Standing Wave Tube Research Articles

Study of the impact of boundary conditions on acoustical behavior of granular materials and their implementation in the finite difference method

Granular materials display significant differences in their acoustical response when tested in a standing wave tube, compared with the behavior of more traditional sound absorbing materials such as fibrous webs and foams. The latter materials can often be modeled as an equivalent fluid with the further assumption that the material properties do not depend on the input signal level. In contrast, the level dependence of the acoustical behavior of granular materials has been observed in measurements of glass bubbles, as reported in previous studies, for example. When the input level is low, the absorption coefficient of the glass bubble stack shows solid-like behavior with multiple peaks associated with modal response of the stack. On the other hand, when the input level is high, glass bubble stacks show fluid-like behavior, with the quarter wavelength resonance in the direction of the tube axis dominating the response. In the current work, the boundary conditions at the air/granule interface and the granule/tube wall boundary are studied, as is the mechanism causing the variation of the apparent stiffness of the granule stack. The proposed model is implemented with a finite difference approach, and the model predictions are compared with acoustic measurements of granule stacks.

Vibration and acoustic radiation control of a panel with piezoelectric oscillators.

In this paper, the vibration of a thin plate system with piezoelectric sheets attached and its acoustic radiation are modeled theoretically. Then the results are compared with those of finite element simulation, and the results are relatively consistent. Finally, sound absorption and isolation experiments at non-intrinsic frequencies of the composite plate are conducted in a standing wave tube. Based on the principle of minimum potential energy, the variation equation of a thin plate with a piezoelectric sheet attached are listed, and the impedance matrix of the acoustic radiation of the plate coupled with each order of the cavity modal is calculated. After the modal displacement response of the plate is obtained, the absorption coefficient and sound insulation volume of the composite plate can be calculated. Through theoretical calculations and finite element simulations, it is found that the plate has a modal reorganization phenomenon at the peak of sound insulation, and the modal response of each order increases at the peak of sound absorption. After that, the sound absorption and isolation experiments were conducted in the standing wave tube, and the control effect of the piezoelectric shunt oscillator at the non-intrinsic frequency of the plate was improved by adding negative capacitance.

MEMS co-vibration combined hydrophone

This paper proposes a MEMS co-vibration combined hydrophone (CCH) to position the weak acoustic source of small-volume UUV acoustic self-guided cabins. With an external diameter of 36 mm, it adopts the MEMS triaxial accelerometer to form the vector channel and the MEMS capacitive omnidirectional microphone to form the scalar channel. This paper first analyzes the acoustic receiving model of an elastic-free sphere in water, designs a MEMS co-vibration combined hydrophone packaging and then simulates its acoustic performance. The average density of the encapsulated CCH is 1.01 g/cm3. The vector channel bandwidth is 20 Hz−1,000 Hz, and the sensitivity is −173 dB @ 1 kHz (re 1 V/ μPa) with good cosine directivity. The scalar channel sensitivity is −171 dB @ 1 kHz (re 1 V/ μPa) with omnidirectional directivity. The error of the orientation test in the standing wave tube is less than 1 degree. The sound source-level test results are mostly consistent with the theoretical calculation based on the actual distance. The above results indicate that the hydrophone can be mounted to UUV to perform sound source detection, which can meet the need for precise positioning, and has a specific application value.

Lightweight Composite Partitions with High Sound Insulation in Hotel Interior Spaces: Design and Application

Sound insulation performance of partitions is one of the key factors contributing to the comfort of the hotel interior spaces. Based on the theory of constrained layer damping, this study proposed the light-weight composite partition structure with high sound insulation, which was composed of gypsum boards of different thicknesses and an isobutylene isoprene rubber board. The normal incidence sound transmission loss of the structure was evaluated through finite element simulations as well as experiments, which were conducted in a standing wave tube. The results show that the simulation and experimental results of two kinds of lightweight high sound insulation multi-layer composite partition walls are closely aligned; the surface density of the optimized partition wall was less than 42 kg/m2, although the normal incidence STL exceeded 51.8 dB at 200 Hz and at 1/3 octave of 1000 Hz with the maximum value of 58.5 dB. The lightweight composite partition wall with high sound insulation has a huge application potential in enhancing the sound environment quality of hotels.

