Prediction by power flow methods of shunt and series damping in building structures

By use of power flow techniques an assessment is made of the effect of damping on the vibrational energy of concrete plates which form a T-junction.The vibrational energies are predicted from knowledge of the loss factors, coupling loss factors, and radiation loss factors which were assessed theoretically and experimentally. Theoretical predictions are compared with measurements.It is seen that a damping layer, as well as reducing the bending wave energy on the plate to which it is applied, will, to a lesser extent, reduce that on other plates which form a common junction. The magnitude of this effect is predicted and measured.     

On the quality of plate reverberation

Metallic plates are used in recording studios to create artificial reverberation. In this paper, the flexural vibrations of such plates are analysed in order to better understand the influence of geometry and materials on the quality of plate reverberation. A comparison is made with acoustic reverberation, both in the time and frequency domain. This comparison is supported by objective criteria such as modal density and density of reflections. From a physical point of view, the internal and external damping mechanisms are examined in detail since they determine the frequency dependence of the reverberation time. Theoretical results are validated through comparison with experiments performed on an EMT140 reverberation plate. The underlying model is aimed at developing numerical simulations of plates (virtual reverberators) allowing a large variety of reverberations based on variations of geometry and materials as input parameters.     

Vibration and damping analysis of multilayered rectangular plates with constrained viscoelastic layers

Governing equations of motion for vibrations of a general multilayered plate consisting of an arbitrary number of alternate stiff and soft layers of orthotropic materials are derived by using variational principles. Extension, bending and in-plane shear deformations in stiff layers and only transverse shear deformations in soft layers are considered as in conventional sandwich structural analysis. In addition to transverse inertia, longitudinal translatory and rotary inertias are included, as such analysis gives higher order modes of vibration and leads to accurate results for relatively thick plates. Vibration and damping analysis of rectangular simply supported plates consisting of alternate elastic and viscoelastic layers is carried out by taking a series solution and applying the correspondence principle of linear viscoelasticity. The damping effectiveness, in term of the system loss factor, for all families of modes for three-, five- and seven-layered plates is evaluated and its variations with geometrical and material property parameters are investigated.     

Prediction of total loss factors of structures Part III: Effective loss factors in quasi-transient conditions

Previous work has been done on the prediction of the total loss factors of structures in steady state [1]. In this paper, the effective loss factors of coupled structures in quasi-transient conditions are considered, which are thought to be important parameters in the prediction of ringing noise radiated from impacting machines. SEA is used and Maidanik's arguments [2] are re-examined in analysis and discussion. A series of measurements have been carried out on two coupled plates (i.e., a structure having two substructures) and a randomly chosen complicated structure. An equation derived from the two coupled substructures model is used to estimate the effective loss factors of the two coupled plates. Good agreement is obtained between the estimated and measured values.     

水下隔声结构设计及评价方法

为使用混响法快捷地测量水下结构物的辐射噪声,需基于港口或海岸建造海上混响水池。针对内外都是水情况下的海上混响水池壁面隔声问题,设计了一种带梁空气夹层板水下隔声结构,通过仿真比较了不同参数的空气夹层板的隔声性能。为评价声波无规入射情况下水下大尺寸隔声结构隔声性能,提出了一种混响评价方法,通过隔声实验比较了混响法与脉冲法的不同。结果表明：带梁空气夹层板的水下隔声性能优异,声波无规入射情况下,面板厚度0.015 m、空气层厚度0.020 m的带梁空气夹层板在2～10 kHz频段插入损失大于20 dB;混响法可以有效评价大尺寸水下隔声结构的平均隔声性能,其反映的声波无规入射的平均隔声性能更接近于实际应用情况。     

Transmission of low-frequency internal sound through pipe walls

Transmission loss measurements are reported for long steel pipes of circular crosssection, with air inside and out, excited by internal sound. At low frequencies (wavelength greater than the pipe diameter), most of the radiated sound is accounted for by pipe bending waves. In order to approach the much higher transmission loss predicted for pure breathing motion of the pipe, bending waves must be suppressed; this has been achieved for a straight pipe by careful isolation. A sharp 90 bend in the pipe is shown to cause significant bending-wave excitation when plane waves are incident on the bend.     

