Fluid-loaded Cylindrical Shell Research Articles

Acoustic radiation from a cylindrical shell with a voided soft elastic coating.

An analytical framework for sound radiation from a fluid-loaded cylindrical shell covered with an acoustic coating is presented. The coating is composed of a soft elastic material embedded with a circumferential layer of equispaced voids. The layer of voids is modeled as an effective fluid medium sandwiched between two layers of the host material. Expressions for the effective impedance of the coating, radial displacement of the elastic shell, and the structure-borne radiated pressure for harmonic excitation of the shell are derived. Results show that the coating design can be tuned to reduce the radiated sound in a broad frequency range.

Vibroacoustic responses of a heavy fluid loaded cylindrical shell excited by a turbulent boundary layer

A fully coupled structural–acoustic model of a cylindrical shell under external turbulent boundary layer excitation is herein developed. The numerical process requires computation of the wall pressure cross spectral density function as well as sensitivity functions for the fluid-loaded cylindrical shell. A semi-empirical model from literature is used to describe the wall pressure field induced by the turbulent boundary layer in the wavenumber–frequency domain. An analytical expression of the wall pressure field for a flat surface is adapted to describe the wall pressure field for a cylindrical surface. Circumferential sensitivity functions are derived using a wavenumber-point reciprocity principle. Results for the near-field and far-field acoustic pressure spectra are presented. Contributions of individual circumferential modes to the acoustic pressure spectra are examined, showing distinct trends below and above the ring frequency. The proposed method is computationally efficient and provides an effective approach to investigate vibroacoustic responses for maritime platforms.

Noise radiated from a periodically stiffened cylindrical shell excited by a turbulent boundary layer

This work proposes a semi-analytical method to model the vibroacoustic behavior of submerged cylindrical shells periodically stiffened by axisymmetric frames and excited by a homogeneous and fully developed turbulent boundary layer (TBL). The process requires the computation of the TBL wall-pressure cross spectral density function and the sensitivity functions for stiffened cylindrical shells. The former is deduced from an existent TBL model and the latter are derived from a wavenumber-point reciprocity principle and a spectral formulation of the problem. The stiffeners' dynamic behavior is introduced in the formulation through circumferential admittances that are computed by a standard finite element code using shell elements. Four degrees of freedom are taken into account for the coupling between the shell and the stiffeners: three translation directions and one tangential rotation. To investigate the effect of the stiffeners on the radiated noise, two case studies are considered. The first one examines a fluid-loaded cylindrical shell with regularly spaced simple supports. The influence of Bloch-Floquet waves and the support spacing on the noise radiation are highlighted. The second case study inspects the fluid-loaded cylindrical shell with two different periodic ring stiffeners, namely stiffeners with T-shaped and I-shaped cross-sections. Their influence on the vibroacoustics of the shell is thoroughly analyzed.

Modal decomposition of exterior acoustic-structure interaction problems with model order reduction

A numerical technique for modal decomposition of the acoustic responses of structures submerged in a heavy fluid medium using fluid-loaded structural modes is presented. A Krylov subspace model order reduction approach to reduce the computational effort required for a fully coupled finite element/boundary element model is described. By applying the Krylov subspace to only the structural part of the global system of equations for the fully coupled problem, only the frequency independent finite element matrices are reduced. A fluid-loaded cylindrical shell closed at each end by hemispherical end caps is examined. The cylinder is excited by a ring of axial or transverse forces acting at one end. The individual contributions of the cylinder circumferential modes to the sound power and directivity of the radiated sound pressure are observed. The technique presented here provides a tool for greater physical insight into exterior acoustic-structure interaction problems using fully coupled numerical models, with significantly reduced computational effort.

Acoustic radiation from fluid-loaded cylindrical shells—A review

The acoustic radiation from fluid-loaded cylindrical shells received significant attention in the past. Reviewing the literature, the number of papers published in this area is significant. The body of work covers thin walled small diameter shells applicable to the sound transmission in pipes, to large diameter shells with internal stiffeners and bulkheads. Also, considered is the influence of full and partial compliant coatings. A significant portion of work was based on analytical techniques useful to understand the phenomena and some of the critical parameters. More recent, with the availability of more capable computers and modeling codes, the focus has been on application of these computational tools to solving field problems. This paper reviews some of the past computational work and how some applications evolved from this work. However when presented with actual submerged cylindrical structures with complex internals, while modeling is useful, when dealing with the acoustic radiation from shell like structures at medium to high frequencies modeling tools still cannot handle the full extent of the problem and the prevalent approach still relies on implementation of good engineering practice.

