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.     

Vibrational response prediction of a pneumatic tyre using an orthotropic two-plate wave model

A wave model to predict the vibrational response of a pneumatic tyre subject to line force excitation is presented. The tread and sidewalls are each modelled as thin, flat orthotropic plates with in-plane tension, which are joined together by a translational stiffness, and to a rigid rim. The dynamic response of the tyre to harmonic excitation is decomposed into spatial harmonics around the circumference, and waves in the meridional direction. At low frequencies (<100 Hz), the response is stiffness-like, and is controlled by the sidewall properties and tension effects resulting from the tyre pressure. In the mid-frequency range (100-500 Hz), a resonant response is observed, associated with modes both across and around the tyre. At high frequencies (>500 Hz), the response tends towards that of an infinite orthotropic plate. Experiments have been conducted on an inflated tyre fitted to a wheel rim to confirm the theoretical findings. The results show reasonable agreement with the predictions, the model accurately reflecting the phenomenological behaviour.     

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 identification of sound generating mechanisms of tyres

Tyre noise is generated by several mechanisms. With a modern tyre, wall vibration, air pumping and air resonant radiation are all considered to be important. But tyre noise generating mechanisms are still not clear due to the complication of tyre vibration behaviour. Vibrations of the tyre shell are the combination of several different wave types which appear at different frequencies. In a low frequency range, where the tyre behaves like an elastically supported beam, the circular ring model is used to analyze the dispersion relations. Above 300 Hz, which is the transition point from one-dimensional to two-dimensional waveguide properties of the passenger car tyre, a cylindrical shell model is used to analyze flexural waves propagation. Two important features on the wave propagation, wave-guide behaviour and the curvature effect of the tyre wall are analyzed. In consideration of noise radiation from tyre waves, most of the tyre waves observed in this study are inefficient sound radiators since their wavenumbers are larger than the acoustic wave number. As a result, It is observed that one of the most important features in sound radiation of a tyre shell is acoustically excited wave motion of the tyre wall.     

ON THE HORN EFFECT OF A TYRE/ROAD INTERFACE, PART II: ASYMPTOTIC THEORIES

In Part I, it was shown that boundary element method calculations could successfully be applied to determine sound amplification by a tyre/road geometry. However, the computations are expensive, limited to frequencies below 2500 Hz, and provide little physical insight. In Part II, two supplementary asymptotic approaches are developed; a ray theory for high frequencies and a compact body scattering model for low frequencies. When tested on a representative tyre geometry, these methods are found to have excellent predictive capabilities, at frequencies above 3k Hz and below 300 Hz respectively. Furthermore, the ray theory shows that the neglect of curvature in Ronneberger's wedge model (1989 Workshop on Rolling Noise Generation, Institut fur Technische Akustik, Technische Universitat, Berlin) leads to erroneous amplification levels and interference effects, and the scattering model intriguingly predicts that low frequency amplification increases with belt width independently of the tyre diameter. Lastly, this work confirms the importance of numerical calculations for the intermediate frequencies, where tyre noise is most significant.     

Apparent mass of the human body in the vertical direction: Inter-subject variability

The biodynamic responses of the seated human body to whole-body vibration vary considerably between people, but the reasons for the variability are not well understood. This study was designed to determine how the physical characteristics of people affect their apparent mass and whether inter-subject variability is influenced by the magnitude of vibration and the support of a seat backrest. The vertical apparent masses of 80 seated adults (41 males and 39 females aged 18-65) were measured at frequencies between 0.6 and 20 Hz with four backrest conditions (no backrest, upright rigid backrest, reclined rigid backrest, reclined foam backrest) and with three magnitudes of random vibration (0.5, 1.0 and 1.5 m s^-2 rms). Relationships between subject physical characteristics (age, gender, weight, and anthropometry) and subject apparent mass were investigated with multiple regression models. The strongest predictor of the modulus of the vertical apparent mass at 0.6 Hz, at resonance, and at 12 Hz was body weight, with other factors having only a marginal effect. After correction for other variables, the principal resonance frequency was most consistently associated with age and body mass index. As age increased from 18 to 65 years, the resonance frequency increased by up to 1.7 Hz, and when the body mass index was increased from 18 to 34 kg m⁻² the resonance frequency decreased by up to 1.7 Hz. These changes were greater than the 0.9-Hz increase in resonance frequency between sitting without a backrest and sitting with a reclined rigid backrest, and greater than the 1.0-Hz reduction in resonance frequency when the magnitude of vibration increased from 0.5 to 1.5 m s⁻² rms. It is concluded that the effects of age, body mass index, posture, vibration magnitude, and weight should be taken into account when defining the vertical apparent mass of the seated human body.     

