A waveguide finite element aided analysis of the wave field on a stationary tyre, not in contact with the ground

Although tyre/road noise has been a research subject for more than three decades, there is still no consensus in the literature as to which waves on a tyre are mainly responsible for the radiation of sound during rolling. Even the free vibrational behaviour of a stationary (non-rotating) tyre, not in contact with the ground, is still not well understood in the mid- and high-frequency ranges. Thus, gaining an improved understanding of this behaviour is a natural first step towards illuminating the question of which waves on a rolling tyre contribute to sound radiation. This is the topic of the present paper, in which a model based on the waveguide finite element method (WFEM) is used to study free wave propagation, on a stationary tyre, in the range 0-1500 Hz. In the low-frequency region (0-300 Hz), wave propagation is found to be rather straightforward, with two main wave-types present. Both have cross-section modes involving a nearly rigid motion of the belt. For higher frequencies (300-1500 Hz) the behaviour is more complex, including phenomena such as ‘curve veering’ and waves for which the phase speed and group speed have opposite signs. Wave-types identified in this region include (i) waves involving mainly sidewall deformation, (ii) belt bending waves, (iii) a wave with significant extensional deformation of the central belt region and (iv) a wave with a ‘breathing’ cross-section mode. The phase speed corresponding to found waves is computed and their radiation efficiency is discussed, assuming free-field conditions. In a future publication, the tyre model will be used in conjunction with a contact model and a radiation model to investigate the contribution of these waves to radiated sound during rolling.     

Interaction of a spherical acoustic wave with an elastic spherical shell

The interaction of a spherical acoustic wave with an elastic spherical shell is treated analytically. The solution includes the coupling between the acoustic sound field and vibration of the shell with any degree of fluid loading. The formulation for the far-field acoustic pressure is derived in terms of natural spherical wave functions, the properties of the acoustic medium, and the material constants of the shell. The far acoustic field is computed for a thin aluminum shell and several sound source locations over a large range of ka, where k is the wavenumber, and a is the shell radius. It is shown that the acoustic pressure depends significantly on whether the shell is in air or is submerged in water, particularly when the sound source is very near the surface. In air, the sound field of the shell is nearly identical to that of a rigid sphere but, in water, the shell is more compliant, which results in a damped radiation field that is characterized by vibrational resonances throughout the range of frequencies considered. As the sound sources is moved further away from the surface, however, this resonance response decreases very rapidly, and the sound field corresponds more closely to that of the shell in air.     

降低加肋双层圆柱壳辐射噪声线谱的结构声学设计

为降低双层圆柱壳辐射噪声线谱,从控制内壳振动响应和衰减壳间振动传递率进行结构声学设计。采用机械阻抗理论分析了环肋圆柱壳模态响应控制机理;由环肋振动方程推导分析了环肋径向机械阻抗特性;基于阻抗失配、波形转换原理提出一种阻抗加强环肋,分析了振动波阻抑特性;利用阻尼减振技术,综合考虑肋板的刚度、阻尼特性,设计了金属橡胶层叠肋板;结合数值计算实例,分析了设计双层壳模型的声辐射性能。结果表明:设计的双层加肋圆柱壳结构能有效降低辐射噪声线谱,在分析频段内辐射声压线谱平均降低约6.6 dB。研究结果对研制低噪声水下航行器具有良好的工程价值和应用前景。      

A WAVE MODEL FOR A PNEUMATIC TYRE BELT

A one-dimensional wave equation of an infinite flattened tyre belt is generated. The belt vibration is controlled by bending, tension, shear and the sidewall stiffness. The dispersion relations for two waves in the belt are calculated and used to find both the input impedance and attenuation on a tyre belt of infinite extent. Tension and the sidewall controls the deformation and stiffness below 100Hz. Waves propagate around the belt above this frequency. The wave speeds due to bending and shear were predicted and measured. The model presented here should be valid for the prediction of tyre response above about 400 Hz when for a car tyre the modal behaviour is observed to cease. In this high-frequency region, the tyre at the input appears to be of infinite extent.     

