Predicting the vibroacoustic response of satellite equipment panels

Modern satellites are constructed of large, lightweight equipment panels that are strongly excited by acoustic pressures during launch. During design, performing vibroacoustic analyses to evaluate and ensure the integrity of the complex electronics mounted on the panels is critical. In this study the attached equipment is explicitly addressed and how its properties affect the panel responses is characterized. FEA and BEA methods are used to derive realistic parameters to input to a SEA hybrid model of a panel with multiple attachments. Specifically, conductance/modal density and radiation efficiency for nonhomogeneous panel structures with and without mass loading are computed. The validity of using the spatially averaged conductance of panels with irregular features for deriving the structure modal density is demonstrated. Maidanik's proposed method of modifying the traditional SEA input power is implemented, illustrating the importance of accounting for system internal couplings when calculating the external input power. The predictions using the SEA hybrid model agree with the measured data trends, and are found to be most sensitive to the assumed dynamic mass ratio (attachments/structure) and the attachment internal loss factor. Additional experimental and analytical investigations are recommended to better characterize dynamic masses, modal densities and loss factors.     

Assessment of sandwich models for the prediction of sound transmission loss in unidirectional sandwich panels

The consistent higher-order approach and the two-parameter foundation formulation are used for the derivation of sound transmission loss in symmetric unidirectional (infinitely wide) sandwich panels with isotropic face sheets. In both models, transmission loss is calculated using decoupled equations representing symmetric and anti-symmetric motions of a sandwich panel. The closed-form expressions for impedances and transmission coefficient of a symmetric sandwich panel with an isotropic core are derived for the two-parameter foundation model. A comparison between the numerical predictions based on the two sandwich models and available experimental data shows that the consistent higher-order formulation can be used to predict the transmission loss in symmetric sandwich panels with both honeycomb and isotropic cores. For prediction of transmission loss of symmetric sandwich panels with an isotropic core, the two-parameter foundation model is more convenient, while the consistent higher-order approach is more accurate.     

金属蜂窝夹芯结构抗水下冲击性能

为揭示高强度水下爆炸冲击载荷作用下金属夹芯结构的抗冲击性能,在实验室开展小尺寸水下爆炸加载技术对金属蜂窝夹芯结构性能影响的实验研究。基于实验结果,开展了全尺寸数值模拟金属蜂窝夹芯结构在水下冲击载荷作用下的动态响应和抗冲击性能研究。结果表明,数值模拟、实验和理论模型计算的结果具有良好的一致性。由于蜂窝芯材相对密度对夹芯结构能量耗散方式和载荷传递机制的影响,结构动态响应、失效模式以及抗冲击性能随着冲击强度的变化表现出较为明显的不同。通过抗冲击参数分析,建立了反映金属蜂窝夹芯结构抗冲击性能的结构横向变形、固支反力、透射脉冲和塑性能耗随冲击强度和芯材相对密度变化的结构-载荷-性能量化关系。     

Analytical Study on the Rate of Sound Transmission Loss in Single Row Honeycomb Sandwich Panel Using a Numerical Method

Honeycomb structures have recently, replaced with conventional homogeneous materials. Given the fact that sandwich panels containing a honeycomb core are able to adjust geometric parameters, including internal angles, they are suitable for acoustic control applications. The main objective of this study was to obtain a transmission loss curve in a specific honeycomb frequency range along with same overall dimensions and weight. In this study, a finite element model (FEM) in ABAQUS software was used to simulate honeycomb panels, evaluate resonant frequencies, and for acoustic analysis. This model was used to obtain acoustic pressure and then to calculate the sound transmission loss (STL) in MATLAB software. Vibration and acoustic analysis of panels were performed in the frequency range of 1 to 1000 Hz. The models analyzed in this design includes 14-single row-honeycomb designs with angles of −45°, −30°, −15°, 0°, +15°, +30°, +45°. The results showed that a-single row and −45°cell angle honeycomb panel in the frequency range of 1 to 1000 Hz had the highest STL as well as the highest number of frequency modes (90 mods). Furthermore, the panel had the highest STL regarding the area under the STL curve (dB∙Hz). The panels containing more frequency mods, have a higher transmission loss. Moreover, the sound transmission loss is more sensitive to the cell angle variable (θ). In other studies, the STL was more sensitive to the number of honeycomb cells in the horizontal and vertical directions, as well as the angle of cells.     

