Light Fluid Loading Research Articles

Asymptotic Analysis of an Elastic Layer under Light Fluid Loading

Asymptotic analysis for an elastic layer under light fluid loading was developed. The ratio of fluid and solid densities was chosen as the main small parameter determining a novel scaling. The leading- and next-order approximations were derived from the full dispersion relation corresponding to long-wave, low-frequency, antisymmetric motions. The asymptotic plate models, including the equations of motion and the impenetrability condition, motivated by the aforementioned shortened dispersion equations, were derived for a plane-strain setup. The key findings included, in particular, the necessity of taking into account transverse plate inertia at the leading order, which is not the case for heavy fluid loading. In addition, the transverse shear deformation, rotation inertia, and a number of other corrections appeared at the next order, contrary to the previous asymptotic developments for fluid-loaded plates not assuming a light fluid loading scenario.

A subspace iteration eigensolver based on Cauchy integrals for vibroacoustic problems in unbounded domains

AbstractDespite the potential and the increasing popularity of the boundary element method (BEM), modal analyses based on BEM are not yet put into engineering practice, mainly due to the lack of efficient solvers for the underlying nonlinear eigenvalue problem (EVP). In this article, we review a subspace iteration method based on FEAST for the solution of vibroacoustic EVPs involving the finite element method (FEM) and BEM. The subspace is obtained by applying a spectral projector and is computed by contour integration, whereas the contour is also used to subsequently solve the projected EVP by rational approximation. The computation of the projection matrices is addressed by two approaches. In the case of heavy fluid loading, we solve the underlying coupled linear systems by an iterative block Krylov method. In the case of light fluid loading, we exploit the fact that the coupled system admits accurate model order reduction solely based on the structural subsystem. Applications to a spherical shell and to a musical bell indicate that only a few contour points are required for an accurate solution without inducing spurious eigenvalues. The results are compared with those of a contour integral method and illustrate the efficiency of the proposed eigensolver.

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.

Structural Acoustics of a Rectangular Panel Backed by a Cavity: An Analytical Matrix Approach

The coupling matrix in structural-acoustic systems carries the entire information about the coupled resonances. We have found an elegant way of presenting this matrix and computing its determinant analytically (in a closed-form) for light fluid loading cases. The determinant gets factorized into a product. This form can be used to gain an insight into the new order of the coupled resonances. The specific example of a rectangular panel backed by a cavity is taken to demonstrate the method. This being the primary objective of the work, secondarily, the form of the matrix so derived is used to compute the new coupled resonances using a simple iterative scheme requiring a starting guess. Numerical values are compared with those given in the literature and also using the commercial package virtual lab.

Sound transmission loss through metamaterial plate with lateral local resonators in the presence of external mean flow.

In the context of sound incident upon a metamaterial plate, explicit formulas for sound transmission loss (STL) are derived in the presence of external mean flow. Metamaterial plate, consisting of homogeneous plate and lateral local resonators (LLRs), is homogenized by using effective medium method to obtain the effective mass density and facilitate the calculation of STL. Results show that (a) vigorously oscillating LLRs lead to higher STL compared with bare plate, (b) increasing Mach number of the external mean flow helps obtain higher STL below the coincidence frequency but decreases STL above the coincidence frequency due to the added mass effect of light fluid loading and aerodynamic damping effect, (c) the coincidence frequency shifts to higher frequency range for the refracted effect of the external mean flow. However, effects of the flow on STL within negative mass density range can be neglected because of the lateral local resonance occurring. Moreover, hysteretic damping from metamaterial can only smooth the transmission curves by lowering higher peaks and filling dips. Effects of incident angles on STL are also examined. It is demonstrated that increasing elevation angle can improve the sound insulation, while the azimuth angle does not.

Asymptotic expansions for the structural wavenumbers of isotropic and orthotropic fluid-filled circular cylindrical shells in the intermediate frequency range

We consider wavenumbers in in vacuoand fluid-filled isotropic and orthotropic shells. Using the Donnell–Mushtari (DM) theory we find compact and elegant asymptotic expansions for the wavenumbers in the intermediate frequency range, i.e., around the ring frequency. This frequency range corresponds to the frequencies where there is a rapid change in the values of bending wavenumbers and is found to exist in isotropic and orthotropic shells (in vacuoand fluid-filled) for low circumferential orders n only. The same is first identified using the n=0 mode of an orthotropic shell. Following this, using the expression for the intermediate frequency, asymptotic expansions are found for other cases. Here, in order to get compact expansions we consider slight orthotropy (ϵ⪡1) and light fluid loading (μ⪡1). Thus, the orthotropy parameter ϵ and the fluid loading parameter μ are used as asymptotic parameters along with the non-dimensional thickness parameter β. The methodology can be extended to any order of ϵ, only the expansions become unwieldy. The expansions are matched with the numerical solutions of the corresponding dispersion relation. The match is found to be good.

