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.     

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.     

Sound transmission through a double panel structure periodically coupled with vibration insulators

In this paper, sound transmission through an aircraft sidewall representative double panel structure is investigated theoretically and parametric and validation studies are conducted. The studied configuration is composed of a trim panel (receiver side panel) attached to a ribbed skin panel (source side panel) with periodically spaced resilient mounts. The structure is considered infinite in order to use space harmonic expansion. The partition is also assumed planar for simplicity. The model allows for a 3D incident field and the panels can be metallic and/or composite. A four-pole formulation is employed for modeling of the mounts and the absorption provided by the fiberglass that fills the cavity between the leaves is addressed with an equivalent fluid model. The investigation of mount stiffness, damping and spacing show that properly designed mounts can increase the TL significantly (up to 20 dB of difference between rigid and resilient mounts). However, they can create undesirable resonances resulting from their interaction with the panels. The influence of cavity absorption is also studied and results illustrate the fact that it is not worth investing in a highly absorbent fiber if the structure-borne transmission path is not adequately insulated, and likewise that it is not worth investing in highly resilient mounts without sufficient cavity absorption. Moreover, the investigation of panel damping confirms that when structure-borne transmission is present, raising skin damping can increase the TL even below coincidence, but that on average, greater improvements are achieved by raising trim damping. Finally, comparison between the periodic model and finite element simulations for structure-borne transmission shows that the average level of transmitted energy is well reproduced with the periodic approach. However, the modes are only captured approximately due to the assumption of an infinite structure.     

Sound insulation standards for buildings adjacent to urban motorways

Buildings can be considered as environmental filters and there is plenty of evidence that the majority of our new urban buildings are not providing an acceptable internal noise environment. Since it has proved physically and economically impossible to modify existing buildings to deal with noise from urban motorways, new building standards are required for new buildings near motorways.     

Energy transmission in finite coupled plates,part II: Application to an L shaped structure

The method presented in the first of these two companion papers is applied to the case of two thin plates coupled in an L shape. Numerical calculations yield values of the vibrational energies of each plate. The influences of damping, thickness and area of the plates and of the excitation type are presented and discussed. The theoretical results are compared with results from a computerized experiment, in which special attention was given to the number and position of point velocity measurements.     

Sound propagation around rigid barriers laterally confined by tall buildings

This paper focuses on the propagation of sound waves in the presence of acoustic barriers placed close to very tall buildings. The boundary element method (BEM) is used to model the acoustic barrier, while the presence of the tall buildings is taken into account by using the image source method. Different geometries are analyzed, representing the cases of a single building, two buildings forming a corner and three buildings defining a laterally confined space. The acoustic barrier is assumed to be non-absorbing, and all the buildings and the ground are modeled as infinite rigid plane surfaces. Calculations are performed in the frequency domain and time signals are then obtained by means of Inverse Fourier Transforms. The sound pressure loss provided by the acoustic barrier is computed, illustrating the importance of the lateral confinements.     

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.     

An investigation of transmission coefficients for finite and semi-infinite coupled plate structures

This paper introduces a method for determining the transmission coefficient for finite coupled plates using an analytical waveguide model combined with a scattering matrix. In the scattering matrix method, the amplitudes of the structural waves impinging on a junction are separated into incident, reflected, and transmitted components. The energy flow due to each of these waves is obtained using a wave impedance method, which is subsequently used to determine the transmission coefficient. Transmission coefficients for semi-infinite and finite L-shaped plates are investigated for single and multiple point force excitations, and for controlled incident wave sources. It is shown that the transmission coefficients can also be calculated from details of the modal transmission coefficients and the modal composition of the energy incident on the junction. Results show that the modal transmission coefficients are largely independent of whether the plates have finite or semi-infinite boundary conditions, and are only dependent on the details of the coupling. Finally, frequency averaged transmission coefficients are compared for semi-infinite and finite structures. In the cases considered, it is found that the semi-infinite system is a good approximation for finite systems after frequency averaging, especially if the system is excited with multiple point force excitation.     

Sound transmission in multilayered structures – Introducing finite structural connections in the transfer matrix method

The transfer matrix technique is an efficient tool for calculating sound transmission through multilayered structures. Recent developments, as to the calculation of the sound reduction index, have given better fit to measurement data, e.g. due to the simulation of finite size samples by the spatial windowing technique. In practice, however, finite size structural connections (points or lines) normally do exist between leaves in wall constructions and these are not “natural” elements in the transfer matrix method. The paper describes a simple method to account for the effect of point- and line-connections in double-leaf constructions in a transfer matrix setup. To cover the frequency range above the critical frequency of the constituent plates, some new developments as to the forced radiation from plates were needed. Predicted results compare favorably with measurement results for a number of different cases, also including a heavy wall.     

Vibration transmission through plate/beam structures typical of lightweight buildings: Applicability and limitations of fundamental theories

This paper examines the modelling of vibration transmission through plate/beam structures typical of lightweight buildings. Key experiments have been carried out on simple structures to identify the applicability and limitations of fundamental theories. The systems tested included a single plate connected along its centre to a beam, two parallel plates attached along their centre to a beam (plates opposite or offset), and four plates connected along their edges to a beam. The analysis focused in particular on the applicability of modelling a beam as a one-dimensional element in point connected systems (widely spaced screws in terms of bending wavelength). Statistical energy analysis (SEA) was the framework of analysis used for all predictions, but the theories examined were independent from SEA. The results obtained indicate that simple point models are only applicable to the single plate and beam system, and to the parallel opposite plates connected along their centre to a beam; even then, the applicability of such models is limited to low and mid frequencies (below 2 kHz for the structures tested). Transmission between two parallel plates connected to a beam with screws closely spaced was also examined, and it was found that rigid and pinned line predictions can provide limits for transmission between panels on the same side of a wall (where junctions with shallow beams tend to behave rigidly, whilst junctions with deep beams are better modelled as pinned).     