Scattering model of a cylindrical shell with internal axisymmetric frames by using the Circumferential Admittance Approach

A numerical model is proposed for predicting scattering pressure by a fluid-loaded cylindrical shell stiffened by axisymmetric internal frames and impacted by an acoustic plane wave. The proposed developments are based on the Circumferential Admittance Approach (CAA) which allows us assembling a numerical model of the fluid loaded shell with finite element models of the internal frames. The scattering pressure model deduced with the CAA can then take into account: (a) internal frames having a cross section with a complex geometry and thickness variations (like T-shaped stiffeners, bulkheads, and hemispherical end caps); (b) variations of frame spacings; and (c) frame-shell coupling in the three translational directions and tangential rotation. Comparison with the numerical and experimental results of the literature for a periodic stiffened shell shows that the scattering from Bragg, Bloch–Floquet, and Helical waves is correctly predicted. The effects on the backscattering pressure of axial and tangential coupling forces are highlighted. Finally, an example of a non-periodically stiffened shell is presented to highlight the versatility of the approach proposed.

Active Control of Sound Radiated by a Submarine Hull in Axisymmetric Vibration Using Inertial Actuators

This paper investigates the use of inertial actuators to reduce the sound radiated by a submarine hull under excitation from the propeller. The axial forces from the propeller are tonal at the blade passing frequency. The hull is modeled as a fluid-loaded cylindrical shell with ring stiffeners and equally spaced bulkheads. The cylinder is closed at each end by circular plates and conical end caps. The forces from the propeller are transmitted to the hull by a rigid foundation connected to the propeller shaft. Inertial actuators are used as the structural control inputs. The actuators are arranged in circumferential arrays and attached to the internal end plates of the hull. Two active control techniques corresponding to active vibration control and discrete structural acoustic sensing are implemented to attenuate the structural and acoustic responses of the submarine. In the latter technique, error information on the radiated sound fields is provided by a discrete structural acoustic sensor. An acoustic transfer function is defined to estimate the far field sound pressure from a single point measurement on the hull. The inertial actuators are shown to provide control forces with a magnitude large enough to reduce the sound due to hull vibration.

Sound scattering by free surface piercing and fluid-loaded cylindrical shells

A vertical flexible, thin, cylindrical shell is considered to be clamped to a rigid base in shallow water and piercing its surface. The shell is composed of an isotropic and homogeneous material and may be empty inside or filled with compressible fluid. Linear acoustics and structural dynamics are used to model sound scattering caused by an external incident sound wave. A solution is derived using a Fourier transform in the tangential and vertical directions. A collocation technique coupled with an orthogonalization procedure is used to account for the edge conditions of the shell. It is shown that zero sound scattering, indicating acoustic invisibility, is theoretically attainable and can be achieved when a continuous distribution of an oscillating pressure load is applied on the shell's wall. Similarly, zero sound transmission into the shell's inner fluid can also be considered. The possibility of using a pre-determined discrete distribution of the applied pressure load is also discussed. The derived equations are numerically solved to examine sound scattering by a thin aluminium shell in shallow water.

Dynamical Characteristic Analysis of a Fluid-Loaded Cylindrical Shell with Structural Discontinuities

By using space-harmonic analysis method, the characteristics of vibrational power flow and sound radiation of an infinite submerged cylindrical shell with internal rings and bulkheads are studied analytically. The harmonic motion of the shell and the pressure field in the fluid are described by Flügge shell equations and Helmholtz equation, respectively. The coupling condition on the outer surface of the shell wall is introduced to obtain the vibrational equation of this coupled system. Both four kinds of forces (moments) between rings and shell and between bulkheads and shell are considered. The solution is obtained in series form by expanding the system responses in terms of the space harmonics of the spacings of both ring stiffeners and bulkheads. The vibrational power flow and radiated sound power are obtained and the influences of various complicating effects such as the ring, bulkhead and fluid loading on the results are analyzed. The analytic model is close to engineering practice, which will give some guidelines for noise reduction of this kind structure.

The effect of hydrostatic pressure fields on the dispersion characteristics of fluid-shell coupled system

The effect of hydrostatic pressure on the vibration dispersion characteristics of fluid-shell coupled structures was studied. Both fluid-loaded cylindrical shells and fluid-filled cylindrical shells were considered. Numerical analysis was applied to solve the dispersion equations for shells filled with or loaded with fluid at various hydrostatic pressures. The results for external pressure showed that non-dimensional axial wave numbers are nearly independent when the pressure is below the critical level. The influence of internal pressure on wave numbers was found significant for the real branch s=1 and the complex branches of dispersion curves. The presence of internal pressure increased the cut on frequencies for the branch s=1 for high order wave modes.