Point mobility of a cylindrical plate incorporating a tapered hole of power-law profile

The paper describes the results of experimental measurements of point mobility carried out on circular plates containing tapered holes of quadratic power-law profile with attached damping layers. The obtained results are compared to the developed numerical model, as a means of validation. The profiles of the tapered hole in the plates are designed to replicate near zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation, also known as acoustic black hole effect. The driving point mobility measurements are provided, showing a comparison of the results for a constant thickness circular plate, a constant thickness plate with a layer of damping film applied and a plate with a quadratic power-law profile machined into the center, which is tested with a thin layer of elastic damping material attached. The results indicate a substantial suppression of resonant peaks, agreeing with a numerical model, which is based on the analytical solution available for the vibration of a plate with a central quadratic power-law profile. The paper contains results for the case of free boundary conditions on all edges of the plates, with emphasis placed on the predictions of resonant frequencies and the amplitudes of vibration and loss factor.     

Thermoelastic damping in torsion microresonators with coupling effect between torsion and bending

Predicting thermoelastic damping (TED) is crucial in the design of high Q MEMS resonators. In the past, there have been few works on analytical modeling of thermoelastic damping in torsion microresonators. This could be related to the assumption of pure torsional mode for the supporting beams in the torsion devices. The pure torsional modes of rectangular supporting beams involve no local volume change, and therefore, they do not suffer any thermoelastic loss. However, the coupled motion of torsion and bending usually exists in the torsion microresonator when it is not excited by pure torque. The bending component of the coupled motion causes flexural vibrations of supporting beams which may result in significant thermoelastic damping for the microresonator. This paper presents an analytical model for thermoelastic damping in torsion microresonators with the coupling effect between torsion and bending. The theory derives a dynamic model for torsion microresonators considering the coupling effect, and approximates the thermoelastic damping by assuming the energy loss to occur only in supporting beams of flexural vibrations. The thermoelastic damping obtained by the present model is compared to the measured internal friction of single paddle oscillators. It is found that thermoelastic damping contributes significantly to internal friction for the case of the higher modes at room temperature. The present model is validated by comparing its results with the finite-element method (FEM) solutions. The effects of structural dimensions and other parameters on thermoelastic damping are investigated for the representative case of torsion microresonators.     

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.     

Practical industrial method of increasing structural damping in machinery,I: Squeeze-film damping with air

There is frequently a need to reduce sound radiation due to resonant flexural motion of stiff machinery panels. This can be achieved by applying squeeze-film damping to the vibrating panel by attaching an auxiliary plate parallel to the surface, thereby trapping a thin layer of air. Relative vibration of the plates pumps this air at high velocities, resulting in energy loss due to the air viscosity. In this study the damping below the critical frequency of the “thick plate” with an “attached plate” and air layer has been investigated by using an impedance approach. This model is incorporated into a two element Statistical Energy Analysis (SEA) model to predict the damping well above the critical frequency of the thick plate. The agreement between the predicted and measured results is remarkably good. Below the critical frequency the damping is pumping controlled, while above critical the plate couplings are the controlling factor.     

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.     

Calculation of the sound transmission between dwellings by partitions and flanking structures

A calculation model is presented for the sound transmission between dwellings by partitions and by flanking structures, based on the application of classical theory.The most important data needed are the sound reduction index for direct transmission of the different structures and the vibration level differences across junctions. Information on the reduction index is given, based on theory, taking into account the influence of boundary conditions by means of the structural reverberation time in situ. The vibration level differences have been determined for different junctions on the basis of in situ measurements. Under some—reasonable—restrictions this model gives the same results as would be achieved by applying the so-called Statistical Energy Analysis (SEA).Comparison between calculation and measurement for seventy-five different situations shows good agreement, the average predictions being correct with a standard deviation of 1·5 dB.     

Prediction of total loss factors of structures,I: Theory and experiments

A method for calculating the total loss factors of a complex structure has been derived by using Statistical Energy Analysis (SEA). The derived formulae have been simplified on the assumption that coupling between substructures except for the measured substructure is very weak. In two limiting situations, “damping addition” formulae have been obtained. The formula has been applied to predict the total loss factors of a steel box and these results are compared with actual experimental measurements. The agreement between estimated and measured values was in most cases quite good.     

