An approximation for the point mobility at the intersection of two perpendicular plates

The problem of point excitation at a T-intersection of two perpendicular plates is studied in order to establish expressions for the point mobility. It is found that the theory for point excitation of the free surface of a semi-infinite elastic solid is applicable in the frequency range associated with structure-borne sound transmission. From this theory the mobility for an infinite system is derived. Based on this model and on an experimental investigation an estimation procedure for the point mobility in the finite dimension case is developed. The agreement with measurements performed in situ is quite acceptable. Both the theoretical and the experimental investigations reveal that the real part of this mobility is small, although it is larger in the experimental results. This indicates that other components of excitation are difficult to eliminate and may contribute to the power input in practice. Because of the small real part of the mobility it is advantageous with respect to the reduction of structure-borne sound power transmission to locate the contact points between a source and the receiver at such intersections. Corrections are deduced for the measured magnitude of the mobility for the case when separate force and motion transducers are used.     

Vibration activity and mobility of structure-borne sound sources by a reception plate method

This paper considers a practical structure-borne sound source characterization for mechanical installations, which are connected to plate-like structures. It describes a laboratory-based measurement procedure, which will yield single values of source strength in a form transferable to a prediction of the structure-borne sound power generated in the installed condition. It is confirmed that two source quantities are required, corresponding to the source activity and mobility. For the source activity, a high-mobility reception plate method is proposed which yields a single value in the form of the sum of the squared free velocities, over the contact points. A low-mobility reception plate method also is proposed which, in conjunction with the above, yields the source mobility in the form of the average magnitude of the effective mobility, again over the contact points. Experimental case studies are described and the applicability of the laboratory data for prediction and limitations of the approach are discussed.     

基于平板冲击声的声源特性表征及自动识别*

以平板结构导纳函数为纽带,建立冲击声信号特征与声源特性之间的关联,获得与声源属性密切相关的特征用于目标分类。针对四边简支矩形被击板,借助信号参数识别算法获得与声源物理属性有关的6维导纳特征,并从冲击声样本中提取80维音色特征,将音色特征和导纳特征做相关性分析,获得与声源物理属性相关的信号特征集。利用BP神经网络进行分类,结果表明,当采用与特定声源物理属性相关的信号特征子集时,分类效果达到同组最优。     

有效线导纳的仿真研究

利用有效导纳复功率流法研究了无限平板线激励下的功率传递规律,得出了线激励下的有效线导纳的理论公式,并对有效线导纳的功率传递特性进行了仿真研究。比较了有效线导纳理论公式和数值估计公式的计算结果,得到了数值估计公式的适用范围。然后研究了梁线激励作用下的功率传递特,并且对平板和梁上的功率传递规律进行了比较,结果为平板线激励的相对传递功率要略大于梁的相对传递功率。表明有效线导纳的理论公式在研究结构的功率传递上的灵活性和适用性。     

双层加筋结构有源隔声物理机制研究

深入分析双层加筋结构有源隔声的物理机制有助于控制系统的优化设计。用模态叠加法和声振耦合理论对双层加筋有源隔声结构建模。在辐射加筋板声功率最小的控制条件下,从模态耦合的角度对有源隔声的物理本质进行了详细阐述。分析结果表明,由于双层加筋板中筋的耦合作用影响,系统的声能量传输规律及有源隔声机理与现有的模态分析结论相比均发生改变。结合筋的耦合影响,对空腔声场的模态抑制与重构机理进行修正和补充,清晰解释了双层加筋结构有源隔声的物理本质。     

Vibro-acoustic response and sound transmission loss analysis of functionally graded plates

This paper presents analytical studies on the vibro-acoustic and sound transmission loss characteristics of functionally graded material (FGM) plates using a simple first-order shear deformation theory. The material properties of the plate are assumed to vary according to power law distribution of the constituent materials in terms of volume fraction. The sound radiation due to sinusoidally varying point load, uniformly distributed load and obliquely incident sound wave is computed by solving the Rayleigh integral with a primitive numerical scheme. Displacement, velocity, acceleration, radiated sound power level, radiated sound pressure level and radiation efficiency of FGM plate for varying power law index are examined. The sound transmission loss of the FGM plate for several incidence angles and varying power law index is studied in detail. It has been found that, for the plate being considered, the sound power level increases monotonically with increase in power law index at lower frequency range (0–500 Hz) and a non-monotonic trend is appeared towards higher frequencies for both point and distributed force excitations. Increased vibration and acoustic response is observed for ceramic-rich FGM plate at higher frequency band; whereas a similar trend is seen for metal-rich FGM plate at lower frequency band. The dBA values are found to be decreasing with increase in power law index. The radiation efficiency of ceramic-rich FGM plate is noticed to be higher than that of metal and metal-rich FGM plates. The transmission loss below the first resonance frequency is high for ceramic-rich FGM plate and low for metal-rich FGM plate and further depends on the specific material property. The study has found that increased transmission loss can be achieved at higher frequencies with metal-rich FGM plates.     

