Fluid-filled Shell Research Articles

Spherical-symmetric steady-state response of fluid-filled laminate piezoelectric spherical shell under external excitation

Spherical-symmetric steady-state response problem of a fluid-filled piezoelectric spherical shell is discussed in the paper. In the absence of body force and free charges, the general solutions of mechanical displacement, stresses, strains, potential and electric displacement are derived from constitutive relations, geometric and motion equations under external excitation (i.e., applied surface traction and potential) in spherical coordinate system. As an application of the general solutions, the problem of a fluid-filled elastic spherical shell with piezoelectric actuator and sensor layers was solved. The results could provide theoretical basis for the spherical-symmetric dynamic control problem of fluid-structure coupling piezoelectric intelligent structure. Furthermore, the solutions can serve as reference for the research on the control of general fluid-structure dynamic problems.

Dynamical and Static Analysis of the Deformation of a Fluid-Filled, Piecewise-Homogeneous Elastic Shell

The dynamical problem of the distribution of a pressure wave initiated at a certain distance from a junction of fluid-filled elastic shells having different properties is investigated. The static problem of two connected, empty (without the fluid) elastic shells having different properties is investigated as a special case of the dynamical problem and as a first step in the investigation of the stated problem. The results are subjected to a comparative analysis, and estimates are obtained for the solution of the dynamical problem in contrast with the static version.

TRANSFORMATION OF A PRESSURE PULSE IN A FLUID-FILLED CYLINDRICAL ELASTIC SHELL

The influence of a tubular elastic insert of finite length in a fluid-filled elastic shell on the propagation of a pressure pulse generated at a certain distance from the insert is investigated. The Laplace integral transform is used to solve the corresponding mathematical problem. Analytical solutions are first obtained in each separate domain of the hydroelastic system, subject to the coupling boundary conditions, and then the Laplace transforms are inverted numerically. The influence of the geometrical parameters of the insert and the shell on the pressure distribution in the fluid, the radial displacement, the bending moments, and the shearing forces are analyzed in detail both quantitatively and qualitatively. It is shown that the transmission of the pressure pulse in the junctions of the insert with the shell is accompanied by highly localized stress concentration there, which is several orders of magnitude greater than in the homogeneous shell.

Coupled vibration analysis of fluid-filled cylindrical shells using the wave propagation approach

The coupled structural-acoustic analysis of finite fluid-filled cylindrical shells is presented using the wave propagation method. For uncoupled analysis the natural frequencies of the shell by the present method are compared with the results available in the literature. For coupled analysis the comparisons of the frequencies by the present method and numerical finite element method boundary element method (FEM/BEM) are carried out. Through the comparisons it is possible to conclude that the present method is correct. It is a simple, non-iterative and relatively less computationally intensive method. It is shown that the fluid effect on the shell is significant. Ignorance of the fluid effect will lead to large errors in the vibration analysis of fluid-filled shells.

Effect of Fluid Presence on the Nonaxisymmetric Dynamic Response of Buried Orthotropic Cylindrical Shells Under a Moving Load

This paper deals with the nonaxisymmetric dynamic behavior of fluid-filled buried orthotropic cylindrical shells/pipes subjected to a load moving along the axis of the shell. A thick shell model including the effects of shear deformation and rotary inertia is considered. A perfect bond between the shell and sur rounding soil is assumed. The linear acoustic equation is used for the wave propagation in the fluid inside the pipe. Results are presented for the axisymmetric as well as the flexural mode for different orthotropy para meters of the shell and for different soil conditions around the pipe. Results of empty and fluid-filled shells are compared. The presence of fluid inside the shell has small effect on the shell response. However, the deformations in the fluid-filled shell are normally more than those in the empty shell. The difference in the displacements of empty and fluid-filled shells is very small in flexural mode as compared to axisymmetric mode. The effect of fluid presence on the shell response is also influenced by the nature of the surrounding soil.

THE EFFECT OF WALL JOINT ON THE VIBRATIONAL POWER FLOW PROPAGATION IN A FLUID-FILLED SHELL

A fluid-filled cylindrical shell comprising a wall joint is investigated by using the concept of vibrational power flow. The power flow in the contained fluid and in the shell wall of this fluid-filled elastic cylindrical shell is studied. The transmission loss of vibrational power flow through the wall joint is studied and an analysis of power flow transmission and reflection at the joint in fluid-filled shells is presented. Material stiffness of the joint and frequency are two important factors that are found to strongly influence the results. It is hoped that the analysis will shed some light on the control of vibrational propagation in shells filled with fluid.

SPACE-HARMONIC ANALYSIS OF INPUT POWER FLOW IN A PERIODICALLY STIFFENED SHELL FILLED WITH FLUID

In this paper, the input power flow from a cosine harmonic circumferential line force into an infinite cylindrical fluid-filled shell with periodic stiffeners is studied. The stiffeners are idealized as line attachments capable of exerting line forces which relate to the stiffeners and the shell. The motion of the shell and the pressure field in the contained fluid are described by the Flügge thin shell theory and the Helmholt equation respectively. A periodic structure theory, space-harmonic analysis, is used to investigate this fluid-filled periodic structure. The concept of the vibrational power flow is introduced and the influence of the parameters of the stiffeners upon the results is also discussed.