A maze structure for sound attenuation

Sonic crystals are periodic arrangement of scatterers made of material with low acoustic impedance or sound hard materials [1]. Sonic crystals have numerous applications such as green belts and sound barriers. Here we showed that a typical maze structure at children playground can attenuate noise effectively for frequencies ranging from 12.5 Hz to 20,000 Hz. The original designer for the maze structure probably does not have that in mind. The maze structure can be viewed as a sonic crystal structure with sound attenuation characteristics. We found that the maze was able to attenuate noise up to 17.9 dBA for frequency range below 1000 Hz and 23 dBA for higher frequency range up to 20,000 Hz. The maze structure was able to mitigate noise at a wide range of frequencies in addition to the center frequency (f_c$f_c$) of 478 Hz which was estimated based on the Bragg’s Law. The periodic effects of the maze was also proven by numerical studies. Our results demonstrated that the maze structure commonly found in children playgrounds was able to attenuate noise covering the whole human hearing range.     

Potential of Global Positioning System (GPS) to measure frequencies of oscillations of engineering structures

Global Positioning System (GPS) has been successfully used to measure displacements of oscillating flexible civil engineering structures such as long suspension bridges and high-rise buildings, and to derive their modal frequencies, usually up to 1 Hz, but there is evidence that these limits can be exceeded using high frequency GPS receivers. Based on systematic experiments in computer controlled oscillations with one- and three-degrees of freedom we investigated the potential of GPS, first to record higher oscillation frequencies, at least up to 4 Hz at the minimum resolution level of this instrument for kinematic applications (?5 mm), and second, to identify more than one dominant frequency. Data were processed using least squares-based spectral analysis and wavelet techniques which permit to analyze entire time series, even those of too short duration or those characterized by gaps, in both the frequency and the time domain.The ability of GPS to accurately measure frequencies of oscillations of relatively rigid (modal frequencies 1-4 Hz) civil engineering structures is demonstrated in the cases of two bridges.The outcome of this study is that GPS is suitable for the identification of dynamic characteristics of even relatively rigid (modal frequencies up to 4 Hz) civil engineering structures excited by various loads (wind, traffic, earthquakes, etc.) if displacements are above the uncertainty level of the method (?5 mm). Structural health monitoring of a wide range of structures appears therefore a promising field of application of GPS.     

Effect of pulse frequency on the microstructure, phase composition and corrosion performance of a phosphate-based plasma electrolytic oxidation coated AM50 magnesium alloy

An AM50 magnesium alloy was plasma electrolytic oxidation treated using a pulsed DC power supply at three different pulse frequencies viz., 10 Hz, 100 Hz and 1000 Hz with a constant pulse ratio for 15 min in an alkaline phosphate electrolyte. The resultant coatings were characterized by X-ray diffraction, energy dispersive spectroscopy and scanning electron microscopy for their phase composition and microstructural features. The 10 Hz condition yielded relatively thick and rough coatings, which was attributed to the higher energy input per individual pulse during the PEO processing. The phase composition was also found to be influenced by the processing frequency. Electrochemical impedance spectroscopy studies performed in 0.1 M NaCl solutions revealed that the coatings produced at 10 Hz condition had a better corrosion resistance, which was attributed to the higher thickness, more compact microstructural features and a relatively stable phase composition.     

Fundamental accuracy of time domain finite element method for sound-field analysis of rooms

This paper presents an assessment of the accuracy and applicability of a time domain finite element method (TDFEM) for sound-field analysis in architectural space. This TDFEM incorporates several techniques: (1) a hexahedral 27-node isoparametric acoustic element using a spline function; (2) a lumped acoustic dissipation matrix; and (3) Newmark time integration method with an absolute diagonal scaled COCG iterative solver. Sound fields in an irregularly shaped reverberation room of 166 m³ are computed using TDFEM. The computed values and measured values for 125-500 Hz are compared, revealing that the fine structure of the computed band-limited impulse responses agree with measured ones up to 0.1 s, with a cross-correlation coefficient greater than 0.93. The cross-correlation coefficient decreases gradually over time, and more rapidly for higher frequencies. Moreover, the computed decay curves, and the reverberation times, agree well with the respective measured ones, and with a better fit the higher the frequency (up to 500 Hz).     

LES-FEM coupled analysis and experimental research on aerodynamic noise of the vehicle intake system

To thoroughly explore the aerodynamic noise in order to achieve a more efficient engineering application for a vehicle intake system, the large eddy simulation and the finite element method were employed in numerical simulations, and the aeroacoustic characteristics were validated through the experimental data. In this research, the k-ε model was adopted to simulate the steady state fluid dynamic, and the static pressure loss was consistent with the bench test data, indicating the computational fluid dynamics model was valid. After acquiring the data from the steady state simulation, the fluctuating pressure of the inner wall was calculated based on the transient state calculation results from the large eddy simulation. Thereafter, the finite element method was used to determine the acoustic performance of the intake system. By comparing the experiment data, the noise reduction indicated that the intake system performed well at various frequencies, e.g. 320 Hz, 520 Hz and 770 Hz, but poorly at 140 Hz, 210 Hz, 420 Hz and 600 Hz. Finally, the far-field aerodynamic noise was calculated based on FW-H equation, and the output showed that the noise of each measuring point agreed well with the test results in trend. In particular, the inlet sound pressure spectrum almost fit the test data with the airflow of 300 m³/h, and several amplitude peaks appeared at 210 Hz, 420 Hz and 600 Hz, corresponding to the low-attenuation region of the noise reduction curve. Moreover, the specific frequencies were not shifted with the airflow changing. In conclusion, the numerical simulation method proves to be effective in calculating the aerodynamic noise accurately.     

Sound source imaging of low-flying airborne targets with an acoustic camera array

Two-dimensional images of sound source distribution from near-ground airborne sounds are created using an array of 32 microphones and time-domain beamforming. The signal processing is described and array configurations spanning a square area with a side length of 3.45 m, approximately five wavelengths for a 500 Hz sound, are examined. Simulations of a 32-element under-populated log₆ × log₆ spaced array are given for sound sources centered over the array at 250 Hz, 500 Hz, and 1000 Hz. Stochastically optimized array geometry with a simulated annealing algorithm is discussed and a 32-element array optimized for a 500 Hz source is given along with a simulated image for direct comparison with the log₆ spaced array. Images from field testing a 32-element under-populated log₆ × log₆ spaced array are provided for a small aircraft flyover. Results show that this type of acoustic camera generates accurate images of sound source location. Suggested uses include monitoring small aircraft flying too low to be detected by radar as well as monitoring ecological events, such as bird migration.     

Ultrasound frame rate requirements for cardiac elastography: experimental and in vivo results

Cardiac elastography using radiofrequency echo signals can provide improved 2D strain information compared to B-mode image data, provided data are acquired at sufficient frame rates. In this paper, we evaluate ultrasound frame rate requirements for unbiased and robust estimation of tissue displacements and strain. Both tissue-mimicking phantoms under cyclic compressions at rates that mimic the contractions of the heart and in vivo results are presented. Sinusoidal compressions were applied to the phantom at frequencies ranging from 0.5 to 3.5 cycles/sec, with a maximum deformation of 5% of the phantom height. Local displacements and strains were estimated using both a two-step one-dimensional and hybrid two-dimensional cross-correlation method. Accuracy and repeatability of local strains were assessed as a function of the ultrasound frame rate based on signal-to-noise ratio values.The maximum signal-to-noise ratio obtained in a uniformly elastic phantom is 20 dB for both a 1.26 Hz and a 2 Hz compression frequency when the radiofrequency echo acquisition is at least 12 Hz and 20 Hz respectively. However, for compression frequencies of 2.8 Hz and 4 Hz the maximum signal-to-noise ratio obtained is around 16 dB even for a 40 Hz frame rate. Our results indicate that unbiased estimation of displacements and strain require ultrasound frame rates greater than ten times the compression frequency, although a frame rate of about two times the compression frequency is sufficient to estimate the compression frequency imparted to the tissue-mimicking phantom. In vivo results derived from short-axis views of the heart acquired from normal human volunteers also demonstrate this frame rate requirement for elastography.     

Suitability of laser Doppler velocimetry for the calibration of pressure microphones

The details of a new approach for absolute calibration of microphones, based on the direct measurement of acoustic particle velocity using laser Doppler velocimetry (LDV), are presented and discussed. The calibration technique is carried out inside a tube in which plane waves propagate and closed by a rigid termination. The method developed proposes to estimate the acoustic pressure with two velocity measurements and a physical model. Minimum theoretical uncertainties on the estimated pressure and minimum measurable pressure are calculated from the Cramer Rao bounds on the estimated acoustic velocity amplitude and phase. These uncertainties and the minimum measurable pressure help to optimize the experimental set up. Acoustic pressure estimations performed with LDV are compared with acoustic pressures obtained with a reference microphone. Measurements lead to a minimum bias of 0.006 dB and a minimum uncertainty of 0.013 dB on the acoustic pressure estimation for frequencies 1360 Hz and 680 Hz.     

Development of a multi-microphone calibrator

This paper presents the theory, design, and validation of a microphone calibrator used to simultaneously calibrate the amplitudes of multiple microphones on a single probe. The probe uses four 6 mm diameter electret microphones to acquire the data needed to compute acoustic energy density. This probe has prompted the need for simultaneous, multi-microphone amplitude calibration. The calibration process simultaneously subject each microphone on the probe to the same known acoustic pressure using four equal-length, small-diameter tubes connected to a single excitation source. A reference microphone connected to a fifth tube is used to calibrate the microphones. Test results show that the calibrator can calibrate each probe microphone within ±0.5 dB up to 2 kHz, and within ±1 dB up to 4.9 Hz with a confidence level of 95%.     

Influence of Co amount on the efficiency of energy absorption of Fe-Co ferrite nanoparticles

We present the chemical synthesis, structural characterization and efficiency of AC field energy absorption of Fe-Co ferrite particles sized between 35 and 100 nm and containing different cobalt amounts up to 3 wt%. Dynamic magnetic measurements in an AC field with frequency of 430 Hz and amplitude of up to 1200 Oe were performed for both solid and liquid dispersions of obtained particles. The energy absorption per one field cycle in function of the field amplitude and Co content was always bigger in liquid systems, under the same conditions, than in solid systems. The obtained results are of significance for the technology of low-frequency ferromagnetic hyperthermia of tumors.     

Investigation of irradiance efficiency for LED phototherapy with different arrays

Red and yellow light emitting diodes (LEDs) are currently utilized as lighting sources during LED phototherapy. These LEDs were arranged on a disk with an external diameter of 70 mm with different arrays — radial, rhombus, square radial, and square rhombus arrays. The radial and square radial arrays had better irradiance efficiency than rhombus and square rhombus arrays by optical simulation. Additionally, the radial array had 76 sets of LEDs, but the square radial array had 100 sets. Thus, a mockup sample of radial array phototherapy was constructed for performance tests. The mixture efficiency of the radial array was observed at distances of 1-100 mm and lighting was well mixed when distance exceeded 50 mm by optical simulation. Irradiance variation with angle was approximated by experiment and theory at a treatment distance of 50 mm and 100 mm using the phototherapy mockup. The radial array was one good choice for LED phototherapy.     

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.     

ON THE HORN EFFECT OF A TYRE/ROAD INTERFACE, PART I: EXPERIMENT AND COMPUTATION

Near the tyre/road contact area, the road surface and the tyre belt form a horn-like geometry, which provides a significant amplification mechanism for sound sources. Measurements have been carried out on a stationary tyre placed on a plane surface in an otherwise anechoic chamber. Following the reciprocal theorem a microphone was placed in the road surface near the contact patch and a white noise source was used in the far field. The amplification by the horn effect can then be determined as a function of frequency for an array of microphone positions relative to the contact patch and the centre of the tyre. These experimental measurements show that the horn effect is responsible for about 10-20dB increase in noise level. The amplification function shows a distinct interference pattern for higher frequencies and is independent of the longitudinal source position for low frequencies and source positions close to the contact patch. Numerical calculations using the indirect boundary element method have been carried out. These show excellent agreement with the measurements in the frequency regime of the BEM, i.e., up to 2500 Hz. The dependence of the horn effect on primary geometrical parameters such as the effect of the radius of curvature of the shoulders, the load and the width of the tyre has been investigated experimentally and numerically. The broad features of the horn effect are given by the cylindrical geometry of the tyre. The rounded edges of the tyre tend to increase the levels of the minima and shift them to higher frequencies, while slightly decreasing the levels of the maxima. Shape variations due to load can be accounted for by correcting the source distance to the edge of the formed contact patch. The amplification at low frequencies increases with width, the results collapsing onto a single curve as a function of the dimensionless widthω /λ.     

The research on semi-active muffler device of controlling the exhaust pipe’s low-frequency noise

In order to control low frequency noise in exhaust pipe, this paper puts forward a new concept of H-Q tube based semi-active muffler device. The semi-active muffler device and bench testing system have been designed and operated. Finite element simulation study on semi-active muffler and experimental study on semi-active muffler and passive muffler have been carried on. The effect of simulation and experiment are consistent. The semi-active muffler device acts well in low frequency band, especially between 50 Hz and 150 Hz. The average level of noise reduction is around 35 dB, which is much better than passive muffler. Between 150 Hz and 350 Hz, semi-active muffler has a better performance than passive muffler; above 350 Hz, it has worse performance compared with the passive muffler.