Structural and acoustic responses of a fluid-loaded cylindrical hull with structural discontinuities

This paper studies the low frequency vibrational behaviour and radiated sound of a submarine hull under axial excitation. The submarine is modelled as a fluid-loaded cylindrical shell with internal bulkheads and ring-stiffeners and closed at each end by circular plates. A smeared approach is used to model the ring stiffeners. The external pressure acting on the hull due to the fluid loading is calculated using an infinite model and is shown to be a good approximation at low frequencies. The radiated sound pressure is obtained by considering the finite cylindrical hull to be extended by two semi-infinite rigid baffles. The sound pressure is then only due to the radial displacement of the cylindrical shell, without taking into account the scattering at the finite ends. The main aim of this paper is to observe the influence of the various complicating effects such as the bulkheads, ring-stiffeners and fluid loading on the structural and acoustic responses of the finite cylindrical shell. Results from the analytical models presented in this paper are compared to the computational results from finite element and boundary element models.

Measurement and modeling of the acoustic field near an underwater vehicle and implications for acoustic source localization

The performance of traditional techniques of passive localization in ocean acoustics such as time-of-arrival (phase differences) and amplitude ratios measured by multiple receivers may be degraded when the receivers are placed on an underwater vehicle due to effects of scattering. However, knowledge of the interference pattern caused by scattering provides a potential enhancement to traditional source localization techniques. Results based on a study using data from a multi-element receiving array mounted on the inner shroud of an autonomous underwater vehicle show that scattering causes the localization ambiguities (side lobes) to decrease in overall level and to move closer to the true source location, thereby improving localization performance, for signals in the frequency band 2-8 kHz. These measurements are compared with numerical modeling results from a two-dimensional time domain finite difference scheme for scattering from two fluid-loaded cylindrical shells. Measured and numerically modeled results are presented for multiple source aspect angles and frequencies. Matched field processing techniques quantify the source localization capabilities for both measurements and numerical modeling output.

The modeling of the radiation and response Green’s function of a fluid-loaded cylindrical shell with an external compliant layer

Scattering and radiation of acoustic waves from a fluid-loaded cylindrical shell with an external compliant layer are of interest. The compliant layer can be modeled by a normally reacting impedance layer, which has the advantage that complex compliant layer geometries, such as partial compliant layers, can be considered. A question may, however, arise as to the accuracy of this approach. A more rigorous approach is to model the elastic shell and compliant layer using a multilayer shell theory, which has the disadvantage that it cannot be extended to consider partial layers. In this paper scattering results from the normally reacting compliant layer model are compared to those from the multilayer shell model to show that the two approaches produce similar results, except for thickness resonances of the compliant layer. Having established the consistency between the two approaches, results for the far-field acoustic radiation as a function of frequency and radiation angle for a fluid-loaded shell with an external compliant layer excited by an internal ring force are obtained using the normally reacting impedance layer model. These results clearly show the reduction in the far field radiation due to the presence of the compliant layer.

An energy finite element formulation for high-frequency vibration analysis of externally fluid-loaded cylindrical shells with periodic circumferential stiffeners subjected to axi-symmetric excitation

A hybrid method is developed for predicting the high-frequency vibration response of fluid-loaded cylindrical shells with periodic circumferential stiffeners. In this method, the cylindrical shell is modeled using the Energy Finite Element Analysis (EFEA) method which includes added mass and radiation effects due to the surrounding exterior fluid medium. The joint matrices of the EFEA formulation at the location of the periodic stiffeners are computed based on Periodic Structure (PS) theory. Thus, the periodicity effects such as pass/stop characteristics are captured in the EFEA solution. The hybrid EFEA-PS method is used to analyze the vibration of a fluid-loaded axisymmetric cylindrical shell with periodic circumferential stiffeners. The flexural energy stored in each periodic section is computed. The results are compared with the solution produced by a very dense axisymmetric Finite Element (FE) model with infinite finite elements for the fluid domain. The good correlation indicates that the new hybrid method captures properly both the heavy fluid effects of the exterior fluid medium and the periodicity characteristics due to periodic stiffeners.

Analytical-numerical matching for fluid-loaded structures with discontinuities

The method of analytical-numerical matching (ANM) is applied to several example problems involving the radiation and vibration of a fluid-loaded cylindrical shell with structural discontinuities. These problems are used to verify the accuracy of the method compared to a purely numerical approach, and to demonstrate the usefulness of ANM for solving problems involving nonaxisymmetric forcing and constraints on structures that are otherwise axisymmetric. The principal advantage of the ANM method for this application is its ability to employ a spectral method (modal decomposition in azimuth) in the solution of a problem that is nonaxisymmetric. ANM divides the original problem into local and global subproblems that are solved separately. The discontinuity is handled using a high-resolution local finite-element model. Smooth forces are derived from solving an analytical matching problem on the local domain, and these smooth forces are then applied to a low-resolution numerical global problem. The superposition of solutions to the subproblems is equivalent to the solution of the original problem. For fluid loading, the local high-resolution model is solved in vacuo, and the effects of fluid loading are included completely by the low-resolution global problem.