Sound velocity and attenuation in bubbly gels measured by transmission experiments

Measurements of the phase velocity and attenuation of sound in concentrated samples of bubbly gels are presented. Hair gel was used as a matrix material to obtain well characterized distributions of bubbles. Ultrasonic measurements were conducted over a large range of frequencies, including the resonance frequencies of the bubbles. Surprisingly good agreement with Foldy's prediction was found, even for monodisperse samples at resonance frequencies, up to volume fraction of 1%. Beyond this concentration, the effects of high-order multiple scattering were observed. These results support the feasability of ultrasonic techniques to investigate the size distribution of bubbles in a weak gel or liquid.     

Sound transmission in pipes with porous walls

Pipes with porous (permeable) walls have received the attention of several authors as a noise control element in automotive intake systems; however, a closed theory of sound transmission including the effect of the coupling of the internal and external acoustic fields and the presence of mean flow does not appear to be available. The present paper proposes an integro-differential system for the propagation of plane sound waves in pipes with porous walls, and presents its general numerical solution, as well as an approximate analytical solution. The predicted effect of the coupling between the internal and external acoustic fields in a circular pipe made of reinforced woven fabric walls is shown, and the transmission loss predictions are compared with the existing experimental data in the literature.     

Determination of sound reduction indices in the presence of flanking transmission

Unlike the standard sound insulation test method, which requires diffuse sound fields in both source room and receiving room, the sound intensity method only requires the source room to be diffuse. Flanking may, in some cases, cause large errors in the sound reduction indices obtained by the standard method, even if the flanking power is measured separately and subtracted from the total power. The sound intensity method allows selective determination of sound reduction indices for test objects surrounded by flanking surfaces, provided the measurement surface in the receiving room is defined in such a way that it encloses nothing but the test object.     

Vibration transmission between coupled plates using finite element methods and statistical energy analysis. Part 2: The effect of window apertures in masonry flanking walls

Part 1 of this paper demonstrated the validity of predictions of vibration transmission across junctions of masonry walls using Finite Element Methods (FEM). Part 2 uses numerical experiments with FEM to calculate the vibration transmission between masonry walls with window apertures at different positions in the flanking wall(s). Results from the numerical experiments are used to assess a simple “rule-of-thumb” estimate for calculating the change in the coupling parameters due to the introduction of an aperture into a flanking wall. Conclusions are drawn concerning use of the “rule-of-thumb” estimate for the coupling loss factor in Statistical Energy Analysis and the vibration reduction index in European standard EN 12354.     

横向各向同性柱状复合结构对超声波的散射

首先描述了横向各向同性复合圆柱结构的入射声场、散射声场及内部的驻波声场,然后利用转移矩阵方法导出了求解散射声场的方程组,计算了铝/各向异性界面层/纤维复合结构对斜入射声波的背向散射谱和散射截面积。将柱状复合结构中各向异性界面薄层相应的转移矩阵作渐近展开,建立了模拟这种界面薄层的弹簧模型及界面处广义边界条件。结果表明,模型中劲度常数仅依赖于界面薄层厚度及界面层媒质的弹性常数c_ll,c₁₂和c₄₄,而振子质量与c_ll,c₄₄,c₁₃和c₃₃有关。     

Sound transmission of cavity walls due to structure borne transmission via point and line connections

The author has published equations for predicting the air borne sound transmission of double leaf cavity walls due to the structure borne sound transmission across the air cavity via (possibly resilient) line connections, but has never published the full derivation of these equations. The author also derived equations for the case when the connections are rigid point connections but has never used them or published them or their derivations. This paper will present the full derivation of the author's theory of the air borne sound transmission of double leaf cavity walls due to the structure borne sound transmission across the air cavity via point or line connections which are modeled as four pole networks. The theoretical results will be compared with experimental results on wooden stud cavity walls from the National Research Council of Canada because the screw spacing is given for these results. This enables connections via studs and screws to be modeled as point connections and avoids the need to make any assumptions about the compliance of the equivalent point or line connections.     

水下多层均匀材料的声特性

本文研究水和空气中由不同厚度的两层弹性板及消声橡胶共同组成的分层介质在斜入射时的声特性,并采用数值方法求解多层结构声场的线性方程组。得到反射,透射系数,当板的厚度远小于波长时,采用弹性薄壳振动模型和弹性波模型进行计算,它们的结果基本相同,但是薄壳振动模型更便于计算和理论分析;对系统反射系数和透射系数的计算结果表明,系统增加消声橡胶层后,极大地改变后射系数和透射系数的频率响应;频率升高,反射系数减小     

Investigation of submicroscopic structures by very-slow-neutron transmission experiments

The transmission of very slow neutrons through a colloidal dispersion of silica particles was investigated at the FRM reactor, Munich. The experimental transmission shows a characteristic wavelength dependence which permits one to deduce several characteristic parameters of the scattering zones, in particular their size and number. The experimental results obtained are consistent with the known data for the substance chosen. This indicates that the simple method of very slow neutron transmission may be applied in certain cases as an alternative to the well-established techniques of X-ray or neutron small-angle scattering.Work supported by the Bundesministerium für Forschung und Technologie