The metre

A musical wind instrument transforms a constant pressure input from the player's mouth into a fluctuating pressure output in the form of a radiating sound wave. In reed woodwind and brass instruments, this transformation is achieved through a nonlinear coupling between two vibrating systems: the flow control valve formed by the mechanical reed or the lips of the player, and the air column contained by the pipe. Although the basic physics of reed wind instruments was developed by Helmholtz in the nineteenth century, the application of ideas from the modern theory of nonlinear dynamics has led to recent advances in our understanding of some musically important features of wind instrument behaviour. As a first step, the nonlinear aspects of the musical oscillator can be considered to be concentrated in the flow control valve; the air column can be treated as a linear vibrating system, with a set of natural modes of vibration corresponding to the standing waves in the pipe. Recent models based on these assumptions have had reasonable success in predicting the threshold blowing pressure and sounding frequency of a clarinet, as well as explaining at least qualitatively the way in which the timbre of the sound varies with blowing pressure. The situation is more complicated for brass instruments, in which the player's lips provide the flow valve. Experiments using artificial lips have been important in permitting systematic studies of the coupling between lips and air column; the detailed nature of this coupling is still not fully understood. In addition, the assumption of linearity in the air column vibratory system sometimes breaks down for brass instruments. Nonlinear effects in the propagation of high amplitude sound waves can lead to the development of shock waves in trumpets and trombones, with important musical consequences.     

Modeling of offshore pile driving noise using a semi-analytical variational formulation

Underwater noise radiated from offshore pile driving got much attention in recent years due to its threat to the marine environment. This study develops a three-dimensional semi-analytical method, in which the pile is modeled as an elastic thin cylindrical shell, to predict vibration and underwater acoustic radiation caused by hammer impact. The cylindrical shell, subject to the Reissner–Naghdi’s thin shell theory, is decomposed uniformly into shell segments whose motion is governed by a variational equation. The sound pressures in both exterior and interior fluid fields are expanded as analytical functions in frequency domain. The soil is modeled as uncoupled springs and dashpots distributed in three directions. The sound propagation characteristics are investigated based on the dispersion curves. The case study of a model subject to a non-axisymmetric force demonstrates that the radiated sound pressure has dependence on circumferential angle. The case study including an anvil shows that the presence of the anvil tends to lower the frequencies and the amplitudes of the peaks of sound pressure spectrum. A comparison to the measured data shows that the model is capable of predicting the pile driving noise quantitatively. This mechanical model can be used to predict underwater noise of piling and explore potential noise reduction measures to protect marine animals.     

Influence of support properties on the sound radiated from the vibrations of rectangular plates

The control of the forced vibration response of structures through the optimal tuning of its supports is desirable in many applications. Tuning may enhance the dissipation of vibration energy within the supports, thereby reducing fatigue and structure-borne noise. Two different models were developed to calculate the optimal support stiffness that minimizes the velocity response of homogeneous plates. The first model, based on the wave propagation at the edge, yields a good first cut approximation of the optimal properties. The optimal viscous and viscoelastic support stiffness for minimal reflection at the edge was calculated. Maximum absorption of the incident waves occurs when the viscous support stiffness matches the characteristic mechanical impedances of the plate. The second model, based on the Rayleigh-Ritz method, yields more accurate estimates of the optimal support stiffness required to minimize the forced velocity response of the finite rectangular plate. The optimal support properties calculated from the two different methods were in good agreement. This suggested that the modal response of the plate is strongly influenced by the wave reflections at the edges. Finally, the effects of support properties on the sound radiated from the plate were investigated. The optimal support stiffness that minimizes the radiated sound power was found to be smaller than the value that minimizes the velocity response. The results show that both the velocity response and sound radiation are strongly influenced by dissipation of vibration energy at the edges, and demonstrate that support tuning can yield significant noise and vibration reduction.     

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.     

Acoustoseismic wave fields generated by surface seismic vibrators

Results of experimental and theoretical studies of acoustoseismic wave fields generated by surface seismic vibrators are presented. In experiments with high-power seismic vibrators operating in a frequency range of 5–10 Hz, acoustic waves were recorded at distances up to 50 km from the source. The long-range sound propagation from seismic vibration sources was observed in a near-surface waveguide arising due to temperature inversion. The effect of the acoustoseismic induction, i.e., excitation of surface seismic waves by the acoustic wave arriving from the vibrator, was also detected. The results of mathematical modeling of the acoustoseismic field generation by an operating seismic vibrator are presented. They include the modeling of the radiation of a harmonic acoustic wave’s by the vibrator, its trapping by the near-surface waveguide, the long-range low-frequency acoustic wave propagation in the presence of the waveguide, and the induction of a surface seismic wave by the arriving harmonic acoustic wave. It is shown that a seismoacoustic wave propagating at the boundary between the elastic earth and the atmosphere is an analog of the Stonely wave that appears in the presence of a near-surface low-temperature layer in the atmosphere.     