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.     

Examination of multi-dimensional vibration isolation measures and their correlation to sound radiation over a broad frequency range

This article examines alternate vibration isolation measures for a multi-dimensional system. The isolator and receiver are modelled by the continuous system theory. The source is assumed to be rigid and both force and moment excitations are considered. Our analysis is limited to a linear time-invariant system, and the mobility synthesis method is adopted to describe the overall system behavior. Inverted ‘L’ beam and plate receivers are employed here to incorporate the contribution of their in-plane motions to vibration powers and radiated sound. Multi-dimensional transmissibilities and effectivenesses are comparatively evaluated along with power-based measures for the inverted ‘L’ beam receiver and selected source configurations. Further, sound pressures radiated from the inverted ‘L’ beam receiver are calculated and correlated with power transmitted to the receiver. Interactions within the ‘L’ beam receiver are also analyzed and measures that could identify dominant transfer paths within a system are examined. Sound measurements and predictions for the inverted ‘L’ plate receiver demonstrate that a rank order based on free field sound pressures, at one or more locations, may be regarded as a measure of isolation performance. Measured insertion losses for sound pressure match well with those based on computed results although further study is needed in relation to some discrepancies shown in the results. Finally, several emerging research topics are identified.     

Mechanisms of active control of noise transmission through triple-panel system using single control force on the middle plate

This paper presents an active triple-panel sound insulation structure with an idealized controllable point force acting on the middle plate. A novel analytical approach based on sound energy transmission rule is proposed to achieve the physical mechanism study. The transfer impedance matrix of the incident and middle plate is calculated using numerical approach. And the rule of sound energy transmission through the triple-panel structure is concluded by indirectly analyzing the radiated sound power of the three plates. Finally the physical mechanism of noise insulation is investigated from the point of view of the change in behaviors of energy transmission in controlled and uncontrolled conditions. Results obtained demonstrate that there exist four different energy transmission paths for four panel mode groups. The energy transmission is independent in each path and they are all of band-pass characteristic. The role of the middle plate and two cavities is very similar to the band-pass filter whose pass-band is different for different mode groups. The essence of active noise insulation lies in the fact that the energy transmission in each path is suppressed in its pass-band after control. This greatly improves sound insulation capability of the triple-panel structure and leads to sound propagation being blocked.     

VIBRATION POWER TRANSMISSION OVER A RECTANGULAR AREA OF AN INFINITE PLATE SUBJECT TO UNIFORM CONPHASE VELOCITY EXCITATION

In the study of vibration isolation, mobility is normally used to reflect the characteristics of power transmission over the contact region between the exciting machine and its supporting structure. However, recent investigations indicated that power transmission is influenced by the dimensions and shape of the contact region and the use of classical point mobility can lead to significant errors. The surface mobility of an infinite plate over a rectangular contact region subject to a uniform conphase velocity excitation has been derived using the effective point mobility concept for various aspect ratios of the contact region. Results show that power transmission is distributed in a ring-like manner, with the transmission in the central region and along the edges of the contact area being rather small. As the width-based Helmholtz number kw/2 increases, the ring-like region expands outward but less power is transmitted. The surface mobility decreases rapidly as Helmholtz number increases. For the same Helomholtz number, the surface mobility decreases as the aspect ratio of the contact region increases and for the same contact area, it is virtually independent of the shape of the contact region for aspect ratio less than 2 or at large Helmholtz numbers (greater than 4). Experimental measurements of a simulated infinite plate confirm the theoretical calculations. Unlike uniform conphase force excitation, the surface mobility due to uniform conphase velocity distribution does not oscillate with Helmholtz number.     

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.     

On effective mobilities in the prediction of structure-borne sound transmission between a source structure and a receiving structure,part II: Procedures for the estimation of mobilities

As is discussed in Part I, the structure-borne sound power transmission between multi-point, coupled structures can theoretically be described by effective mobility. The results from full scale measurements of transfer and point mobilities of compound structures show that in some cases the effective point mobility can be approximated by the ordinary point mobility. Estimation procedures for the ordinary point mobilities containing manageable expressions for engineering applications have been developed and some examples are presented. The basic reasoning behind these procedures are described. Promising agreement has been obtained with measurement results. Also, correction factors for the ordinary point mobility to obtain an approximate point mobility and their approximate frequency bounds are given. Comparison with measured effective point mobility shows good agreement.     

