Noise transmission from a curved panel into a cylindrical enclosure: analysis of structural acoustic coupling

Much of the research on sound transmission through the aircraft fuselage into the interior of aircraft has considered coupling of the entire cylinder to the acoustic modes of the enclosure. Yet, much of the work on structural acoustic control of sound radiation has focused on reducing sound radiation from individual panels into an acoustic space. Research by the authors seeks to bridge this gap by considering the transmission of sound from individual panels on the fuselage to the interior of the aircraft. As part of this research, an analytical model of a curved panel, with attached piezoelectric actuators, subjected to a static pressure load was previously developed. In the present work, the analytical model is extended to consider the coupling of a curved panel to the interior acoustics of a rigid-walled cylinder. Insight gained from an accurate analytical model of the dynamics of the noise transmission from the curved panels of the fuselage into the cylindrical enclosure of an aircraft is essential to the development of feedback control systems for the control of stochastic inputs, such as turbulent boundary layer excitation. The criteria for maximal structural acoustic coupling between the modes of the curved panel and the modes of the cylindrical enclosure are studied. For panels with aspect ratios typical of those found in aircraft, results indicate that predominately axial structural modes couple most efficiently to the acoustic modes of the enclosure. The effects of the position of the curved panel on the cylinder are also studied. Structural acoustic coupling is found to not be significantly affected by varying panel position. The impact of the findings of this study on structural acoustic control design is discussed.     

Reduction of sound transmission into a circular cylindrical shell using distributed vibration absorbers and Helmholtz resonators

A modal expansion method is used to model a cylindrical enclosure excited by an external plane wave. A set of distributed vibration absorbers (DVAs) and Helmholtz resonators (HRs) are applied to the structure to control the interior acoustic levels. Using an impedance matching method, the structure, the acoustic cavity, and the noise reduction devices are fully coupled to yield an analytical formulation of the structural kinetic energy and acoustic potential energy of a treated cylindrical cavity. Lightweight DVAs and small HRs tuned to the natural frequencies of the targeted structural and acoustic modes, respectively, result in significant acoustic and structural attenuation when the devices are optimally damped. Simulations show that significant interior noise reduction can only be achieved by adding damping to both structural and acoustic modes, which are resonant in the frequency bandwidth of interest. In order to be independent of the azimuth angle of the excitation and to avoid unwanted modal interactions, the devices are distributed evenly around the cylinder in rings. This treatment can only achieve good performance if the structure and the acoustic cavity are lightly damped.     

Modeling of offshore pile driving noise using a semi-analytical variational formulation

Underwater noise radiated from offshore pile driving got much attention in recent years due to its threat to the marine environment. This study develops a three-dimensional semi-analytical method, in which the pile is modeled as an elastic thin cylindrical shell, to predict vibration and underwater acoustic radiation caused by hammer impact. The cylindrical shell, subject to the Reissner–Naghdi’s thin shell theory, is decomposed uniformly into shell segments whose motion is governed by a variational equation. The sound pressures in both exterior and interior fluid fields are expanded as analytical functions in frequency domain. The soil is modeled as uncoupled springs and dashpots distributed in three directions. The sound propagation characteristics are investigated based on the dispersion curves. The case study of a model subject to a non-axisymmetric force demonstrates that the radiated sound pressure has dependence on circumferential angle. The case study including an anvil shows that the presence of the anvil tends to lower the frequencies and the amplitudes of the peaks of sound pressure spectrum. A comparison to the measured data shows that the model is capable of predicting the pile driving noise quantitatively. This mechanical model can be used to predict underwater noise of piling and explore potential noise reduction measures to protect marine animals.     

Comparison of various decentralised structural and cavity feedback control strategies for transmitted noise reduction through a double panel structure

This paper compares various decentralised control strategies, including structural and acoustic actuator–sensor configuration designs, to reduce noise transmission through a double panel structure. The comparison is based on identical control stability indexes. The double panel structure consists of two panels with air in between and offers the advantages of low sound transmission at high frequencies, low heat transmission, and low weight. The double panel structure is widely used, such as in the aerospace and automotive industries. Nevertheless, the resonance of the cavity and the poor sound transmission loss at low frequencies limit the double panel's noise control performance. Applying active structural acoustic control to the panels or active noise control to the cavity has been discussed in many papers. In this paper, the resonances of the panels and the cavity are considered simultaneously to further reduce the transmitted noise through an existing double panel structure. A structural–acoustic coupled model is developed to investigate and compare various structural control and cavity control methods. Numerical analysis and real-time control results show that structural control should be applied to both panels. Three types of cavity control sources are presented and compared. The results indicate that the largest noise reduction is obtained with cavity control by loudspeakers modified to operate as incident pressure sources.     

