The effect of the structure-borne sound transmission between panel and stud via screw connections for a double leaf partition

In additional to the screw connection affecting the sound transmission characteristics of the panel-stud partition,the spacing of screws is also considered as a factor in predicting the sound insulation of the partition.It can be modeled either as a series of independent point connections,or as a line connection depending on the screw spacing.For small screw spacing,the connection between panel and stud can be treated as a line connection,from which a higher sound transmission effect can be achieved.Whilst for a larger screw spacing,it can be treated as an independent point connection,from which a lesser sound transmission through the partition can be achieved accordingly.The distinction between these two kinds of connection is also related to the frequency.Usually,half bending wavelength of a panel will be treated as a distinct frequency.Experimental results of double leaf partition with diverse screw spacing significantly demonstrated their influences on sound reduction.Some prediction methods for partitions with different screw spacing are also reviewed in this paper.It should be noted that the impact of screw spacing effecting on the sound insulation of partitions of wood stud and light-weight metal stud is different.     

Non-resonant sound transmission through double walls using statistical energy analysis

Although SEA is a suitable framework for predicting sound transmission through double walls it has been found that the standard method of computing the non- resonant coupling loss factor from a room to cavity underestimates the coupling. A revised model for computing this coupling loss factor is presented which gives much better agreement with measured data. This allows better predictions to be made of sound transmission through lightweight double walls.     

Sound transmission through finite lightweight multilayered structures with thin air layers

The sound transmission loss (STL) of finite lightweight multilayered structures with thin air layers is studied in this paper. Two types of models are used to describe the vibro-acoustic behavior of these structures. Standard transfer matrix method assumes infinite layers and represents the plane wave propagation in the layers. A wave based model describes the direct sound transmission through a rectangular structure placed between two reverberant rooms. Full vibro-acoustic coupling between rooms, plates, and air cavities is taken into account. Comparison with double glazing measurements shows that this effect of vibro-acoustic coupling is important in lightweight double walls. For infinite structures, structural damping has no significant influence on STL below the coincidence frequency. In this frequency region, the non-resonant transmission or so-called mass-law behavior dominates sound transmission. Modal simulations suggest a large influence of structural damping on STL. This is confirmed by experiments with double fiberboard partitions and sandwich structures. The results show that for thin air layers, the damping induced by friction and viscous effects at the air gap surfaces can largely influence and improve the sound transmission characteristics.     

Analytical evaluation of the acoustic insulation provided by double infinite walls

The acoustic insulation provided by infinite double panel walls, when subjected to spatially sinusoidal line pressure loads, is computed analytically. The methodology used extends earlier work by the authors on the definition of the acoustic insulation conferred by a single panel wall. It does not entail any simplification other than the assumption that the panels are of infinite extent. The full interaction between the fluid (air) and the solid layers is thus taken into account and the calculation does not involve limiting the thickness of any layer, as the Kirchhoff or Mindlin theories require. The problem is first formulated in the frequency domain. Time domain solutions are then obtained by means of inverse Fourier transforms using complex frequencies.The model is first used to compute the sound reduction provided by a double homogeneous brick wall, with identical panels, when illuminated by plane sound waves. The results are then compared with those provided by the simplified method proposed by London, which was later extended by Beranek (London-Beranek method). The limitations of the simplified London-Beranek model, namely, its applicability only to double walls with identical mass, subjected to plane waves, and its failure to account for the coincidence effect, are overcome by the method proposed.Time signatures are produced to illustrate the different sound transmission mechanisms. Several types of body and guided waves are originated, giving rise to a complex dynamic system with multiple reflections within the solid and fluid layers and the global resonance of the system. The effect of the cavity absorption is considered by attributing a complex density to the air filling the space between the two wall panels. Absorption attenuates the dips of insulation controlled by the cavity resonances. Several simulations are then performed for different combinations of wall and air layer thickness to assess the influence of this variable on the final acoustic insulation. The influence of the air cavity on sound reduction was found to be dependent on the frequency. At low frequencies a better performance was achieved for thicker air layers, while at higher frequencies a thinner air layer is preferable. The use of wall panels with different mass resulted in the wall performing better, particularly for high frequencies.     

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.     

The finite layer method for modelling the sound transmission through double walls

The finite layer method (FLM) is presented as a discretisation technique for the computation of noise transmission through double walls. It combines a finite element method (FEM) discretisation in the direction perpendicular to the wall with trigonometric functions in the two in-plane directions. It is used for solving the Helmholtz equation at the cavity inside the double wall, while the wall leaves are modelled with the thin plate equation and solved with modal analysis. Other approaches to this problem are described here (and adapted where needed) in order to compare them with the FLM. They range from impedance models of the double wall behaviour to different numerical methods for solving the Helmholtz equation in the cavity. For the examples simulated in this work (impact noise and airborne sound transmission), the former are less accurate than the latter at low frequencies. The main advantage of FLM over the other discretisation techniques is the possibility of extending it to multilayered structures without changing the interpolation functions and with an affordable computational cost. This potential is illustrated with a calculation of the noise transmission through a multilayered structure: a double wall partially filled with absorbing material.     