Study of Noise Reduction and Sound Absorption Performance of Drainage Asphalt Pavement Based on Indoor Tire Accelerated Falling Method

In order to study the noise reduction and sound absorption performance of drainage asphalt pavement and porous asphalt concrete (PAC) and the difference of noise reduction and sound absorption effects of conventional AC pavement, single-layer and double-layer PAC pavements are compared and analyzed by improving the indoor noise test of tire accelerated falling method, and then the sound absorption coefficient of single-layer and double-layer PAC pavement is further tested using the standing wave tube method. Based on the standing wave interference principle of sound, the sound absorption characteristics of drainage asphalt pavement are described, the influence of void ratio on the sound absorption coefficient of PAC pavement is analyzed, and the data model between the void parameters and sound absorption coefficient is established. The results show that: (1) using the improved indoor tire accelerated falling method and using the sound level meter to measure the A-weighted sound pressure level and 1/3 octave frequency spectrum of noise under three distance conditions, the noise value of drainage asphalt pavement is 2 to 5 dB(A) lower than that of traditional AC pavement, and the noise reduction ability decreases with the increase of distance from the sound source and increases with the increase of void ratio. The sound absorption coefficient curve of drainage asphalt pavement is measured using the standing wave tube double transfer function method. The average sound absorption coefficient of PAC specimens decreases with the decrease of the void fraction. (2) The sound absorption coefficient curve of single-layer PAC pavement presents a “single peak type”. The sound absorption peak frequencies of a single layer 4 cm-thick PAC pavement and 10 cm-thick PAC pavement are around 1100 Hz and 800 Hz respectively. The corresponding frequencies of the sound absorption peaks of the two specimens are within the common frequency range of traffic noise, which is helpful to alleviate traffic noise. (3) Through CT scanning and three-dimensional reconstruction software, the void parameters of the PAC specimen are obtained, and the sound absorption coefficient prediction model is established. The sound absorption coefficient calculated by the model has a high correlation with the measured value of standing wave tube method, which verifies the accuracy of the sound absorption coefficient model in predicting the sound absorption characteristics of drainage asphalt pavement.

Estimating the airflow resistivity of porous materials in an impedance tube using an electroacoustic technique

Airflow resistivity is an essential parameter for characterizing air-saturated porous sound-absorbing materials theoretically and selecting sound-absorbing materials in practice. Although standardized methods can determine this non-acoustic parameter in the laboratory, many indirect alternative methods have been proposed to measure it. One of them is the technique presented in the 1980s by Ingard and Dear using a standing wave tube, a loudspeaker, and two microphones. This paper suggests an electroacoustic procedure based on a modification of the Ingard and Dear setup. Equations are derived through the transfer matrix method. After a simple calibration, the airflow resistivity of a material sample is indirectly estimated from the total electric impedance measured at the loudspeaker input connection terminals. Thus, implementing the proposed method is straightforward and inexpensive, since microphones and complex instrumentation are unnecessary. The method is tested by comparing measured values of the airflow resistivity of different material samples with those obtained through the Ingar and Dear approach and the ISO standardized method. Reasonably good agreement is observed, confirming the validity of the electroacoustic method.

The vibroacoustic characteristics and regulation rules of Panel–Cavity–Panel System controlled by Piezoelectric Shunt Oscillators with negative capacitors

Piezoelectric Shunt Oscillators (PSOs) are widely used in the passive and semi-active control of the vibration and acoustic radiation of flexible structures, due to PSOs’ high electromechanical coupling coefficients, robustness, effectiveness and adjustability at low frequencies. Panel–Cavity–Panel System (PCPS) is a common type of flexible structures, such as interior panels and windows of automobiles. In this paper, a theoretical model of PCPS controlled by PSOs and its vibration equations are established. The vibroacoustic characteristics of PCPS, including sound absorption coefficient (SAC), energy loss coefficient (ELC) and transmission loss (TL), are calculated using a unified mathematical form based on the vibroacoustic radiation impedance matrix, damping matrix and displacement response of PCPS, while a lumped parameter model of PCPS is derived to simplify the comprehension and extension of PCPS. Then the finite element simulation is used to calculate the vibroacoustic characteristics of the PCPS, which achieves good agreement with theoretical results, while three basic regulation modes are also summarized and verified. The regulation mechanism of PCPS controlled by PSOs is further analyzed by the velocity response of each panel. Finally, experiments of PCPS controlled by PSOs with negative capacitors are conducted in a standing wave tube, at non-eigenfrequencies ranging from 70 Hz to 220 Hz. It is found in experiments that PSOs with negative capacitor can increase the TL of PCPS about 8 dB to 25 dB, which depends on the target frequency. SAC and ELC can also be increased, which means less acoustic energy is reflected and more acoustic energy is dissipated in the shunt circuits.