Vibro-acoustic behaviors of an elastically restrained double-panel structure with an acoustic cavity of arbitrary boundary impedance

An analytical study on the vibro-acoustic behaviors of a double-panel structure with an acoustic cavity is presented. Unlike the existing studies, a structural–acoustic coupling model of an elastically restrained double-panel structure with an acoustic cavity having arbitrary impedance on sidewalls around the cavity is developed in which the two dimensional (2D) and three dimensional (3D) modified Fourier series are used to represent the displacement of the panels and the sound pressure inside the cavity, respectively. The unknown expansions coefficients are treated as the generalized coordinates and the Rayleigh–Ritz method is employed to determine displacement and sound pressure solutions based on the energy expressions for the coupled structural–acoustic system. The effectiveness and accuracy of the present model is validated by numerical example and comparison with finite element method (FEM) and existing analytical method, with good agreement achieved. The influence of key parameters on the vibro-acoustic behaviors and sound transmission of the double-panel structure is investigated, including: cavity thickness, boundary conditions, sidewall impedance, and the acoustic medium in the cavity.     

Simulative and experimental investigations on pressure-induced structural vibrations of a rear muffler

The periodically blown out exhaust gas of a combustion engine may excite structural vibrations of the exhaust system. In addition to the noise of the orifice, these vibrations contribute to the overall noise radiation of the exhaust system. In this work, the excitation of structural vibrations of a rear muffler via the acoustic path is investigated both in experiments and simulations. In both cases transfer functions from the acoustic pressure at the inlet to the structural deflection on the surface of the rear muffler are determined and compared to each other. For the simulation an FE-FE (finite element) coupling is applied to account for the fluid-structure interaction. To efficiently predict the fluid-structure coupled behavior, a model reduction technique for the finite element method based on the Craig-Bampton method and the Rubin method is presented. In a last step, the sound radiation is evaluated by solving the exterior acoustic problem with the fast multipole boundary element method. For this purpose, the results of the FE computation are used as boundary datum.     

Acoustic signature of a submarine hull under harmonic excitation

The structural and acoustic responses of a submarine under harmonic force excitation are presented. The submarine hull is modelled as a cylindrical shell with internal bulkheads and ring stiffeners. The cylindrical shell is closed by truncated conical shells, which in turn are closed at each end using circular plates. The entire structure is submerged in a heavy fluid medium. The structural responses of the submerged vessel are calculated by solving the cylindrical shell equations of motion using a wave approach and the conical shell equations with a power series solution. The far-field radiated sound pressure is then calculated by means of the Helmholtz integral. The contribution of the conical end closures on the radiated sound pressure for the lowest circumferential mode numbers is clearly observed. Results from the analytical model are compared with computational results from a fully coupled finite element/boundary element model.     

The identification of tyre induced vehicle interior noise

Sound transmission into a vehicle is classified as either airborne or structure borne sound. From the point view of noise control, the reduction of noise transferred by different paths requires different solutions. Coherence function analysis is often used to identify transmission paths. However it can be difficult to separate the airborne from structure borne components. The principle of acoustic reciprocity offers a convenient method for overcoming this difficulty. The principal states that the transfer function between an acoustic volume velocity source and an acoustic receiver is independent of a reversal of the position of source and receiver. The work done on this study involves exciting a stationary tyre and measuring the surface velocity of the tyre at a number of discrete points. The acoustic transfer functions between each point on the tyre and a receiver point are measured reciprocally. Two sets of measurements are then combined to yield a measure of the sound pressure due to a point force on the tyre via the acoustic transmission path only. This technique also provides information on the relative contributions of various regions of the tyre wall to the resultant noise. Also the sound radiation characteristics, the horn effect, and resonance at the wheel housing are identified through the reciprocal measurement.     

内部体积源作用下的圆柱壳内外声场特性

圆柱壳内各型体积源辐射噪声特性研究是声场建模和声场预报的前提.为了研究具有指向性的大尺度体积源特性对水下航行器结构内外声场的影响,本文结合薄壳理论、等效源和柱腔Green函数构造了体积源激励下的壳体振动耦合方程,研究了体积源表面声散射作用和指向性强弱对圆柱壳内外声场的影响.数值计算结果表明,体积源构造的准确性与其等效源位置有关,等效源配置在体积源几何中心与其结构表面之间0.4—0.6时,可以提高声场计算结果的准确性;大尺度体积源表面的声散射作用会导致壳体内部声场结构发生改变,内声场声腔共振峰发生偏移,并且在部分频段引起较强的声透射现象;此外,体积源指向性变化对壳体内外声场强弱影响较小,其显著作用表现在改变了外辐射声场的远场指向性.该研究结果对噪声预报和控制有一定的参考价值.     