Sound transmission across lightweight all-metallic sandwich panels with corrugated cores

The transmission of sound through all-metallic sandwich panels with corrugated cores is investigated using the space-harmonic method. The sandwich panel is modeled as two parallel panels connected by uniformly distributed translational springs and rotational springs, with the mass of the core sheets taken as lumped mass. Based on the periodicity of the panel structure, a unit cell model is developed to provide the effective translational and rotational stiffness of the core. To check the validity of the model, it is used first to study the sound insulation properties of double-panel structures with air cavity, and the analytical predictions agree well with existing experimental data. The model is then employed to quantify the influence of sound incidence angle and the inclination angle between facesheet and core sheet on sound transmission loss （STL） across sandwich panels with corrugated cores. The results show that the inclination angle has a significant effect on STL and it is possible to avoid STL dips by altering the inclination angle. Moreover, it is found that sandwich panels with corrugated cores are more suitable for the insulation of sound waves having small incidence angles.     

STATISTICAL ENERGY ANALYSIS OF COUPLED PLATE SYSTEMS WITH LOW MODAL DENSITY AND LOW MODAL OVERLAP

Finite element methods, experimental statistical energy analysis (ESEA) and Monte Carlo methods have been used to determine coupling loss factors for use in statistical energy analysis (SEA). The aim was to use the concept of an ESEA ensemble to facilitate the use of SEA with plate subsystems that have low modal density and low modal overlap. An advantage of the ESEA ensemble approach was that when the matrix inversion failed for a single deterministic analysis, the majority of ensemble members did not encounter problems. Failure of the matrix inversion for a single deterministic analysis may incorrectly lead to the conclusion that SEA is not appropriate. However, when the majority of the ESEA ensemble members have positive coupling loss factors, this provides sufficient motivation to attempt an SEA model. The ensembles were created using the normal distribution to introduce variation into the plate dimensions. For plate systems with low modal density and low modal overlap, it was found that the resulting probability distribution function for the linear coupling loss factor could be considered as lognormal. This allowed statistical confidence limits to be determined for the coupling loss factor. The SEA permutation method was then used to calculate the expected range of the response using these confidence limits in the SEA matrix solution. For plate systems with low modal density and low modal overlap, relatively small variation/uncertainty in the physical properties caused large differences in the coupling parameters. For this reason, a single deterministic analysis is of minimal use. Therefore, the ability to determine both the ensemble average and the expected range with SEA is crucial in allowing a robust assessment of vibration transmission between plate systems with low modal density and low modal overlap.     

Low frequency sound insulation using stiffness control with honeycomb panels

A new honeycomb core design has been used to increase the stiffness of the panel and applied to improve the noise transmission loss at frequencies between 100 and 200 Hz. A model is presented to predict the transmission loss of the honeycomb panels based on the structural modal parameters. A new test specimen with fiber reinforced plastic cores and face sheets had been used to investigate the effect of stiffness and damping on noise transmission loss. The measurements of noise transmission loss have been compared with data for common structural panels. The results show that the new core fabrication techniques using moulding to improve the noise transmission are effective. In comparison to a cement panel of the same mass, the honeycomb panels have higher TL at low frequencies between 100 and 200 Hz due to higher stiffness and damping. The honeycomb panels have more significant vibration responses above 500 Hz but these are limited by damping.     

Optimal design of acoustical sandwich panels with a genetic algorithm

An optimization study is performed to design a sandwich panel with a balance of acoustical and mechanical properties at minimal weight. An acoustical model based on higher-order sandwich beam theory is used with mechanical analysis of the maximum deflection at the center of the sandwich panel under a concentrated force. First, a parametric study is performed to determine the effects of individual design variables on the sound transmission loss of the sandwich panel. Next, by constraining the acoustical and mechanical behavior of the sandwich panel, the area mass density of the sandwich panel is minimized using a genetic algorithm. The sandwich panels are constructed from eight face-sheet and sixteen core materials, with varying thicknesses of the face sheets and the core. The resulting design is a light-weight, mechanically efficient sound insulator with strength and stiffness comparable to sandwich structures commonly used in structural applications.     

Sound transmission prediction by 3-D elasticity theory

The problem of sound transmission through layered panel structures is studied with the exact theory of three-dimensional (3-D) elasticity. The exact solution to the 3-D elasticity equations is obtained by the use of the Fourier spectral method. Based on this analytical solution, a transfer matrix is derived that relates the spectral displacements and stresses on the one surface of the panel to those on the opposite panel surface. The transfer matrix is then used to develop the analytical solutions for sound reflection and transmission coefficients. Explicit, concise expressions are obtained for the analytical solutions of the acoustic transmission and reflection coefficients under the general conditions of layered anisotropic panels. Examples are given for both single-layer and sandwich panels. Predictions on sound transmission from the 3-D elasticity theory are compared with available data from other methods, and the results are discussed.     

非对称夹芯板隔声量的解析计算模型及影响因素

提出了一种计算上下面板非对称的三明治夹芯板隔声性能的方法.通过对非对称夹芯梁表观抗弯曲刚度的计算,得到对应夹芯板随频率变化的表观抗弯刚度,代入4阶的控制方程,应用模态展开法可以方便地计算简支非对称夹芯板的隔声量.对4种定制的3层非对称碳纤维夹芯板进行了理论计算和实验测试对比,在频率范围100～3150Hz内,计权隔声量...     