Standing wave tube for the calibration of acoustic vector sensors

Acoustic vector sensors are useful in a variety of applications as they provide directional information for ambient noise by sensing the acoustic particle motion in addition to the acoustic pressure. Traditionally, the motion sensor is an accelerometer that is calibrated separately from the associated hydrophone. There are certain advantages that can be realized by calibrating the accelerometer and hydrophone concurrently in a standing wave tube at low frequencies. First, since the pressure and acceleration are simply related in this environment both sensors can be calibrated against a single reference hydrophone. Second, the vector sensor can be calibrated along with the suspension that will be used to mount it thereby taking into account any effects of the suspension’s dynamics. Third, the vector sensor is calibrated to the fluid acceleration rather than its own acceleration thereby accounting for any mismatch in its density relative to the fluid as well as the suspension dynamics. And fourth, the phase response of the acceleration output relative to the pressure output is measured in the calibration. This technique was implemented using a travelling wave tube that was developed for other applications and found to be accurate and convenient.

A finite difference approach to study the impact of boundary conditions on the acoustical behavior of particle stacks

The responses of particle stacks to incident sound waves show interesting features that are very different from those of a homogeneous continuum. Further studies of the acoustical performance of particle stacks can help both to discover potential noise control applications of these types of materials, and to help provide better insight into the internal status of the particle stacks. In the current study, a finite difference (FD) model for a particle stack was built based on the Biot poro-elastic theory. The intention in developing this model is to describe the acoustical behavior of particle stacks with consideration of not only the finite stiffness of the particles, but also the influence of gravity and friction between the particles and the inner wall of their enclosure: i.e., the cylindrical sample holder of a standing wave tube, in this work. The derivation of governing equations and boundary conditions is introduced, together with acoustic measurement results of particles stacks consisting of micron-scale glass bubbles, including absorption coefficients and surface impedances that are compared with the theoretical predictions. The possible application scenarios of such materials, and potential developments that will further improve the FD model will also be discussed.

Laboratory investigation on influence of mixture parameters on noise reduction characteristics of porous asphalt concrete

ABSTRACT To investigate the influence of PAC mixture type and parameters on noise reduction performance and their variation patterns. This study investigated: the mixes’ gradation characteristics parameters, the coefficient of uniformity (CU) and coefficient of curvature (CC); the nominal maximum size (DT), the material’s composition parameter; the void ratio (VV) and thickness (H), the mixes’ structural composition parameters, and finally, the surface density (BD). PAC specimens’ sound absorption coefficient was measured indoors by the standing wave tube method, and the variation law were observed under different PAC parameters. PAC parameters’ degree of influence on noise reduction performance was investigated through grey correlation theory and correlation analysis. The results indicated that increasing the void ratio and thickness improved the peak absorption coefficient and enhanced PAC’s noise reduction performance effectively. Increasing the nominal maximum particle size weakened the noise reduction performance. In addition, the mix type and thickness had a greater influence on the basic trend in the absorption coefficient spectrogram. PAC’s noise reduction effect was reflected primarily in the middle and high frequency band, and moved to the high frequency band gradually as the thickness increased. Overall, VV, H, and DT had a relatively large effect on PAC’s noise reduction performance.

A finite difference approach for predicting acoustic behavior of the poro-elastic particle stacks

The physical properties of particle stacks have been of interest for a long time, and the acoustic properties of such materials have been actively investigated in recent times. Traditional acoustic theories, such as the Biot theory, can serve as a guide for determining the general properties of the stacks, but they do not allow the identification of the differences between the particle stacks and traditional acoustic materials, which are usually modeled as homogeneous continua. Recent research suggests that the Biot theory, combined with depth-dependent stiffness and equivalent density, can be used to model such materials. In this work, a finite difference (FD) scheme based on the Biot theory has been developed based on the idea that the apparent stiffness of the particle stack varies with depth within of the stack. This FD scheme is two-dimensional in cylindrical coordinates with an axisymmetric condition imposed at the axis of the cylinder. This approach is thus suitable for modeling common scenarios in which particle stacks are tested in a cylindrical standing wave tube. The results of several example cases are shown in this paper.

Numerical simulation for porous hemp plastic composites sound absorption properties

Hemp is an environmentally friendly porous fiber, and has good sound absorption properties, which can be used to reduce noise. In recent years, hemp-based composites have been widely studied, but most of them study the preparation methods of materials, Therefore, this paper studies the topic. Firstly, the material and specimens with different thickness and diameter were prepared, then, the standing wave tube method experiment was carried out, and the values of sound absorption coefficient of the specimens were measured and analyzed, while a novel model using genetic algorithm and artificial neural network is proposed. Secondly, the artificial neural network structure was designed, and the training data, verification data, test data are divided and the data is preprocessed. Thirdly, improved genetic algorithm is proposed to design to determine an optimal solution. Fourthly, the optimal solution was as the initial weight and threshold, and were input into the artificial neural network together with training data and verification data. Levenberg Marquardt algorithm were used to train the network. Finally, input the test data into the trained network to test the model. The results showed that there is only a minor deviation between the model output values and the measured values, the values of sound absorption coefficient of specimens with 10 mm thickness are between 0.9 and 1. It was also found that compared with artificial neural network model without genetic algorithm, the proposed model has the lower root mean squared error (RMSE) value, the larger coefficient of determination (R2) value.