Vibration Localization in a Fluid-Loaded Rectangular Plate with Rib Irregularity

This paper studies the vibration localization of fluid-loaded irregularly ribbed plate analytically. The modal expansion method was adopted to solve the multi-coupled system, the ribs were considered as Timoshenko beams attached to the plate. The localization mechanism was investigated by comparing different coupling effect at the plate-beam interface, it was found the ribs space irregularity only localize the modes associated with the shear force coupling. Both the light and heavy fluid loading pressure were concerned by Rayleigh integral , the study showed that obvious vibration localization phenomenon can be achieved by the ribs space irregularity, and the localization effect was weakened by the long range interaction through the heavy fluid, although the response amplitude of the modes decreased obviously. The investigation may be quite significant for vibration confinement and noise control in engineering.

On Dowell’s simplification for acoustic cavity-structure interaction and consistent alternatives

A widely employed description of the acoustical response in a cavity whose walls are compliant, which was first proposed by Dowell and Voss [(1962). AIAA J. 1, 476-477], uses the modes of the corresponding cavity with rigid walls as basis functions for a series representation of the pressure. It yields a velocity field that is not compatible with the movement of the boundary, and the system equations do not satisfy the principle of reciprocity. The simplified formulation is compared to consistent solutions of the coupled field equations in the time and frequency domains. In addition, this paper introduces an extension of the Ritz series method to fluid-structure coupled systems that satisfies all continuity conditions by imposing constraint equations to enforce any such conditions that are not identically satisfied by the series. A slender waveguide terminated by an oscillator is analyzed by each method. The simplified formulation is found to be very accurate for light fluid loading, except for the pressure field at frequencies below the fundamental rigid-cavity resonance, whereas the Ritz series solution is found to be extremely accurate in all cases.

The effect of fluid loading on radiation efficiency.

The metric "radiation efficiency," used to estimate a panel's radiated acoustic power from a measure of its normal velocity, is typically derived under the condition of very light fluid loading. This paper shows that efficiencies calculated in this manner can significantly overestimate the radiated power when the condition of light fluid loading is not met, as can be the case for steel plates in water. It is also shown that, when fluid loading is not light, a baffled semi-infinite plate is not a good model for an interior support. Numerical results are presented for radiation efficiencies calculated for steel plates in water, and are compared to those calculated under the assumption of vanishing fluid loading.

𝕊-matrix theory applied to acoustic scattering by asymmetrically fluid-loaded elastic isotropic plates

Exact and approximate formalisms describing the interactions of acoustic plane waves with an elastic isotropic plate immersed between two different fluids (asymmetrically fluid-loaded plate) are presented. This constitutes an extension of the Fiorito, Madigosky, and Überall (FMU) [R. Fiorito et al., J. Acoust. Soc. Am. 66, 181 (1979)] theory, refined later by Freedman [A. Freedman, J. Sound Vib. 82, 181 (1982); ibid. 82, 197 (1982)]. The method, based upon the multichannel resonant scattering theory derived from quantum physics [A. Bohm, Quantum Mechanics, Foundations, and Applications (Springer, New York, 1993)], consists of two parts. First, a 2×2 scattering 𝕊-matrix in which the diagonal elements are the two reflection coefficients and the off-diagonal elements are the two transmission coefficients, is built. Second, in order to compare our results with the FMU theory, resonant approximations are given for these coefficients, assuming light fluids when compared to the plate. The approximated coefficients show that the resonance widths are the sum of two independent partial widths, each of them being related to one fluid and to the plate physical properties. Of importance in this extension is the fact that the eigenvalues of the matrix, which reveal all the resonant features of the immersed plate, allow the separation between antisymmetrical and symmetrical modes, contrary to the reflection and transmission coefficients. The eigenvalues also allow the analysis of resonances despite the overlapping phenomenon. For the computations, the exact coefficients and eigenvalues, rather than their approximate forms, are used. This allows us to check the validity of the exact part of the theory under any fluid loading and not especially for light fluid loading.