Three methods for analyzing forced vibration of a fluid-filled cylindrical shell

The forced vibration of an infinite elastic circular cylindrical shell filled with fluid is studied. Three methods are employed to analyze the forced vibration problem of this shell-fluid coupled system, that is, wave propagation approach (wave mode superposition), theorem of residues and a numerical integral method. In order to explain these methods more explicitly, before being used to investigate the vibration of an infinite fluid-filled elastic circular cylindrical shell, all these three methods are employed firstly to analyze the forced vibration problem of an infinite beam and an infinite elastic circular cylindrical shell in vacuo. Advantage and disadvantage of these three methods are discussed and their interesting relationship is revealed. That is, to any circumferential wavenumber and frequency of the external force, there is an unchangeable relationship between the general coordinates of various waves in the wave propagation approach and the residuals in the theorem of residues.     

Control of sound and vibration for cylindrical shells by utilizing a periodic structure of functionally graded material

A periodic shell made of functionally graded material (FGM) is proposed in this Letter. Wave propagation and vibration transmission in the FGM periodic shell for different circumferential modes are investigated. By illustrating the dynamical behavior of the periodic FGM shell within the pass/stop band frequency ranges, the mechanism of wave propagation and vibration transmission in the shell are illuminated. Moreover, the suppression characteristics of structure-borne sound in the internal field of the shell, either within the stop or pass band frequency ranges, are studied.     

Wave interpretation of numerical results for the vibration in thin conical shells

The dynamic behaviour of thin conical shells can be analysed using a number of numerical methods. Although the overall vibration response of shells has been thoroughly studied using such methods, their physical insight is limited. The purpose of this paper is to interpret some of these numerical results in terms of waves, using the wave finite element, WFE, method. The forced response of a thin conical shell at different frequencies is first calculated using the dynamic stiffness matrix method. Then, a wave finite element analysis is used to calculate the wave properties of the shell, in terms of wave type and wavenumber, as a function of position along it. By decomposing the overall results from the dynamic stiffness matrix analysis, the responses of the shell can then be interpreted in terms of wave propagation. A simplified theoretical analysis of the waves in the thin conical shell is also presented in terms of the spatially-varying ring frequency, which provides a straightforward interpretation of the wave approach. The WFE method provides a way to study the types of wave that travel in thin conical shell structures and to decompose the response of the numerical models into the components due to each of these waves. In this way the insight provided by the wave approach allows us to analyse the significance of different waves in the overall response and study how they interact, in particular illustrating the conversion of one wave type into another along the length of the conical shell.     

Ventilation duct with concurrent acoustic feed-forward and decentralised structural feedback active control

This paper presents theoretical and experimental work on concurrent active noise and vibration control for a ventilation duct. The active noise control system is used to reduce the air-borne noise radiated via the duct outlet whereas the active vibration control system is used to both reduce the structure-borne noise radiated by the duct wall and to minimise the structural feed-through effect that reduces the effectiveness of the active noise control system. An elemental model based on structural mobility functions and acoustic impedance functions has been developed to investigate the principal effects and limitations of feed-forward active noise control and decentralised velocity feedback vibration control. The principal simulation results have been contrasted and validated with measurements taken on a laboratory duct set-up, equipped with an active noise control system and a decentralised vibration control system. Both simulations and experimental results show that the air-borne noise radiated from the duct outlet can be significantly attenuated using the feed-forward active noise control. In the presence of structure-borne noise the performance of the active noise control system is impaired by a structure-borne feed-through effect. Also the sound radiation from the duct wall is increased. In this case, if the active noise control is combined with a concurrent active vibration control system, the sound radiation by the duct outlet is further reduced and the sound radiation from the duct wall at low frequencies reduces noticeably.     

The horizontal directivity of noise radiated by a rail and implications for the use of microphone arrays

Structural waves propagating along a railway rail form an extended source of sound radiation. Using an equivalent source model the distribution of this sound in a horizontal plane is investigated and shown to consist mainly of sound propagation at a particular angle to the normal. This direction is determined by the ratio of the wavenumbers in the rail and in air. Due to the extended nature of the rail as a source, the spatial distribution of the sound field in the direction along the track does not lend itself to the use of a simple directivity factor. The consequences for the measurement of noise from the rail using a microphone array are then explored. It is shown that a microphone array focussed normal to the rail does not detect most of the sound radiated by the rail. By turning the focus angle, the sound detected becomes a maximum when this angle corresponds to the angle of propagation of the sound radiation. Measurements on a test track using artificial excitation and measurements during the passage of a train confirm these conclusions.     