Effects of cavity resonances on sound transmission into a thin cylindrical shell

In the context of the transmission of airborne noise into an aircraft fuselage, a mathematical model is presented for the effects of internal cavity resonances on sound transmission into a thin cylindrical shell. The “noise reduction” of the cylinder is defined and computed, with and without including the effects of internal cavity resonances. As would be expected, the noise reduction in the absence of cavity resonances follows the same qualitative pattern as does transmission loss. Numerical results show that cavity resonances lead to wide fluctuations and a general decrease of noise reduction, especially at cavity resonances. Modest internal absorption is shown to greatly reduce the effect of cavity resonances. The effects of external airflow, internal cabin pressurization, and different acoustical properties inside and outside the cylinder are also included and briefly examined.     

Sound transmission through layered cylindrical shells with applied damping treatment

Sound transmission through closed circular cylindrical shells with unconstrained damping treatment and sandwich shells with constrained damping treatment is considered in an acoustoelastic formulation in which the full interaction between the structural vibration and the internal cavity pressure field are taken into account. Only the axisymmetric modes of vibration of the shell are considered in an initial formulation. The structural response and the sound transmission characteristics for an external random pressure field are computed through an efficient matrix inversion procedure. Results indicate insensitivity of noise reduction and structural response to variations in core parameters of the sandwich shell. The sandwich shell has better noise transmission characteristics in the higher frequency ranges as compared to an equivalent layered shell with unconstrained damping treatment.     

On sound transmission into a thin cylindrical shell under “flight conditions”

In the context of the transmission of airborne noise into an aircraft fuselage, a mathematical model for sound transmission into a thin cylindrical shell is used to study sound transmission under “flight conditions”: i.e., under conditions of external air flow past a pressurized cylinder at flight altitude. Numerical results for different incidence angles are presented for a typical narrow-bodied jet in cruising flight at 10 660 m (35 000 ft) with interior pressure at 2440 m (8000 ft). A comparison is made between no-flow sound transmission at standard conditions on the ground to sound transmission under flight conditions. It is shown that at M = 0, the cylinder transmission loss has dips at f_R (cylinder ring frequency) and f_c (critical frequency for a flat panel of same material and thickness as shell). Below f_R cylinder resonances affect TL. Between f_R and f_c, cylinder TL follows a masslaw behavior. Flow provides a modest increase in TL in the mass-law region, and strongly interacts with the cylinder resonances below f_R. For normally-incident waves, TL is unaffected by flow.     

矢量拖线阵水听器流噪声响应特性

针对传统拖线阵流噪声理论的局限性, 建立了完善的矢量拖线阵流噪声理论分析方法, 可全面准确地揭示矢量拖线阵流噪声响应特性. 基于细长圆柱的湍流边界层压力起伏Carpenter模型, 采用波数-频率谱分析方法对矢量拖线阵流噪声响应特性进行了理论研究, 导出了圆柱形矢量水听器流噪声响应的声压和振速自功率谱及其互功率谱的解析表达式, 定量分析了流噪声响应功率谱与拖曳速度、水听器尺寸、套管尺寸和材料等参数之间变化规律; 另外, 还讨论了圆柱形矢量水听器偏离护套轴线时矢量拖线阵流噪声响应, 导出了流噪声响应的声压、径向和轴向振速自功率谱及其互功率谱的解析表达式, 数值计算结果表明: 轴线偏移距离对声压和轴向振速的高频噪声的影响要大于对低频噪声的影响, 而对径向振速的全频段噪声都有明显影响, 且对振速分量影响要远大于对声压影响.     

Analytical prediction of break-out noise from a reactive rectangular plenum with four flexible walls

This paper describes an analytical calculation of break-out noise from a rectangular plenum with four flexible walls by incorporating three-dimensional effects along with the acoustical and structural wave coupling phenomena. The breakout noise from rectangular plenums is important and the coupling between acoustic waves within the plenum and structural waves in the flexible plenum walls plays a critical role in prediction of the transverse transmission loss. The first step in breakout noise prediction is to calculate the inside plenum pressure field and the normal flexible plenum wall vibration by using an impedance-mobility approach, which results in a compact matrix formulation. In the impedance-mobility compact matrix (IMCM) approach, it is presumed that the coupled response can be described in terms of finite sets of the uncoupled acoustic subsystem and the structural subsystem. The flexible walls of the plenum are modeled as an unfolded plate to calculate natural frequencies and mode shapes of the uncoupled structural subsystem. The second step is to calculate the radiated sound power from the flexible walls using Kirchhoff-Helmholtz (KH) integral formulation. Analytical results are validated with finite element and boundary element (FEM-BEM) numerical models.     

The surface variational principle applied to an acoustic cavity.