SEA and contribution analysis for interior noise of a high speed train

This paper presents a detailed Statistical Energy Analysis (SEA) and contribution analysis of the interior noise of a high-speed train through extensive simulations and measurements. The SEA model was developed based on the actual geometrical parameters of a benchmark high-speed coach. Sound transmission loss levels of the structural components of the car body, which are required in the SEA model, were tested in a dedicated acoustic laboratory following international standard ISO 140-3:1995. Modal densities of these structural components were derived from measured frequency response functions using the modal counting method. Damping loss factors were obtained using the half-power bandwidth method and the vibration attenuation method. By considering the relationship between sound radiation and power transmission, coupling loss factors between structures and cavities were estimated. Source inputs to the SEA model were derived from field experiment data. Interior noise due to those sources was predicted using the SEA model and the prediction was generally in good agreement with measurement. Contribution analysis was then performed using this validated model through parametric study, and this analysis was further examined experimentally. In conclusion, for the coach that was investigated in this paper, the key factors for interior noise are sidewall vibration, bogie area noise, and floor sound transmission loss. Based on this and other engineering considerations, an interior noise control strategy can be defined.     

基于散射矩阵法的飞机壁板声学优化设计

采用散射矩阵法分析夹层板结构声学特性,并对典型的夹层板结构即飞机壁板进行声学优化,预计飞机壁板隔声特性,获得蒙皮、隔声隔热层、内饰板及它们的组合结构的声学性能。针对尾吊飞机客舱后部噪声过大问题,通过增加铺设隔热隔声层以及部分区域优化安装阻尼层等一系列被动降噪处理方法,对主要传递路径的飞机壁板结构进行优化,降低客舱后部噪声水平,并进行试验验证。试验结果表明:散射矩阵法可快速准确获得夹层结构的隔声性能,并与混响室法测试结果吻合较好;在厚度不变的前提下,改变隔热隔声层的铺设方式和材料密度对壁板隔声性能影响较小,但在蒙皮内侧粘贴阻尼层能在一定频段范围提高壁板隔声性能;将优化的壁板构型应用到飞机后舱段侧壁板,舱内噪声水平可降低约3 dB。     

Wave speeds of honeycomb sandwich structures: An experimental approach

In this study, the influence of different design parameters, such as core density, core material, and cell size on the wave speeds of honeycomb sandwich structures was experimentally analyzed. Bending and shear wave speeds were measured and related to the transmission loss performance for various material configurations. The shear modulus of the core showed maximum influence on the wave speeds of the samples, while cell size did not have a significant influence on the wave speeds or on the transmission loss. Skin material affected wave speeds only in the pure bending regime. Honeycomb sandwich structures with a subsonic core and reduced wave speed showed increased transmission loss compared to samples without a subsonic core.     

Comparison of decentralized velocity feedback control for thin homogeneous and stiff sandwich panels using electrodynamic proof-mass actuators

Theoretical and experimental work is presented to compare the effect of decentralised velocity feedback control on thin homogeneous and sandwich panels. The decentralised control system consists of five control units, which are composed of a proof-mass electrodynamic actuator with an accelerometer underneath its footprint and an analogue controller. The stability of the feedback loops is analysed by considering the sensor-actuator open-loop frequency response function of each control unit and the eigenvalues of the fully populated matrix of open-loop frequency response functions between the five sensors and five actuators. The control performance is then analysed in terms of the time-averaged total kinetic energy and total sound power radiated by the two panels. The results show that for a stiff sandwich panel higher stable feedback gains can be implemented than on a thin homogeneous panel of comparable weight per unit area. Moreover the implementation of decentralised velocity feedback can offset some of the undesirable sound transmission properties of lightweight sandwich structures by efficiently reducing structural vibration and sound power radiation in the mid audio frequency range.     

Local feedback control of light honeycomb panels

This paper summarizes theoretical and experimental work on the feedback control of sound radiation from honeycomb panels using piezoceramic actuators. It is motivated by the problem of sound transmission in aircraft, specifically the active control of trim panels. Trim panels are generally honeycomb structures designed to meet the design requirement of low weight and high stiffness. They are resiliently mounted to the fuselage for the passive reduction of noise transmission. Local coupling of the closely spaced sensor and actuator was observed experimentally and modeled using a single degree of freedom system. The effect of the local coupling was to roll off the response between the actuator and sensor at high frequencies, so that a feedback control system can have high gain margins. Unfortunately, only relatively poor global performance is then achieved because of localization of reduction around the actuator. This localization prompts the investigation of a multichannel active control system. Globalized reduction was predicted using a model of 12-channel direct velocity feedback control. The multichannel system, however, does not appear to yield a significant improvement in the performance because of decreased gain margin.     

