High frequency vibration energy transfer in a system of three plates connected at discrete points using statistical energy analysis

Vibration energy transfer in a system of three plates separated by a small distance and connected at a few discrete points, like solar panels in a spacecraft, is investigated. Coupling loss factors are obtained experimentally using the power injection technique. The system is then subjected to the acoustic excitation in a reverberant chamber. The measured responses of the inner plate are significant. But the measured responses of the inner plates are higher than the responses estimated based on the coupling loss factors obtained. When the system is subjected to mechanical excitation the measured responses of the inner plate closely match with the estimated responses. The difference is perhaps due to the sound radiated from the outer plates not being considered for the calculation, requiring further studies.     

A hybrid SEA/modal technique for modeling structural-acoustic interior noise in rotorcraft

This paper describes a hybrid technique that combines Statistical Energy Analysis (SEA) predictions for structural vibration with acoustic modal summation techniques to predict interior noise levels in rotorcraft. The method was applied for predicting the sound field inside a mock-up of the interior panel system of the Sikorsky S-92 helicopter. The vibration amplitudes of the frame and panel systems were predicted using a detailed SEA model and these were used as inputs to the model of the interior acoustic space. The spatial distribution of the vibration field on individual panels, and their coupling to the acoustic space were modeled using stochastic techniques. Leakage and nonresonant transmission components were accounted for using space-averaged values obtained from a SEA model of the complete structural-acoustic system. Since the cabin geometry was quite simple, the modeling of the interior acoustic space was performed using a standard modal summation technique. Sound pressure levels predicted by this approach at specific microphone locations were compared with measured data. Agreement within 3 dB in one-third octave bands above 40 Hz was observed. A large discrepancy in the one-third octave band in which the first acoustic mode is resonant (31.5 Hz) was observed. Reasons for such a discrepancy are discussed in the paper. The developed technique provides a method for modeling helicopter cabin interior noise in the frequency mid-range where neither FEA nor SEA is individually effective or accurate.     

Effectiveness of T-shaped acoustic resonators in low-frequency sound transmission control of a finite double-panel partition

Double-panel partitions are widely used for sound insulation purposes. Their insulation efficiency is, however, deteriorated at low frequencies due to the structural and acoustic resonances. To tackle this problem, this paper proposes the use of long T-shaped acoustic resonators in a double-panel partition embedded along the edges. In order to facilitate the design and assess the performance of the structure, a general vibro-acoustic model, characterizing the interaction between the panels, air cavity, and integrated acoustic resonators, is developed. The effectiveness of the technique as well as the optimal locations of the acoustic resonators is examined at various frequencies where the system exhibits different coupling characteristics. The measured optimal locations are also compared with the predicted ones to verify the developed theory. Finally, the performance of the acoustic resonators in broadband sound transmission control is demonstrated.     

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.     

On the growth rate of bending induced edge cracks in acoustically excited panels

Parts of an aircraft structure may be made to vibrate as a result of acoustic waves generated by various aircraft noise sources impinging on the structure. The stresses associated with this acoustically induced vibration may be sufficiently large to result in fatigue failure of portions of the structure. If acoustically induced fatigue cracks occur in the stiffened skin structures widely used in aircraft construction they may initiate in the skin panels near the stiffener attachment points. The initiation and subsequent propagation of these cracks at the panel edges is primarily due to the bending stresses arising from the out-of-plane vibration of the individual skin panels.The emphasis of the work described in this paper is on examining the growth rate of edge cracks in acoustically excited panels. A single panel with an edge crack is considered and this structural element is modelled as a flat plate clamped on three edges and part of the fourth. The crack is represented by the unclamped part of the fourth edge. Fracture mechanics principles are used to predict the crack growth rates associated with the first two modes of vibration of the edge cracked panel. The crack tip stress intensity factors associated with these panel modes are estimated by a technique based on finding the nominal bending stresses at the crack tips. The nominal bending stresses are in turn found from mode shapes determined by the Rayleigh Principle. The validity of the various assumptions is assessed by comparing the predicted crack growth rates with measured growth rates in panels representative of those used in aircraft construction.     

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.     

接触缺陷的振动调制超声导波检测技术研究

针对常规线性超声检测方法无法实现板结构接触类缺陷(如微裂纹、脱粘等)检测问题,将超声导波技术与振动声调制技术相结合,利用稀疏分布传感器发展了一种板结构中接触缺陷非线性超声检测方法。通过低频振动改变缺陷的接触状况,使得通过接触面的高频导波信号的相位和幅值受到调制。对受低频振动调制的超声导波二维时间序列进行时频分析,由于接触类缺陷的存在,在振动调制超声导波序列的时频分布上出现明显的低频振动频率分量。利用提取出的低频振动频率下的超声导波信号,进行了结构接触缺陷成像处理。检测试验表明,基于振动声调制的超声导波缺陷成像方法可以实现结构中的接触类缺陷检测。      

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.     