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.     

Estimation of broadband power levels radiated from turbulent boundary layer-driven ribbed plates having dissimilar sections

Previous papers developed an approach for estimating the vibration-related broadband acoustic power radiated by a ribbed steel plate in water driven by turbulent boundary layer pressures. This was extended to apply to plates composed of identical ribbed sections joined at infinite impedance supports. In this paper the basic model is modified so that it can be applied to plates composed of dissimilar sections joined at clamped supports. The response is formulated directly in terms of power and the effects of the supports are accounted for by power scattering coefficients, which are calculated through a Wiener-Hopf analysis. Sample calculations are shown to agree with results of other formulations. Only frequencies below bending coincidence are considered.     

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.     

Estimation of broadband acoustic power radiated from a turbulent boundary layer-driven reinforced finite plate section due to rib and boundary forces

Previous papers considered an infinite fluid-loaded plate with parallel line attachments, driven by a wave-number-white pressure excitation invariant in the direction of an attachment, and established the conditions and procedure for estimating the broadband radiated power by assuming the ribs to radiate independently. This paper applies those results to a finite rectangular ribbed plate, and extends the methodology to include the contribution of the plate's boundary support forces to the radiation and the consideration of excitation that varies in the direction parallel to the ribs. The approach is relevant to problems of sound radiation by underwater stiffened steel plates driven by turbulent boundary layer (TBL) pressures, and is also applicable to stiffened circular cylindrical shells when the response is dominated by bending. Comparisons of sample calculations with results of rigorous models validate the approximation.     

THE ENERGY MOBILITY

The energy mobility method is presented and applied both numerically and experimentally to thin plates of high modal density. The energy mobility is defined as the ratio of the frequency averaged quadratic velocity at one point of a structure to the frequency averaged active power injected at one point of the structure. It can be calculated using only classic input and transfer mobilities. The property of energy additivity of the contributions of several external loads is shown to be a good approximation in the case of a single structure. To quantify the approximations on typical structures one is interested in, numerical simulations are presented on plates. A good agreement is found between the predictions using the energy mobility and the exact calculations. An experiment conducted on a plate with a real excitation confirms that the prediction of the energy mobility approach can be quite satisfactory. Finally, a remarkable property for the energy mobility (contrary to standard mobility) is noted: the insensitivity to the presence of a mass heterogeneity at driving points. This property allows one to simplify considerably the characterization of industrial structures that have in general a lot of heterogeneities. The energy mobility concept is further applied to the vibrational behaviour of an assembly. For each subsystem the connection is described by adding injected power and coupling power into the energy additivity. The equality of the frequency averaged quadratic velocity and the power flow balance at each coupling point allows one to calculate the coupling power at connection points with energy mobilities of uncoupled subsystems. A system of two plates has been used to compare the energy mobility calculation and the exact one given by the classic mobility method. The comparison shows that a connectivity factor must be introduced to keep the same formalism generally used with classic mobilities. A generalized definition for the energy mobility is then established.     

Reception plate method for characterisation of structure-borne sound sources in buildings: Assumptions and application

A method for characterisation of structure-borne sound sources is proposed and investigated for the special but common case of machines in heavy-weight homogeneous building structures. The method is based on the concept of the reception plate where the total structure-borne sound power from the machine under test is assumed equal to the power dissipated by a plate attached to the machine. The method is relatively simple and allows comparison of sources on a power basis, and of tests results at different laboratories. Additionally the data obtained is in a form suitable for transformation into an installed structure-borne power and thence for the resultant sound pressure generated in buildings. The method is validated by cross-spectral and mobility methods. A study of the uncertainty of the power estimate was performed by numerical modelling and measurement.     

平面声波由空气经加肋板向水中传输的数值计算研究

采用有限元法和边界元法计算研究了平面声波由空气经加肋板向水中的声传输。数值计算表明:板的刚度对声传输的影响只有在板的刚度较大时才是重要的,当板的刚度较小时,空气和水之间的声阻抗失配对声传输起支配作用;板厚或肋骨惯性矩的变化会引起结构传声损失曲线上隔声低谷位置的变化;增大板厚或肋骨惯性矩可增大结构的传声损失,特别是当激励频率低于结构基频时,可通过增大板厚或肋骨惯性矩来增大结构刚度进而明显增大结构的传声损失。