Active Control of Vibration and Noise Radiation from Fluid-Loaded Cylinder using Active Constrained Layer Damping

Vibration and sound radiation from fluid-loaded cylindrical shells are controlled using patches of Active Constrained Layer Damping (ACLD). The performance and the enhanced damping characteristics via reduced vibrations and sound radiation in the surrounding fluid is demonstrated both theoretically and experimentally. A prime motivation for this work is the potential wide applications in submarines and torpedoes where acoustic stealth is critical to the effectiveness of missions. A finite element model is also developed to predict the vibration and the acoustic radiation in the surrounding fluid of the ACLD-treated cylinders. The developed model is used to study the effectiveness of the control and placement strategies of the ACLD in controlling the fluid-structure interactions. A water tank is constructed that incorporates test cylinders treated with two ACLD patches placed for targeting specific vibration modes. Using this arrangement, the effectiveness of different control strategies is studied when the submerged cylinders are subjected to internal excitation, and the radiated sound pressure level in the water is observed. Comparisons are made between the experimental results and the theoretical predictions to validate the finite element model.

Passive Control of the Vibration and Sound Radiation from Submerged Shells

Vibration and noise radiation from fluid-loaded cylindrical shells are controlled using multiple stiffeners and Passive Constrained Layer Damping treatment. Dynamic and fluid finite element models are developed to study the fundamental phenomena governing the interaction between the stiffened shell, with and without damping, and the fluid domain surrounding it. The models are used to predict the response of the shell and to evaluate the effect of the stiffening rings and damping treatment on both the structural vibration and noise radiation in the fluid domain. The prediction of the models are validated experimentally and against the predictions of a commercial FE software package (ANSYS). It is shown that stiffening of the shell reduces the amplitude of the vibration and noise radiation, particularly for high order lobar modes. The attenuation of the shell response and sound radiation can be significantly increased through the application of Passive Constrained Layer Damping treatment on the inner surface of the stiffening rings. The numerical and experimental validations demonstrate the accuracy of the developed models and emphasize its potential extension to the application of smart materials for active control of vibration and noise radiation from fluid-loaded shells.

Finite element modeling of vibration and sound radiation from fluid-loaded damped shells

The vibration and noise radiation from fluid-loaded cylindrical shells are controlled by using multiple stiffeners and passive constrained layer damping treatment. Dynamic and fluid finite elements are developed to study the fundamental phenomena governing the coupling between the stiffened shell, with and without damping, and the fluid domain surrounding it. The models are used to predict the response of the shell and to evaluate the effect of stiffening rings and damping treatment on both the structural vibration and noise radiation in the fluid domain. The geometry of the shell and fluid domain allows the formulation of a harmonic-based model, which uncouples the fluid–structural response of modes corresponding to different numbers of circumferential nodes. In this study, it is shown that stiffening of the shell reduces the amplitude of the vibration and noise radiation, particularly for high-order lobar modes. The attenuation of the shell response and sound radiation can be increased significantly through the application of passive constrained layer damping treatments on the inner surface of the stiffening rings.

Scattering from fluid-loaded cylindrical shell with periodic circumferential constraints using analytical/numerical matching

Acoustic scattering from an infinitely long, thin elastic cylindrical shell with axially periodic circumferential constraints leads to the excitation of flexural, longitudinal, and shear waves on the shell. Of interest is the interaction of these structural waves with the discontinuous constraints, and the effect of this interaction on the resultant scattered sound field. This three-dimensional, fully coupled, structural acoustic problem is solved using a method called analytical/numerical matching (ANM). The method combines high-resolution local analytical solutions and low-resolution global numerical solutions to more efficiently model structural discontinuities. The ANM local solutions have been developed to efficiently capture the rapid variation in system response across the discontinuous constraint. The local solutions are combined with a smooth global solution, modeled by modal methods, to form an accurate, uniformly valid composite solution. The ANM composite solution is more accurate and converges much more rapidly than the traditional modal approach. An important observation is that this scattering problem exhibits considerable sensitivity to modeling accuracy and convergence of structural response in the region of the discontinuities. Errors in these regions have an overall effect on the structure and the associated scattered field.

Acoustic scattering by a closed semi-infinite fluid-loaded elastic cylindrical shell

A plane sound wave is obliquely incident upon a semi–infinite elastic circular cylindrical shell, closed at one end by a rigid but movable disk, with exterior fluid loading. Expanding the unknown pressure on the end plate as a Dini series and applying half–range Fourier transforms allows the problem to be formulated as a Wiener–Hopf equation with unknown coefficients which satisfy a system of simultaneous linear equations. The solution is presented for the axisymmetric, n = 0 harmonic, component of the scattered sound, which in the far–field consists of the cylindrically spreading waves, in appropriate regions, which would have been present if the shell had been infinitely long, together with a spherically spreading component which is due to the semi–infinite length of the shell. Some numerical results are presented for the spherically spreading component of the scattered field.