This paper presents the development and application of the Surface Variational Principle (SVP) for the evaluation of axisymmetric interior acoustic domains. The interior form of the SVP is first developed in the same manner as the existing exterior form. Then, the surface pressure and normal velocity are represented with a Ritz expansion using basis functions that span the entire wetted surface of the object of interest. The resultant formulation is used to analyze the interior acoustic response of a harmonically forced, right circular elastic cylinder. This validation model was chosen as both the structural and acoustic responses can be solved analytically. Results are presented for two models: one with a length to radius ratio of 2.4, and another with a ratio of 12.3. The SVP is shown to well reproduce the analytical solution for this geometry, and displays the asymptotic convergence expected of its variational formulation. The SVP formulation developed here is not restricted to right-circular cylindrical geometries, and may, indeed, be readily applied to any axisymmetric body.     

Acoustic transmission analysis on cavity resonance sound in a cylindrical cavity system: application to a Korean bell

This paper presents an analytical model for acoustic transmission characteristics of a cylindrical cavity system representing the acoustic resonance conditions of a Korean bell. The cylindrical cavity system consists of an internal cavity, a gap, an auxiliary cavity, and a rigid base. Since the internal cavity is connected to the external field through a gap, determination of the acoustic transmission characteristics becomes a coupling problem between the internal cavity and external field. The acoustic field of the internal cavity is considered by expanding the solution method of the mixed boundary problem, and the external field is addressed by modifying the radiation impedance model of a finite cylinder. The analytical model is validated by comparison with both experiment and a boundary element method. Using the analytical model, the resonance conditions are determined to maximize the resonance effect. Thus, the resonance frequencies of the bell cavity system are investigated according to the gap size and auxiliary cavity depth. By adjusting gap size or auxiliary cavity depth, the cavity resonance frequency is tuned to resonate partial tones of the bell sound. Finally, the optimal combination of gap size and auxiliary cavity depth is determined.     

Acoustic radiation from shear deformable stiffened laminated cylindrical shells

An analytical model of acoustic radiation from shear deformable laminated cylindrical shells with initial axial loadings and doubly periodic rings is presented. The shear deformation and rotary inertia of the rings are taken into account and the rings interact with the cylindrical shell only through the normal forces. The far-field sound pressure is found by using the Fourier wavenumber transform and stationary phase method. High frequency limitation issues of the first-order shear deformation theory are discussed and the effects of the second set of rings, axial initial loadings and multiple external loadings on the far-field acoustic radiation are explored. Further, the helical wave spectra of the radial displacement and sound pressure are used to study the vibrational and acoustic characteristics of the laminated shells. Above the ring frequency, the profile of the helical wave spectra of the far-field sound pressure induced by the cylindrical shell is an ellipse and the patterns of the helical wave spectra of the far-field sound pressure keep unchanged. Moreover, the ellipse distinguishes the supersonic wavenumbers and subsonic wavenumbers from the helical wave spectra of the radial displacement and surface sound pressure in the wavenumber domain. The bright spots and highlights of the helical wave spectra show that the corresponding waves are dominant.     

部分浸没圆柱壳声固耦合计算的半解析法研究

部分浸没圆柱壳-流场耦合系统的声振分析是一种典型的半空间域内声固耦合问题,其振动及声学计算目前主要依赖于数值方法求解,但无论从检验数值法还是从机理上揭示其声固耦合特性,解析或半解析方法的发展都是不可或缺的.本文提出了一种半解析方法,先将声场坐标系建立在自由液面上,采用正弦三角级数来满足自由液面上的声压释放边界条件;接着基于二维Flügge薄壳理论建立了以圆柱圆心为坐标原点的壳-液耦合系统的控制方程;然后再利用Galerkin法处理声固耦合界面的速度连续条件,推导得到声压幅值与壳体位移幅值之间的关系矩阵并求解该耦合系统的振动和水下声辐射.与有限元软件Comsol进行了耦合系统自由、受迫振动和水下辐射噪声计算结的对比分析,表明本文方法准确可靠.本文的研究为解析求解弹性结构与声场部分耦合的声振问题提供了新的思路.     

Coupled FEM/BEM for control of noise radiation and sound transmission using piezoelectric shunt damping

In this paper, we present a coupled finite element/boundary element method (FEM/BEM) for control of noise radiation and sound transmission of vibrating structure by passive piezoelectric techniques. The system consists of an elastic structure (with surface mounted piezoelectric patches) coupled to external/internal acoustic domains. The passive shunt damping strategy is employed for vibration attenuation in the low frequency range. The originality of the present paper lies in evaluating the classically used FEM/BEM methods for structural–acoustics problems when taking account smart systems at the fluid–structure interfaces.