Dynamic and acoustic response of bidirectionally stiffened plates with eccentric stiffeners subject to airborne and structure-borne excitations

An analytical method based on the modal expansion technique was developed to predict the vibro-acoustic response of both unidirectionally and bidirectionally stiffened flat panel. This paper presents the response to diffuse acoustic field (DAF) and turbulent boundary layer (TBL) excitations in terms of their joint acceptance. Numerical results for the dynamic and acoustic responses are compared with finite element method (FEM) and boundary element (BEM) results for stiffened panel with complex and eccentrically shaped stiffeners subject to point force excitation. A theoretical prediction of the transmission loss (TL) is also compared with laboratory measurements conducted on flat panels representing aircraft models as well as with hybrid statistical energy analysis (SEA)-FEM periodic model. The results confirm that the stiffened panel has the same acoustic response as the skin without stiffeners at frequencies where the structural wavelengths are equal to the spacing between the stiffeners. In addition, the transmission loss is lowered by the presence of the stiffeners at some particular region of frequencies below the critical frequency with respect to the unstiffened panel.     

Extension of SEA model to subsystems with non-uniform modal energy distribution

In order to widen the application of statistical energy analysis (SEA), a reformulation is proposed. Contrary to classical SEA, the model described here, statistical modal energy distribution analysis (SmEdA), does not assume equipartition of modal energies.Theoretical derivations are based on dual modal formulation described in Maxit and Guyader (Journal of Sound and Vibration 239 (2001) 907) and Maxit (Ph.D. Thesis, Institut National des Sciences Appliquées de Lyon, France 2000) for the general case of coupled continuous elastic systems. Basic SEA relations describing the power flow exchanged between two oscillators are used to obtain modal energy equations. They permit modal energies of coupled subsystems to be determined from the knowledge of modes of uncoupled subsystems. The link between SEA and SmEdA is established and make it possible to mix the two approaches: SmEdA for subsystems where equipartition is not verified and SEA for other subsystems.Three typical configurations of structural couplings are described for which SmEdA improves energy prediction compared to SEA: (a) coupling of subsystems with low modal overlap, (b) coupling of heterogeneous subsystems, and (c) case of localized excitations.The application of the proposed method is not limited to theoretical structures, but could easily be applied to complex structures by using a finite element method (FEM). In this case, FEM are used to calculate the modes of each uncoupled subsystems; these data are then used in a second step to determine the modal coupling factors necessary for SmEdA to model the coupling.     

自由阻尼复合板的模态密度研究

模态密度是统计能量分析（SEA）的一个重要参数,尽管有关阻尼复合板振动特性的文献很多,便至今为止,研究其模态密度及变化规律的论文尚未见到,为此本文利用弹性最小势能原理和变分法,并考虑振动阻尼的影响,导出了自由阻尼复合板的弯曲振动模态密度计算公式,系统地分析了模态密度随阻尼层厚度、温度和频率而变化的规律。     

复材结构刚度与隔声量的计算及参数优化

论文旨在满足结构刚度指标的前提下最大程度地提高复合材料(以下简称“复材”)结构的隔声性能。首先针对复材结构进行刚度分析，在铺层数和铺层比例不变的前提下，分析不同铺层构型对结构刚度的影响。然后利用统计能量分析法，确定铺层角度对结构隔声性能的影响，并与试验结果进行对比验证模型的有效性。最后以铺设在复材壁板上的隔音棉厚度和密度为两个优化参数，分析不同厚度和密度的隔音棉的插入损失，并进行参数最优化分析，寻找最佳组合方式。得出结论：不同铺设角度顺序对复材整体结构的弯曲刚度和吻合效应频率有影响，在相同尺寸和边界条件下，构型1屈曲稳定性承载能力较强，隔声效果最好，铺层方式最优；隔音棉密度对插入损失影响较小，而隔音棉厚度对插入损失影响较大。论文选取的隔音棉密度和厚度已经使壁板、隔音棉及内饰板的组合结构隔声量达到了收敛状态，是最优化的组合设计。     

Analysis of the sound transmission loss of panels with resonant systems on the basis of equivalent representations

Effects of increasing the sound transmission loss of panels with the help of resonant systems on the basis of equivalent representations are analyzed. Emphasis is placed on the least-studied resonant systems, the inertial bodies of which simultaneously interact with media on each side of the panels. A universal expression for the sound transmission loss of panels with an arbitrary system of resonant elements with one degree of freedom is presented. It includes the parameters common to all types of resonators (the total mass, compressibility, quality factor, and characteristic frequencies). The expression can be directly used to compare the efficiency of different types of resonant systems mounted on a panel and to determine their optimum parameters.