Prediction of airborne sound transmission across a timber–concrete composite floor using Statistical Energy Analysis

This paper concerns the development and experimental validation of prediction models using Statistical Energy Analysis (SEA) to calculate the airborne sound insulation of a timber–concrete composite floor. The complexity in modelling this floor is due to it having (1) a multilayer upper plate formed from concrete and Oriented Strand Board (OSB), (2) multiple types of rigid connector between the upper plate and the timber joists and (3) a resiliently suspended ceiling. A six-subsystem model treats the concrete–OSB plate as a single subsystem and three different five-subsystem models treat the combination of concrete, OSB and timber joists as a single orthotropic plate subsystem. For the orthotropic plate it is suggested that bending stiffnesses predicted using the theories of Huffington and Troitsky provide a more suitable and flexible approach than that of Kimura and Inoue. All SEA models are able to predict the weighted sound reduction index to within 2 dB of the measurement. The average difference (magnitude) between measurements and predictions in one-third octave bands is up to 4 dB. These results confirm that SEA can be used to model direct transmission across relatively complex floor constructions. However, this requires the inclusion of measured data in the SEA model, namely the dynamic stiffness of the resilient isolators and the cavity reverberation time.     

The measurement of sound transmission at structural junctions by an impulse method

With short duration impulsive signals used to provide the excitation the vibration level difference across a T-junction of Perspex plates has been measured both as a function of frequency and angle of incidence. Problems associated with high velocity waves and relatively short path differences have been reduced or eliminated by suitable choice of material and geometry, and by use of spatial as well as temporal averaging. Problems associated with the dispersive nature of bending waves have been reduced by use of low pass filtering. Results are presented for point source excitation and comparison is made with plane wave excitation theory. In addition, plane wave excitation has been simulated by means of line averages of the plate response to a point source and these results are also presented and compared with the theoretical ones.     

Mechanics and finite elements for the damped dynamic characteristics of curvilinear laminates and composite shell structures

Integrated mechanics and a finite element method are presented for predicting the damping of doubly curved laminates and laminated shell composite structures. Damping mechanics are formulated in curvilinear co-ordinates from ply to structural level and the structural modal loss factors are calculated using the energy dissipation method. The modelling of damping at the laminate level is based on first order shear shell theory. An eight-node shell damping finite element is developed. Comparisons of the present model with classical and discrete layer laminate damping theory predictions are shown. Modal damping and natural frequencies of composite plates and open cylindrical shells were measured and correlated with predicted results. Parametric studies illustrate the effect of curvature and lamination on modal damping and natural frequency.     

光子晶体光纤弯曲损耗特性研究

对光子晶体光纤的损耗特性进行了分析,并在实验上对两种典型的光子带隙型和全内反射型光子晶体光纤进行了研究.分别对两种不同结构的光子晶体光纤在弯曲半径2~15 mm范围内的损耗进行了测量.与传统光纤损耗实验结果的对比表明,两种光子晶体光纤的弯曲损耗均不明显,具有很强的抗弯曲损耗能力.实验也证实了光子晶体光纤弯曲损耗存在临界弯曲半径,在大于临界半径的情况下,几乎没有弯曲损耗.从结构上分析并证明光子晶体光纤弯曲损耗随填充比(d/Λ)的增加而减小,填充比越高弯曲损耗越小.     

The influence of random drift of resonance-scattering harmonics on the frequency spectrum of surface acoustic reverberation in the ocean

We propose a modified model for the frequency spectrum of surface reverberation with allowance for random drift of Bragg resonance harmonics due to long wind-generated waves. The dependence of this effect on the parameters of large-scale surface waves is analyzed. Analytical expressions for the reverberation frequency spectrum are obtained for both narrow-band and wideband sounding signals. It is shown that for matched filtering of wideband signals, the considered effect leads to an increase in the effective pulse reverberation volume. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 1, pp. 20–30, January 2007.     

Vibration of L-shaped plates under a deterministic force or moment excitation: a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary.