A new approach to model tyre/road contact

In the Structural Dynamics and Acoustics group at the University of Twente, we aim to develop a quantitative tyre/road noise model. An essential part of this model is an accurate contact algorithm which is fast enough to simulate tyre vibrations up to the acoustic frequencies. In this paper we present a contact algorithm, describing the contact between a tyre and a road surface, which has the potential to be made very fast using the multigrid techniques developed in the field of elasto-hydrodynamic lubrication. For the development of the algorithm a flexible ring model is used to describe the tyre. The friction model is based on Coulomb’s friction. We present (quasi-)static results obtained from the algorithm for various friction coefficients, as well as frictionless results for a rotating tyre. The vibrations of the tyre obtained by this model have been used to calculate the radiated sound field by means of a boundary element program (BEMSYS)

Optimised Sound Absorbing Trim Panels for the Reduction of Aircraft Cabin Noise

The EU project FACE (Friendly Aircraft Cabin Environment) aims to improve the environmental comfort in aircraft cabins. As part of this project, this paper focuses on the reduction of noise in aircraft cabins. For modern aircraft flying at cruise conditions, this cabin noise is known to be dominated by turbulent boundary layer noise. The purpose of this work is to reduce the resulting sound pressure levels in the cabin by means of optimised sound absorbing trim panels with quarter-wave resonators. Sound absorption with quarter-wave resonators is mainly realised by dissipation of sound energy as a result of viscous and thermal losses. The viscothermal wave propagation of the air inside the resonators is efficiently and accurately described by the so-called low reduced frequency model. By optimisation of the dimensions of the resonators, desired sound absorption characteristics can be obtained for different specified frequency ranges. This means that the panels can be tailored to different positions in the aircraft cabin with different prevailing sound pressure levels. Results of optimisations for various frequency ranges show that a very good agreement is obtained between the desired and the calculated absorption curves. With the same optimisation procedure, panels have also been tuned for the dominant frequency range of a sound spectrum measured in a modern aircraft. Experimental validation of the numerically predicted optimal configurations, by means of impedance tube measurements, shows that a fairly good agreement is obtained between the numerical and experimental results

Elliptical side resonators for broadband noise reduction: theory and experiments

Previous research of the authors pointed out that side-resonators can be applied to reduce fan noise. However, the noise reduction capabilities of most resonator geometries, e.g. tube resonators, cylindrical resonators (cylindrical air layers) and circular resonators (disc shaped air layers), are relatively narrow banded. This is disadvantageous in case resonators are used in combination with a noise source that emits broadband noise or tonal noise at varying frequencies (for instance a speed controlled fan). It was found that the choice of the resonator geometry influences the broadband reduction capabilities (circular resonators offering the best broadband reduction capabilities). In the present study, it is investigated to what extent elliptical resonators, consisting of an elliptically shaped air layer, can be used to achieve broadband noise reduction. A semi-analytical model is proposed that describes the wave propagation in the elliptically shaped air layer. This model is connected to the analytical solution for wave propagation in a tube. The dimensions of the elliptical resonator can be optimized for broadband\ud noise reduction using this model. In addition, an experimental setup was built to verify\ud the semi-analytical model of the elliptical resonator

An acoustic finite element including viscothermal effects

In acoustics it is generally assumed that viscous- en thermal boundary layer effects play a minor role in the propagation of sound waves. Hence, these effects are neglected in the basic set of equations describing the sound field. However, for geometries that include small confinements of air or thin air layers, this assumption is not valid. Special models that include viscous and thermal effects are available (for example the Low Reduced Frequency model) but only for a limited number of geometries. To overcome these limitations and provide a solution that can be used for arbitrary geometries, an acoustic finite (2D) element that includes viscous and thermal effects is developed. The model is based on the linearized Navier stokes equations (including shear), the equation of continuity, the equation of state for an ideal gas and the energy equation. The method of weighed residuals is used in combination with a mixed formulation of pressure, temperature and particle velocity degrees of freedom. The results of the developed element code are compared with the results of an existing (analytical) Low Reduced Frequency solution and a viscothermal element that was found in literature

A finite element for viscothermal wave propagation

The well known wave equation describes isentropic wave propagation. In this equation, non-isentropic\ud boundary layer effects are neglected. This is allowed if the characteristic dimensions of the acoustic domain\ud are large with respect to the thickness of the boundary layers. However, in small acoustic devices such as\ud hearing aid loudspeakers, the boundary layer effects are significant and can not be neglected. A model that\ud describes viscothermal wave propagation is needed to model such devices.\ud For viscothermal wave propagation, the compressibility of air depends on the thermal behavior that can\ud range from adiabatic to isothermal. Moreover, the propagation behavior can range from propagation with\ud negligible viscosity to propagation with negligible inertia (Stokes flow). This complete range is accurately\ud described by the low reduced frequency model. This model’s major drawback is that it is only defined for\ud simple geometries such as thin layers and narrow tubes. It is not valid for arbitrary geometries.\ud To overcome this drawback, a three dimensional viscothermal finite element has been developed. Like the\ud LRF model, it covers the complete range from isothermal Stokes flow to isentropic acoustics. As opposed to\ud the LRF model, the viscothermal finite element can be used to analyze complicated geometries.\ud This paper presents the weak formulation of the finite element. Furthermore, two examples are presented in\ud which the results of the finite element models are compared to measurements

Application of Viscothermal Wave Propagation Theory for Reduction of Boundary Layer Induced Noise

Boundary layer induced noise, i.e. noise inside the aircraft resulting from the turbulent boundary layer enclosing the fuselage, is known to dominate air-cabin noise at cruise conditions. In this paper a method is described to design trim panels containing a large number of coupled tubes to effectively reduce this type of noise. The theory of viscothermal wave propagation in tubes, as presented by Tijdeman [3], is discussed. To illustrate the procedure the absorption coefficient for a panel containing a number of non-coupled tubes is calculated. Initial results optimising the tubes’ length and radii for a desired fictive absorption coefficient are presented and prove the applicability of the method

Fast evaluation of the Rayleigh integral and applications to inverse acoustics

In this paper we present a fast evaluation of the Rayleigh integral, which leads to fast and robust solutions in inverse acoustics. The method commonly used to reconstruct acoustic sources on a plane in space is Planar Nearfield Acoustic Holography (PNAH). Some of the most important recent improvements in PNAH address the alleviation of spatial windowing effects that arise due to the application of a Fast Fourier Transform to a finite spatial measurement grid. Although these improvements have led to an increase in the accuracy of the method, errors such as leakage and edge degradation can not be removed completely. Such errors do not occur when numerical models such as the Boundary Element Method (BEM) are used.Moreover, the forward models involved converge to the exact solution as the number of elements tends to infinity. However, the time and computer memory needed to solve these problems up to an acceptable accuracy is large. We present a fast (O(n log n) per iteration) and memory efficient (O(n)) solution to the planar acoustic problem by exploiting the fact that the transfer matrix associated with a numerical implementation of the Rayleigh integral is Toeplitz. In this paper we will address both the fundamentals of the method and its application in inverse acoustics. Special attention will be paid to comparison between experimental results from PNAH, IBEM and the proposed method

A finite element approach to the prediction of sound transmission through panels with acoustic resonators

Previous research by the authors has shown that sound radiated by a vibrating panel can be reduced considerably by using tuned acoustic resonators. The length of the tube resonators determines the frequency range in which sound is reduced. The shape of the spectrum is determined by the ratio of the cross-sectional areas of the resonators to the area of the panel. Maximum sound reduction is achieved if the volume velocities at the surface of the vibrating panel and those at the entrance of the resonators are equal in magnitude but opposite in phase. Up to now, the effect of the resonators on the radiated sound has been studied with a one-dimensional analytical model. In this paper, a three-dimensional acousto-elastic model is developed using the finite element method. The purpose of this model is to study the influence of the flexibility and the boundaries of the panel, as well as the presence of rooms behind and in front of the panel on the sound transmission. Modelling the complete structure, including the resonators and the interaction with the air inside the resonators, is computationally expensive. Therefore, an alternative approach is developed. Because of the repetitive pattern of resonators in the panel, the structural part of the panel is modelled with superelements. To enable coupling between the structural part of the model and the air behind and in front of the panel, a new interface element is derived. The formulation of this interface element also includes the acoustic behaviour of the resonators. Sound transmission loss calculations are made for one configuration and the results are compared with the results obtained with a one-dimensional analytical model