The modelling of the dynamic behaviour of tyre tread blocks

The interaction between tyre and road constitutes the dominant noise source for road vehicles at speeds above 50 km/h. The understanding and control of tyre/road noise generation mechanisms is still one of the main challenges in the field of acoustics, covering a wide area of topics, such as the structure-borne sound properties of tyres, the non-linear contact between tyre and road and the sound radiation from vibrating tyres. The work presented here only covers a small part of this complex field, the modelling of the tread blocks in order to incorporate the dynamic behaviour into a simulation model for a rolling tyre on a rough road. A finite element model is made for individual blocks in order to investigate their first eigenfrequencies and mode shapes. This information is used to build an equivalent model consisting of a simple mass and springs. The equivalent model has the advantage of being handier when coupling to a model of the tyre structure. The impedance coupling method is used. The results of the driving point mobility in the radial and tangential directions to the surface of the block are compared with measurements on tyres. The results show good agreement for the radial direction, while for the tangential direction, the agreement is poor. This is mainly due to the fact that the model for the tyre structure does not include in-plane motion. The results also show that, for the frequency range up to 3 kHz, the influence of the blocks depends strongly on their geometry. The geometry of the tread blocks determines the contact geometry as a kind of macro roughness. It also determines the eigenfrequencies, which for typical tread blocks are expected to be situated, at least, in the range above 2000 Hz.     

ANALYSIS AND MEASUREMENT OF SOUND TRANSMISSION THROUGH A DOUBLE-WALLED CYLINDRICAL SHELL

Sound transmission through a double-walled cylindrical shell is studied. The solution that describes the system response is obtained by combining the solutions of two different models of the system. The first model, which describes the sound transmission due to the interaction between the acoustic waves and the bending waves in the shells, is formulated by three acoustic wave equations and two shell vibration equations. The second model describes the sound transmission by one-dimensional waves propagating through the layers of the shells and the air-gap. The transmission losses calculated from the two models are combined to represent the system response in the entire frequency range. Analytical solutions are compared to corresponding measured results, which shows reasonable agreements if the extent of the simplifications used in the analytical model is considered. The effects of important design parameters such as the air-gap size and the thickness ratio are studied using analytical solutions.     

Non-linear acoustic radiation by an underwater vibrating spherical shell

I.IntroductionMostofthepublishedstudiesontheacousticwaveradiationfromelasticbodyconcen-tratedon1ineartheory.However,iftheamplitudeislargeandthefrequencyishigh,theresultingsoundwavepropagatinginthemediumwillgenerateconsiderablenonlineardistor-tion.Sothest.di.s[1]inthisfieldarelimited.Inthispaperwetreatedasphericalshell.Itconsistsoftwoaspects:oneisthestructuralresponseofasphericalshellinacousticfield.Becausethenonlineareffectofacousticwavecumulateswithpropagatingdistance,itisnegligibleonthesph…     

A theoretical study of passive control of duct noise using panels of varying compliance.

It is theoretically demonstrated that, in a duct, a substantial amount of sound energy can be transferred to flexural waves on a finite wall panel when the upstream portion of the panel is made to couple strongly with sound. The flexural wave then loses its energy either through radiating reflection sound waves or by internal friction. The effectiveness of the energy transfer and damping is greatly enhanced if the panel has a gradually decreasing in vacuo wave speed, which, in this study, is achieved by using a tapered membrane under tension. A high noise attenuation rate is possible with the usual viscoelastic materials such as rubber. The transmission loss has a broadband spectrum, and it offers an alternative to conventional duct lining where a smooth air passage is desired and nonacoustical considerations, such as chemical contamination or cost of operation maintenance, are important. Another advantage of the tapered panel is that, at very low frequencies, typically 5% of the first cut-on frequency of the duct, sound reflection occurs over the entire panel length. This supplements the inevitable drop in sound absorption coefficient, and a high transmission loss may still be obtained at very low frequencies.     

黏弹介质包裹的充液管道中低频轴对称波传播特性

研究埋地充液管道中低频轴对称波传播特性。将土壤考虑为黏弹介质,结合Kennard薄壳方程和Kelvin-Voigt线性黏弹性模型,引入土壤载荷矩阵,推导出土-管滑移情形下流体主导波和管壁压缩波的相速度表达式。通过数值模拟计算得到流体主导波和管壁压缩波的频散和衰减曲线并进行可靠性验证,分析两种波引起的管壁径向位移之比,讨论厚径比和品质因子对流体主导波传播的影响。结果表明,黏弹介质对流体主导波和管壁压缩波的相速度影响较小,但对衰减影响较大;流体主导波对管壁径向位移有较大的影响,是泄露噪声传播的主要载体;厚径比越大,流体主导波的相速度越大,衰减越小;而品质因子越大,流体主导波的频散和衰减都越小。研究结果可为埋地充液管道的泄漏检测提供一定的理论参考。