measure of the degree of orthotropy. For the first study, an isotropic shell is considered (by setting ε=0) and expansions are found for the coupled wavenumbers using a regular perturbation approach. In the second study, asymptotic expansions are found for the coupled wavenumbers in the limit of small orthotropy (ε≪1). For each study, isotropy and orthotropy, expansions are found for small and large values of the fluid-loading parameter μ. All the asymptotic solutions are compared with numerical solutions to the coupled dispersion relation and the match is seen to be good. The differences between the isotropic and orthotropic solutions are discussed. The main contribution of this work lies in extending the existing literature beyond in vacuo studies to the case of fluid-filled shells (isotropic and orthotropic).

Coupled Wavenumbers in an Infinite Flexible Fluid-Filled Circular Cylindrical Shell : Comparison between Different Shell Theories

Analytical expressions are found for the wavenumbers in an infinite flexible in vacuo I fluid-filled circular cylindrical shell based on different shell-theories using asymptotic methods. Donnell-Mushtari theory (the simplest shell theory) and four higher order theories, namely Love-Timoshenko, Goldenveizer-Novozhilov, Flugge and Kennard-simplified are considered. Initially, in vacuo and fluid-coupled wavenumber expressions are presented using the Donnell-Mushtari theory. Subsequently, the wavenumbers using the higher order theories are presented as perturbations on the Donnell-Mushtari wavenumbers. Similarly, expressions for the resonance frequencies in a finite shell are also presented, using each shell theory. The basic differences between the theories being what they are, the analytical expressions obtained from the five theories allow one to see how these differences propagate into the asymptotic expansions. Also, they help to quantify the difference between the theories for a wide range of parameter values such as the frequency range, circumferential order, thickness ratio of the shell, etc.

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric spherical shell and the associated radiation of sound

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric sphere, with radial polarization, submerged in a compressible viscous fluid medium are investigated. The oscillations are harmonically driven by an axisymmetrically applied electric potential difference across the surface of the shell. A theoretical formulation cast the piezoelectric shell problem into a corresponding problem of an elastic shell with the contribution of piezoelectricity confined to slightly modified in vacuum natural frequencies and their associated mode shapes. It is noted that the fluid inside the shell will have a dominating influence on the vibrational characteristics of the submerged shell. The circular components of the natural frequency spectra closely follow those of the fluid-filled shell in vacuo. Furthermore, the corresponding damping components of those natural frequencies are rather small, making acoustic radiation and under-damped oscillation possible for an infinite number of natural frequencies. The characteristics of natural frequencies are elucidated using a fluid-filled polyvinglindene fluoride (PVDF) shell submerged in both air and water as an example. It is found that the piezoelectric parameters that contribute to the shell's natural frequencies is of a small order for thin PVDF shells, and is thereby negligible. It is noted that, with the mechanical constant typically associated with piezoelectric materials, fluid viscosity could have a significant effect on some vibrations. In certain cases, a natural frequency associated with a minimum viscous damping and a maximum of total damping (indicating highly efficient acoustic radiation) is possible with such a frequency. The vibrational characteristics, fluid loading, and energy flow are evaluated for a fluid-filled PVDF shell submerged in air and water. The inclusion of fluid inside the shell is shown to produce various narrow band peaks responses, vibrational absorbing frequencies, and non-dissipating frequencies. Those vibrational characteristics could have many potential applications. For example, the interior fluid could offer the option of generating a desired narrow band near resonant sound radiation while keeping power dissipation due to fluid viscosity to a minimum. Those well-defined narrow band characteristics also open up possibilities of using a vibrating, fluid-filled shell as a micro scale sensor for sensing and detection applications.