On linear modeling of interface damping in vibrating structures

Dissipation of mechanical vibration energy at contact interfaces in a structure, commonly referred to as interface damping, is an important source of vibration damping in built-up structures and its modeling is the focus of the present study. The approach taken uses interface forces which are linearly dependent on the relative vibration displacements at the contact interfaces.The main objective is to demonstrate a straightforward technique for simulation of interface damping in built-up structures using FE modeling and simple, distributed, damping forces localized to interfaces where the damping occurs.As an illustration of the resulting damping the dissipated power is used for evaluation purposes. This is calculated from surface integrals over the contact interfaces and allows for explicit assessment of the effect of simulated interface forces for different cases and frequencies. The resulting loss factor at resonance is explicitly evaluated and, using linear simulations, it is demonstrated that high damping levels may arise even though the displacement differences between contacting surfaces at damped interfaces may be very small.     

Power flow boundary element analysis for multi-domain problems in vibrational built-up structures

A power flow boundary element methodology for the treatment of multi-domain problems is developed to predict the vibrational responses of coupled structures in medium-to-high frequency ranges. In the proposed methodology, a matrix equation is formulated by utilizing the power flow coupling relationships at the interface of the domains. This analysis method is successfully applied to the treatment of simply supported coupled beams and coupled plates. The vibration analysis of these structures is then considered for all wave components. The vibrational energy density and intensity of two coupled structures obtained through numerical simulations are compared with those of the original power flow analysis, and these results show good agreement.     

Sound transmission loss of foam-filled honeycomb sandwich panels using statistical energy analysis and theoretical and measured dynamic properties

Comparisons between the experimental and predicted sound transmission loss values obtained from statistical energy analysis are presented for two foam-filled honeycomb sandwich panels. Statistical energy analysis (SEA) is a modeling procedure which uses energy flow relationships for the theoretical estimation of the sound transmission through structures in resonant motion. The accuracy of the prediction of the sound transmission loss using SEA greatly depends on accurate estimates of: (1) the modal density, (2) the internal loss factor, and (3) the coupling loss factor parameters of the structures. A theoretical expression for the modal density of sandwich panels is developed from a sixth-order governing equation. Measured modal density estimates of the two foam-filled honeycomb sandwich panels are obtained by using a three-channel spectral method with a spectral mass correction to allow for the mass loading of the impedance head. The effect of mass loading of the accelerometer is corrected in the estimations of both the total loss factor and radiation loss factor of the sandwich panels.     

Vibration localization of simplified mistuned cyclic structures undertaking external harmonic force

Critical fatigue problems often occur in mistuned cyclic structures since their forced vibration responses are often much larger than those of perfectly tuned structures. Therefore, it is of great importance to predict the forced vibration responses of mistuned cyclic structures for their safe and reliable designs. In this paper, a simplified model for mistuned cyclic structures is chosen to investigate vibration localization phenomena. The effects of mistuning, stiffness coupling, and damping on the variations of maximum forced vibration responses of the model are examined through numerical study. It is found that strong vibration localization occurs under certain relations among mistuning, stiffness coupling, and damping. It is also found that the maximum forced vibration response asymptotically increases as the number of repeated subcomponents of the cyclic structure increases.     

Analysis of the causes of formation of negative loss factors

I-IatroductionStatisticalEnergyAnalysis(SEA)isakindofeffective,simpleanddirectapproachforan-alyzingvibrationandsound,andithasbeenfoundwidelyapplicationsinanalysisofmechanicalnoiseandvibrationcolltrolsince198osl1-4].However,forgeneralindustrialmachineswhichalwayconsistofcomPlexandheaVystructures,thedeterminationmethodsofSEAparametersintheclassicalSEAtheoryareinapplicable[5]because:(1)SEAparametersofthesekindsofstructuresaredifficulttoobtainfromthetheory(2)theconditionofconservativeandweak…     

Frequency average loss factors of plates and shells

This paper describes a thorough investigation of the measurement of frequency band average loss factors of structural components for use in the statistical energy analysis (SEA) method of computation of vibration levels. The “traditional” method of measurement is to excite the structure by a random force having a flat spectral density in the frequency band of interest. The force is then cut off and the decay of the modes excited in the band is noted. The average loss factor is deduced from the decay curve. The alternative energy method is the subject of this study. In this test the power input from the band limited random force is measured and the spatial average vibration level of the structure is estimated from several surface accelerometers. It is shown that when the modes in the band have similar loss factors (as is usually the case) the energy method gives a result which is very close to that obtained from the decay method. These in turn are close to the arithmetic average of the loss factors of the individual modes in the band. It is shown that only when the band contains one or two very lightly damped modes amongst several more heavily damped modes is there a difference between the two methods. In this case it is better to use the energy result in the SEA calculations.     