Relationship between material parameters and target strength of fluid-filled spherical shells in water: calculations and observations

Thin fluid-filled spherical shells have been used as passive sonar targets for many years. They possess a large target strength which is highly dependent on the sound-speed mismatch between the fluid contained within the shell and the exterior fluid surrounding the shell. In the past, to obtain the appropriate mismatch, the interior fluid mixture contained chlorofluorocarbons (CFCs). Due to a recent production ban on CFCs, it is necessary to choose alternative fluids. The present research analyzes the backscattering target strength of a fluid-filled spherical shell as a function of several material parameters as a guide to choosing alternative fluids and shell materials. Calculations over a broad range of material values display the target strength dependence on the interior fluid parameters as well as the parameters defining the metallic shell. The range of material values presented here is far larger than any previous study addressing the focusing effects of fluid-filled spherical shells. The results should aid in determining liquid fillers and shell materials which yield the maximum possible backscattered returns. Also, several experiments were conducted with stainless steel shells containing a hydrochlorofluorocarbon (HCFC), dichlorofluoroethane. The results are compared with results found from calculations as well as from other experiments involving shells containing a previously used CFC mixture.

Strong Potential Magnetic Field Influence on Slightly Differentially Rotating Spherical Shell

An electrically conducting viscous fluid-filled spherical shell is permeated by an axisymmetric strong potential magnetic field with large Elssaser number λ2 ≫ 1. We describe analytically the steady flow driven by a slightly faster rotation of the conducting inner boundary of the shell. The main flow is controlled by Ekman-Hartmann boundary layers with a small thickness δ/λ, where δ2is the Ekman number. Asymptotics based on small λ−1 ≪ 1 reveal the nature of a free shear layer O((δ/λ)1/2) and a super-rotation that allows a part of the fluid to rotate faster than the inner sphere. The free shear is following an imposed field line that is tangent to the inner or outer sphere. Meridional flux is concentrated in the shear and boundary layers. Fluid tends to rotate with the inner sphere and to expel azimuthal magnetic field from an\( \ell \)-region restricted by the free shear in the spherical shell.

Some regular perturbation solutions in fluid mechanics

We examine two problems in steady incompressible viscous flow with a view to generating high-order perturbation solutions as regular expansions in powers of the Reynolds number. Thus, computer-algebra techniques are used to study the motions produced (a) by a Landau momentum source placed at the centre of a fluid-filled spherical shell, and (b) by a rotating sphere in both unbounded and bounded fluids.

Free vibration of a partially fluid-filled cross-ply laminated composite circular cylindrical shell

Free vibration of a partially fluid-filled cross-ply laminated composite circular cylindrical shell is investigated using a semi-analytical procedure based on the Reissner–Mindlin theory and compressible fluid equations. The shell is modeled using unaxisymmetric shear deformable circular cylindrical shell elements. The fluid is modeled using column fluid elements. The equation of motion of the partially fluid-filled shell is derived using the Hamilton’s variational principle. Numerical examples are given for free vibrations of partially fluid-filled orthotropic and cross-ply laminated composite circular cylindrical shells with various boundary conditions. Numerical results indicate that the fluid filling can reduce significantly the natural frequencies of orthotropic and cross-ply laminated composite circular cylindrical shells.

Free vibration response of multilayered orthotropic fluid-filled circular cylindrical shells

A theoretical analysis for the free vibration of multilayered orthotropic circular cylindrical shells filled with non-viscous, incompressible fluid has been developed. Transverse shear and rotary inertia terms are included in the thin shell theory used herein. Axial dependence of modal forms is taken in the form of simple Fourier series instead of exponential axial dependence which is more commonly used. The approximate method adopted here yields a polynomial equation in the frequency parameter which can then be solved to study the influence of boundary conditions on the vibration characteristics. Some results in the case of a simply-supported fluid-filled shell are given here. The effect of the frequency response due to variations in the fluid height is studied. The effect on the natural frequencies of variation in the axial and meridional stiffness of the shell is also analysed.

Free Vibration of a Fluid-Filled Circular Cylindrical Shell with Lumped Masses Attached, Using the Receptance Method

The receptance method is applied to the analytical study of the free vibrations of a simply supported circular cylindrical shell that is either empty or filled with an in viscid, incompressible fluid and with lumped masses attached at arbitrary positions. The receptance of the fluid-filled shell is obtained using the added virtual mass approach to model the fluid–structure interaction. The starting data for the computations is the modal properties of the cylinder that can be obtained using any theory of shells. Numerical results are obtained as roots of the frequency equation and also by considering the trivial solution. They are compared to data obtained by experimental modal analysis performed on a stainless steel tank, empty, or filled with water, with a lead mass attached.