Experimental estimation of the transmission loss contributions of a sound package placed in a double wall structure

The objective of this paper is to propose a practical impedance tube method to optimize the sound transmission loss of double wall structure by concentrating on the sound package placed inside the structure. In a previous work, the authors derived an expression that breakdown the transmission loss of a double wall structure containing a sound absorbing blanket separated from the panels by air layers in terms of three main contributions; (i) sound transmission loss of the panels, (ii) sound transmission loss of the blanket and (iii) sound absorption due to multiple reflections inside the cavity. The sound transmission loss contributions of the blanket can thus be estimated from three acoustic measurements using impedance tube techniques: two reflection coefficients at the front face and the rear face of the blanket placed in specific positions characteristic of its position inside the double wall structure and its sound transmission coefficient. The method is first validated in the case of a double wall structure filled with a 2 in. foam material. Next, it is applied to investigate (i) the effect of frame compression of a 2 in. fibre glass in an aeronautic-type double wall structure and (ii) the effect of double porosity with or without porous inclusions in a building-type double wall structure.     

Sound insulation of double-leaf walls - Allowing for studs of finite stiffness in a transfer matrix scheme

In a recent paper by the present author the effect of finite structural connections on the sound reduction index of double walls was predicted by modifying a model based on the transfer matrix technique. However, the model did not include any means to account for the flexibility of the studs; they were assumed to be of infinite stiffness. Based on data for the effective stiffness of flexible steel studs, the model is extended to take account of this flexibility. A number of comparisons are performed, mainly with the measured sound reduction index of lightweight double walls with gypsum boards. Cases include walls with cavity filling as well as with empty (air-filled) cavities. In the latter cases, the energy losses of the cavity are simulated using a model of a porous layer with a minute flow resistivity. Predicted results compare favourably with measurement results. It is assumed that different basic types of studs, i.e. other than the TC-type simulated here may successfully be included in the model.     

Mechanism and calculation of the niche effect in airborne sound transmission

The goal is to interpret and calculate the "niche effect" for the airborne sound transmission through a specimen mounted inside an aperture in the wall between the source and receiving reverberation rooms. The low-frequency sound insulation is known to be worse for the specimen placed at the center than for the specimen mounted at either edge of the aperture. As shown, the aperture with a tested specimen can be simulated at low frequencies as a triple partition where the middle element is the specimen and the role of the edge leaves is played by the air masses entrained at the aperture edges. With a centrally located specimen, such a triple system is symmetric and has two main natural frequencies close together. In this case, the resonant transmission is higher than for the edge arrangement simulated as a double system with one natural frequency. Analogous resonant phenomena are known to reduce the low-frequency transmission loss for symmetric triple windows or solid walls with identical air gaps and lightweight boards on both sides. The theoretical results obtained for the mechanical and acoustical models are in a good agreement with the experimental data.     

An analytical study of sound transmission through unbounded panels of functionally gradedmaterials

The problem of sound transmission and reflection from unbounded panels of functionally graded materials is studied using an analytical approach. By means of matrix manipulation and Fourier component analysis, the three-dimensional (3-D) governing equations of elastodynamics are converted into a system of ordinary differential equations with variable coefficients in the frequency and wavenumber domain. Integration of the ordinary differential equation system across the panel thickness leads to a closed-form solution for the transfer matrix. Analytical expressions are then obtained for sound reflection and transmission coefficients for panels of functionally graded materials. The present model is used to predict sound transmission losses for various panel examples. The results compare well with published data from other methods, thereby validating the accuracy of the formulation developed in this study.     

腔体内传输线耦合的电磁仿真软件与传输线方程的混合算法

研究了一种有限积分法软件与传输线方程相结合的混合算法,用于解决复杂电磁环境下屏蔽腔体内传输线的电磁耦合问题。利用有限积分法软件实现屏蔽腔体的建模,仿真得到腔体内部空间电磁场分布,并设置电场探针提取出传输线的激励场。利用传输线方程建立腔体内传输线的耦合模型,将得到的传输线激励场引入到传输线方程作为等效分布电压和电流源。利用时域有限差分(FDTD)格式对传输线方程进行离散,从而迭代求解出传输线终端负载上的电压和电流响应。通过与文献以及传统数值算法的计算结果进行对比,验证混合算法的正确性。研究表明,该混合算法在模拟电大尺寸腔体内传输线的电磁耦合方面,具有较高的精度和计算效率。     

Sound transmission at low frequencies through the walls of distorted circular ducts

A theoretical treatment of sound transmission through the walls of distorted circular ducts is given, for plane mode transmission within the duct. The transmission mechanism is essentially that of “mode coupling”, whereby higher structural modes in the duct walls are excited, because of the wall distortion, by the internal sound field. The theory is in two parts: an approximate analytical model for the structural response of the walls to the internal sound field, and a structural radiation model. Computed results, based on the theory, are compared to measurements on “long-seam” air conditioning ducts. Where the duct geometry can be reliably specified, reasonably good agreement is obtained between theoretical and experimental data. It is concluded that mode coupling effects serve to account for the discrepancies between ideal and observed behaviour in sound transmission through duct walls.     