Sound insulation provided by single and double panel walls—a comparison of analytical solutions versus experimental results

The predicted values for acoustic insulation of single and double panel walls, using analytical models previously developed by the authors, are compared with experimental findings. The analytical method used fully takes into account the coupling between the air and the solid panels, and there is no restriction on their thickness, as the Kirchhoff or Mindlin approaches require. The laboratory experiments involved placing test specimens between standard chambers. Results are presented for panels made of glass, concrete and steel. From the results we can conclude that the predictive analytical solutions are in good agreement with the experimental results, except when the area of the panels is very small and the frequencies are very low. At low frequencies, the experimental results appear to be significantly affected by the resonance effects associated with the creation of stationary waves within the acoustic chambers, and the vibration modes introduced into the dynamic system by the restriction on the movement of the panel along its boundary.     

Predistortion techniques for synthesizing coupled microring filters with loss

A general method based on the predistortion technique is presented for determining the optimum coupling parameters of multiple-coupled microring filters in the presence of known uniform resonator loss. The technique involves predistorting the filter transfer function by shifting its poles and zeros to compensate for loss in the microring resonators due to material absorption, surface roughness scattering, coupling loss and bending loss. It is shown that by sacrificing some in-band insertion loss, both the amplitude and group delay responses of the filter can be recovered when loss is present. Application of the method to synthesizing lossy microring filters in both the digital z-domain and analog s-domain will be presented. The proposed technique is general in that it can be applied to both amplitude and phase filters constructed of coupled microresonators in the most general two-dimensional coupling topology.     

Structural-acoustic finite element analysis of the automobile passenger compartment: A review of current practice

This paper contains a brief review of the formulation of the finite element method for structural-acoustic analysis of an enclosed cavity, and illustrations are given of the application of this analytical method at General Motors Corporation to investigate the acoustics of the automobile passenger compartment. Low frequency noise in the passenger compartment (in approximately the 20–200 Hz frequency range) is of primary interest, and particularly that noise which is generated by the structural vibration of the wall panels of the compartment. The topics which are covered in the paper include the computation of acoustic modes and resonant frequencies of the passenger compartment, the effect of flexible wall panels on the cavity acoustics, the methods of direct and modal coupling of the structural and acoustic vehicle systems, and forced vibration analysis illustrating the techniques for computing panel-excited noise and for identifying critical panels around the passenger compartment. The capabilities of the finite element method are illustrated by applications to the production automobile, and experimental verifications of the various techniques are presented to illustrate the accuracy of the method.     

高温超导悬浮系统的振动属性研究

本文研究了YBCO高温超导磁悬浮系统在竖直方向上不同的悬浮高度,不同的振动频率扰动下的振动属性．研究表明在一般的小的扰动下,悬浮系统类似于一个弹簧系统,该系统可以恢复到初始的悬浮高度．而当系统受到一个共振频率的扰动时,系统会发生剧烈的振动,会引起能量的损失,悬浮高度的降低．系统的共振频率会随着系统初始悬浮高度的降低而增...     

An efficient model of an equipment loaded panel for active control design studies

An effective investigation of alternative control strategies for the reduction of vibration levels in satellite structures requires realistic, yet efficient, structural models to simulate the dynamics of the system. These models should include the effects of the sources, receivers, supporting structure, sensors, and actuators. In this paper, a modeling technique which meets these requirements is developed and some active control strategies are briefly investigated. The particular subject of investigation is an equipment-loaded panel and the equations of motion are derived using the Lagrange-Rayleigh-Ritz (LRR) approach. The various pieces of equipment on the panel are mounted on active or passive suspensions, and resonators are used to represent the internal dynamics of the mounted equipment. Control of the panel, which transmits vibrations from sources to receivers, is by means of piezoelectric patches and the excitation consists of dynamic loads acting on the equipment enclosures and/or directly on the panel. The control objective is to minimize the displacement at an arbitrary output location. The LRR model developed is verified against one produced by using the finite-element method. Finally, some initial controller design studies are undertaken to investigate and compare the effectiveness of different control strategies (e.g., minimization at the source, along the vibration path, or at the receiver).     

Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators

In this paper, the incremental finite element equations for geometric non-linear analysis of piezoelectric smart structures are developed using a total Lagrange approach by using virtual velocity incremental variational principles. A four-node first order shear plate element model with reduced and selective integration is also developed. Geometrically non-linear transient vibration response and control of plates with piezoelectric patches subjected to pulse loads are investigated. Active damping is introduced on the plates by coupling a self-sensing and negative velocity feedback algorithm in a closed control loop. The numerical results show that piezoelectric actuators can introduce significant damping and suppress transient vibration effectively. The effects of the number and locations of the piezoelectric actuators on the control system are also discussed.