Approximation of plate edge diffraction

Edge diffraction from thin plates and structural elements remains an area closely connected with the name of David Crighton. He developed the tools for solving the Wiener–Hopf problems that were inevitably obtained, and derived useful asymptotic approximations under light and heavy fluid loading. His approach and his philosophy of obtaining physical insight are applied in this lecture to the fundamental configuration of a semi-infinite thin plate in a fluid. The acoustic diffraction coefficient is strongly dependent upon frequency, unlike the analogous coefficients from hard or soft screens. At low frequencies the diffraction is like that from a soft or pressure release screen, while at high frequencies the hard screen approximation is more appropriate. An approximate but simple diffraction coefficient is proposed which has the correct limiting behavior at low and high frequencies. The transition from the low to high frequency response occurs when the acoustic wavelength matches the ratio of the areal to volumetric densities of the plate and fluid. The approximate formula is compared with the exact diffraction coefficient, showing good agreement for all frequencies.

Dynamic Analysis of a Rigid Body Mounting System with Flexible Foundation Subject to Fluid Loading

This paper presents an investigation of the force transmission from a rigid body mounting system to a flexible foundation with light and heavy fluid loading under the force and moment excitation. The analytical expression has been derived in which the flexible foundation effects are incorporated into a revised system stiffness matrix that is derived from the receptance matrix at mounting points. A typical case with a thin infinite plate as the foundation has been studied with the point and transfer receptances theoretically and numerically analysed in the case of light and heavy fluid loading. The results show that, compared with the rigid foundation, the force transmission is reduced and system natural frequencies are shifted. The detailed analysis demonstrates that the force reduction and frequency shifting are more obvious at low frequencies where the receptance value is significant. The study is also carried out to compare the transfer receptances from different waves in plate as it couples with water with the objective to simplify the calculation of receptance. It is found that, in the low frequency and after a short distance from driving point, the transfer receptance calculation for the heavy fluid loading can be simplified by only accounting the contribution from free wave which may easily be evaluated from the point receptance in air. It implies the plate response under heavy fluid loading could be directly derived from that with light fluid loading.

Noise Reduction Using Finite-Length Flexible Segments

In this work, the reduction of acoustic noise in piping systems through the installation of finite flexible segments is explored. A mathematical model describing the relevant parameters is developed. To verify the model, experimental work is undertaken using rubber hoses as flexible segments and air as the contained fluid. The effect of the segment on propagating acoustical energy is studied in terms of its insertion loss. Both theoretical and experimental results indicate that, for light fluid loading, the flexibility of the segment is only important when significant axial shell resonances exist, or when one or both acoustical termination impedances at the ends of the segment are much larger or smaller than the characteristic impedance of the medium. Further, the model indicates that for heavier fluid loading (i.e., when the compressibility of the flexible section is significant in relation to the bulk compliance of the fluid), in addition to higher associated insertion losses, the finite length resonances become more pronounced, and performance is less sensitive to small variations in the termination impedances. [S0739-3717(00)00402-5]

On the acoustic Zeeman effect

Thin, square plates subject to uniform boundary conditions vibrating in flexural motion have an enumerable set of resonances, some of them having multiple resonant modes. This holds for plates vibrating in vacuo. If the plate motion is subject to fluid loading, the resonant properties modify. Fluid loading induces all resonances to shift downwards (added mass effect), while acoustic radiation contributes to the damping of the modes. These features are well known and understood, although the actual calculation requires considerable computational effort. A perturbation method is presented for dealing with the effect of light fluid loading on the degenerate resonances. Removal of degeneracy is found for repeated modes having different coefficients for added mass and radiation damping. Symmetry is preserved for degenerate resonances that are modified by fluid loading in an identical way. Numerical results are presented that show how resonances split for the modes umn±unm of simply supported plates, where m and n have the same parity, i.e., m+n is even. Simple physical arguments, like equivalent multipole sources of the mode shapes and their spatial modulation, are used to interpret the results. Mode shapes with the highest degree of symmetry show the largest shift in frequency.