Prediction of sound flanking transmission through two adjacent rooms within a residence building

Flanking transmission has significant effects on the overall sound insulation of two adjacent rooms within a residence building. This study investigates the mechanism of the sound flanking transmission by dividing it into several subsystems with the statistical energy analysis method. The sound energy equations of these subsystems are obtained first, and then,the sound transmissions on each flanking path are predicted and the dominant sound transmission path is determined by solving these equations and calculating the total loss factors of the subsystems and coupling loss factors between subsystems. With respect to a masonry building with heavy-weight homogeneous structure, the results show that:(1) the flanking transmission paths instead of the separating wall may become the dominant ones at low frequencies;(2) all sound transmissions on the flanking paths tend to be consistent at medium and high frequencies, so the sound insulation between two adjacent rooms depends on the direct path of the separating wall;(3) heavy-weight separating walls can be used to reduce the frequency range of the flanking transmission.     

Low frequency acoustic transmission through the walls of rectangular ducts

A simple theory is described for the transmission of low frequency sound through the walls of rectangular ducts, particularly those in air conditioning systems. The model is based on a coupled acoustic/structural wave system, and it is assumed that the duct radiates in the same way as a finite-length line source incorporating a single travelling wave. Measurements of wall transmission loss on two types of duct system are compared to theoretical predictions, and good agreement is obtained within the frequency range of validity of the theory. It is concluded that the present approach should give reliable estimates of noise transmission in practical situations.     

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.     

An improved transmission line laser model for multimode laser diodes incorporating thermal effects

An improved transmission line model to study the thermal effects in semiconductor laser diodes is reported in this paper. The temperature effects in the laser characteristics are obtained by incorporating temperature dependent gain and carrier density equations for the laser cavity. These primary factors are introduced in the regular transmission line laser model to estimate the static and dynamic characteristics of an 1.3μm InGaAsP double heterostructure laser diode. The results show good agreement with the experimental observation and solution of rate equations referred in the literature. The key feature of this model is that it provides the laser spectra at various temperatures. Based on the model, time dependent evolution of optical spectrum, temperature dependent optical output and frequency chirp are evaluated. Further the distribution of photon and electron density within the cavity is also determined.     

Estimation method for parameters of construction on predicting transmission loss of double leaf dry partition

For improving sound insulation of a double leaf dry partition, each leaf is often consisted of more than one panel. Previous study on predicting a transmission loss of double leaf partition, treats with the leaf varied just two kinds of panels and restricted to a leaf having same kind and same thickness. These restrictions are unfit for variety of current building materials and constructions. This study makes a prediction formula for a transmission loss of the double leaf partition with laminated leaves by a theoretical analysis and an experiment, and will discuss the predicted value with measured value in previous studies and catalogs.     

An empirical model for the equivalent translational compliance of steel studs

The effect of the resilience of the steel studs on the sound insulation of steel stud cavity walls can be modeled as an equivalent translational compliance in simple models for predicting the sound insulation of walls. Recent numerical calculations have shown that this equivalent translational compliance varies with frequency. This paper determines the values of the equivalent translational compliance of steel studs which make a simple sound insulation theory agree best with experimental sound insulation data for 126 steel stud cavity walls with gypsum plaster board on each side of the steel studs and sound absorbing material in the wall cavity. These values are approximately constant as a function of frequency up to 400 Hz. Above 400 Hz they decrease approximately as a non-integer power of the frequency. The equivalent translational compliance also depends on the mass per unit surface area of the cladding on each side of the steel studs and on the width of the steel studs. Above 400 Hz, this compliance also depends on the stud spacing. The best fit approximation is used with a simple sound insulation prediction model to predict the sound insulation of steel stud cavity walls whose sound insulation has been determined experimentally.     

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.     

A deterministic model of impact noise transmission through structural connections based on modal analysis

Vibration transmission through structural connections is modelled in a deterministic way by means of modal analysis. This model is used first to study the effect of elastic joints across the floor in the transmission of impact noise. They are an effective means of reducing impact noise propagation, and can almost eliminate it for small values of the joint stiffness. The method is also used to study the acoustic relevance of studs in lightweight floor transmission. Different ways of modelling the studs are presented and compared. For the examples developed, the best option is to use springs for modelling the studs rather than more complex models involving springs and beams. Also the different behaviour of point and line connections is verified, as well as the influence of the position of the studs.