Free Vibration of a Fluid-Filled Circular Cylindrical Shell with Lumped Masses Attached, Using the Receptance Method

The receptance method is applied to the analytical study of the free vibrations of a simply supported circular cylindrical shell that is either empty or filled with an in viscid, incompressible fluid and with lumped masses attached at arbitrary positions. The receptance of the fluid-filled shell is obtained using the added virtual mass approach to model the fluid–structure interaction. The starting data for the computations is the modal properties of the cylinder that can be obtained using any theory of shells. Numerical results are obtained as roots of the frequency equation and also by considering the trivial solution. They are compared to data obtained by experimental modal analysis performed on a stainless steel tank, empty, or filled with water, with a lead mass attached.

Acoustic scattering from fluid-filled, concentric, submerged, cylindrical, elastic shells

The present study addresses the scattering of plane (cw) sound waveforms by concentric, fluid-filled, elastic shells in water from the viewpoint of an impedance-based formulation. For a single fluid-filled shell, this impedance formulation is shown to agree with (the exact form of) the earlier resonance scattering theory (RST) which used elastic potentials and matches various stresses and displacements at the boundaries. The comparison cannot be established for more than one (concentric) shell, since there is no RST formulation for such cases. However, the present formulation is used to generate predictions for double shells with various fillers. A number of conclusions emerge from the present analysis and calculations, particularly for the case of two concentric fluid-filled shells. In this instance, if the filler of the annular region in between the shells is air, then the structural components inside that region do not contribute to the scattered field, and can be safely ignored. For a water-filled annular region, the total backscattering form function (at θ=π) will automatically display the isolated shell resonances, without any need for any ‘‘background’’ subtraction. Furthermore, the total angular form functions, evaluated at resonance, will exhibit the typical shape of rhodonea patterns, again without subtracting any type of background. These cases in which background subtraction is not needed are contrasted with various others in which it is needed, and how resonance isolation is achieved in all cases considered is shown. Many computer generated graphs for single and double shells illustrate all these points.

Non-Axisymmetric Dynamic Response Of Imperfectly Bonded Buried Fluid-Filled Orthotropic Cylindrical Shells Due To Incident Shear Wave

A theoretical analysis is presented of the non-axisymmetric dynamic response of an imperfectly bonded fluid-filled buried orthotropic pipeline subjected to a combination of SV- and SH-waves travelling in the surrounding medium of infinite extent. Numerical results have been presented for the case of an incident SV-wave only. An infinite cylindrical shell model including the effects of shear deformation and rotary inertia has been considered for the pipeline. The linear acoustic equation has been used for the wave propagation in the fluid inside the pipe. The results for a fluid-filled shell have been compared with those for an empty shell. The relative effects of fluid presence and the bond imperfection on the dynamic response have also been studied.

Dynamic stability characteristics of fluid-filled shells under multiple excitations

The membrane forces induced by horizontal ground motion are derived to be used in the coupled Hill's equations for a complete dynamic stability analysis. Excellent agreement between theoretical and available experimental results is obtained. A majority of buckling modes can be correctly identified by considering a geometrical imperfection. The influence of the imperfection on the dynamic buckling characteristics is also discussed.

Formulation of dynamic stability of fluid-filled shells

A method of analysis is introduced to study the dynamic stability characteristics of fluid-filled shells. The governing equations including dynamic fluid-structure interaction are derived using a Galerkin/Finite Element approach. The induced modal coupling in circumferential and axial directions is identified. The importance of geometrical imperfection is emphasized in the derivation of the set of equations which govern the dynamic stability of fluid-filled shells.

Effect of the presence of fluid on the dynamic response of buried orthotropic cylindrical shells under a moving load

This paper deals with the theoretical analysis of the axisymmetric steady state dynamic response of a buried fluid-filled orthotropic cylindrical shell subjected to a radial line load moving along the axis of the shell. A thin shell is assumed to be perfectly bonded to the surrounding medium of infinite extent, and only the axisymmetric response has been included. A linear acoustic equation has been used for the wave propagation in fluid. The nature of variation of differences between the results of the empty and fluid-filled shells has been studied for varying soil conditions. Changes in results due to variation in the orthotropy parameters have been compared with the difference in results due to the presence of fluid inside the shell.

Transient failure analysis of liquid-filled shells PART II: Applications

In this paper, applications of the theory developed in the companion paper by Liu and Uras [1] are presented. The effects of various types of ground motion on the dynamic stability of the fluid-structure system are analyzed. The stability criteria of liquid-filled shells subjected to horizontal and rocking excitation, shear loading, bending/shear combined loading, and vertically applied load are established. The resulting instability regions and stability charts are given in tables and in ω-ϵ plots. Under horizontal and rocking motion, modal coupling in the circumferential direction as well as in the axial direction is observed. The possible buckling modes for a tall tank can be identified as cos2θ, cos3θ and cos4θ under horizontal and rocking motion, and cos5θ and cos6θ, under vertically applied load. For a broad tank two sets of instability modes are found: cos6θ through cos9θ, and cos12θ through cos14θ under horizontal and rocking motion. When subjected to vertically applied load, the failure modes of a broad tank shift to cos10θ through cos12θ, and cos14θ through cos15θ. The effect of shear load on a broad tank appears to be important only if damping is relatively small. Under bending/shear combined loading, the bending forces dominate the stability of the fluid-filled shells.