Active structural acoustic control of an infinite ribbed plate under light fluid loading

Active control can be applied to a vibrating structure to attenuate the acoustic radiation from the structure. In this paper, active structural acoustic control (ASAC) techniques are applied to a ribbed plate in order to minimize the structurally radiating sound fields. Using feedforward control strategies, multiple control forces are applied to the reinforcing beam. Modifying the structural response results in attenuation of the radiating sound fields. Cost functions are developed for the minimization of the far-field radiating sound pressure and far-field sound power. Optimization of the control system is achieved by using information on the structural coincidence conditions, and in determining the optimal error sensor location. Results demonstrate that significant reduction in the far-field sound pressure and sound power can be achieved in a large range away from the grazing angles. The effect of the control system on the structural response is also investigated.

Sound radiation by a simply supported unbaffled plate

Sound radiation by a simply supported unbaffled plate is presented using a double layer integral representation of the acoustic pressure. Both the pressure jump and the plate displacement are developed in series of the simply supported plate modes. This leads to modal coupling coefficients, which are numerically calculated for this specific unbaffled problem. The unbaffled problem is then transformed in the presentation of the baffled one which allows us to define original modal radiation impedance coefficients to the unbaffled plate. Baffled and unbaffled radiation impedances are then compared versus nondimensional frequency, in real and imaginary parts for a set of representative modes. An approximate expression for the direct unbaffled radiation impedance is presented, which is useful for light fluid loading. Finally, the influence of the baffle on sound radiation both in light and in heavy fluid, on the acoustic radiated power, the plate velocity, and the radiation factor is investigated.

Active Control of the Structural and Acoustic Responses of a Fluid-Loaded Plate; Part I: Analysis of the Physical System

The nature of the fluid–loading on a line–driven elastic plate significantly affects the structural and acoustic responses. As the fluid–loading increases, the fluid–structure interaction affects the wave propagation in the structure, as well as both the level and directivity of the sound radiation from the structure into the fluid field. The structural and acoustic responses of a line–force driven infinite plate under various fluid–loading conditions are considered. A detailed understanding of the fluid–structure interaction, including the effects of both heavy and light fluid–loading on the radiated sound pressure, sound power and structural response are clearly illustrated by numerical examples using the exact solution of the system equations. The results from this analysis of the physical system also provide useful information for the design of an active control system to effectively reduce the structural and acoustic responses of the fluid–loaded plate.

The light fluid loading limit for fluid/solid interactions

Many elastodynamic solutions exist for wave interactions with defects upon or within an elastic half space bounded above by a vacuum. The aim of this paper is to significantly widen the scope of these solutions by showing that they can be directly utilized, when the vacuum is replaced by a fluid, to find the leading order acoustic (or elastic) responses in the light fluid-loading limit. Using the procedure developed here one can take virtually any elastodynamic solution and use it to generate the leading-order solution for a fluid-loaded elastic solid.

Wavefront expansions for pulse scattering by a surface inhomogeneity

Much recent interest has arisen in the coupled dynamics of fluid-solid interfaces, mainly with regard to the use of the acoustic microscope as a valuable technique for material characterization and the detection of surface, and subsurface, flaws; there is also interest in structural acoustics and geophysical applications. The majority of recent work has dealt with time-harmonic waves; in this paper solutions for transient disturbances are developed and analysed in detail. The resulting fluid and solid responses are found in closed form allowing specific wavefronts to be identified and explicit results are given. Wavefront expansions for the head waves and cylindrical wave in the fluid are found explicitly together with the disturbance generated by the leaky Rayleigh wave; these are the dominant fluid responses detected experimentally and such exact solutions will be of value. The limit of light fluid loading is examined separately; it is shown that the leading-order fluid-solid results are reconstructed by considering simpler problems where the fluid loading is taken to be absent. An unambiguous interpretation of the disturbance in the fluid created by the leaky Rayleigh wave is given in this light fluid-loading limit.

Scattering by objects at fluid/solid interfaces

Canonical diffraction and scattering problems involving fluid/elastic solid interfaces are solved exactly using the Wiener–Hopf technique; the farfield directivities are explicitly identified. When fluid loading is light, there are regions of nonuniform behavior and intense beam formation that occur. In addition, an heuristic method is devised that partly decouples the fluid and solid responses. This leads to accurate results in the light fluid loading limit and allows one to utilize some results directly from elastodynamic problems solved when the fluid is absent.