An iterative transfer matrix approach for estimating the sound speed and attenuation constant of air in a standing wave tube.

In this work, an iterative method based on the four-microphone transfer matrix approach was developed for evaluating the sound speed and attenuation constant of air within a standing wave tube. When the air inside the standing wave tube is treated as the material under test, i.e., as if it were a sample of porous material, the transfer matrix approach can be used to identify the air's acoustic properties. The wavenumber within the tube is complex owing to the formation of a visco-thermal boundary layer on the inner circumference of the tube. Starting from an assumed knowledge of the air properties, an iterative method can be applied in the post-processing stage to estimate the complex wavenumber. Experimental results presented here show that although the results are sensitive to ambient temperature, a semi-empirical formula previously proposed by Temkin [(1981). Elements of Acoustics (John Wiley & Sons)] matches closely with the measured sound speed and attenuation constant, as does a theoretical formulation proposed by Lahiri et al. [(2014). J. Sound Vib. 333(15), 3440-3458]. Further, it is shown that the Temkin [(1981). Elements of Acoustics (John Wiley & Sons)] and Lahiri et al. [(2014). J. Sound Vib. 333(15), 3440-3458] predictions accurately represent the variation of sound speed with frequency, in contrast to the formula recommended in the ASTM E1050 standard [(2019). American Society for Testing and Materials], in which the sound speed is assumed to be independent of frequency.

Development and Optimization of Broadband Acoustic Metamaterial Absorber Based on Parallel-Connection Square Helmholtz Resonators.

An acoustic metamaterial absorber of parallel–connection square Helmholtz resonators is proposed in this study, and its sound absorption coefficients are optimized to reduce the noise for the given conditions in the factory. A two–dimensional equivalent simulation model is built to obtain the initial value of parameters and a three–dimensional finite element model is constructed to simulate the sound absorption performance of the metamaterial cell, which aims to improve the research efficiency. The optimal parameters of metamaterial cells are obtained through the particle swarm optimization algorithm, and its effectiveness and accuracy are validated through preparing the experimental sample using 3D printing and measuring the sound absorption coefficient by the standing wave tube detection. The consistency between the experimental data and simulation data verifies feasibility of the proposed optimization method and usefulness of the developed acoustic metamaterial absorber, and the desired sound absorption performances for given conditions are achieved. The experimental results prove that parallel–connection square Helmholtz resonators can achieve an adjustable frequency spectrum for the low frequency noise control by parameter optimization, which is propitious to promote its application in reducing the noise in the factory.

Effects of asphalt pavement characteristics on traffic noise reduction in different frequencies

To evaluate the effects of asphalt pavement characteristics on traffic noise reduction in different frequencies, stone mastic asphalt with crumb rubber and porous asphalt concrete were prepared. Dynamic modulus test, air voids test, standing wave tube test, improved tire acceleration method, water submerged test and voids-clogging test were utilized. The results showed that the deformation characteristics of stone mastic asphalt have significant effects on the tire-pavement noise reduction in intermediate-frequency and high-frequency bands. Larger connected air voids of porous asphalt concrete could obtain better ability of noise reduction, especially in the low-frequency band. Both the water submerged and voids-clogging have slight effects on the noise reduction of stone mastic asphalt, while having greater influences on porous asphalt concrete. Water submerged mainly increases the high-frequency band noise, and voids-clogging affects the noise at low-frequency and high-frequency bands. These findings provide significant guidance in the application and promotion of ecological low noise pavements.

An Optimized Neural Network Acoustic Model for Porous Hemp Plastic Composite Sound-Absorbing Board

Current acoustic modeling methods face problems such as complex processes or inaccurate sound absorption coefficients, etc. Therefore, this paper studies the topic. Firstly, the material samples were prepared, and standing wave tube method experiments were conducted. Material acoustic data were obtained, while a model using improved genetic algorithm and neural network was subsequently proposed. Secondly, the acoustic data obtained from the experiment were analyzed; a neural network structure was designed; and the training, verification, and test data were all divided. In order to facilitate data processing, a symmetrical method was used to inversely normalize all the data. Thirdly, by the design of real coding scheme, fitness function, crossover, and mutation operators, an improved genetic algorithm was proposed to obtain the optimal solution, as the initial weight and threshold, which were then input into the neural network along with the training and verification data. Finally, the test data were input into the trained neural network in order to test the model. The test results and statistical analysis showed that compared with other algorithms, the proposed model has the lower root mean squared error (RMSE) value, the maximum coefficient of determination (R2) value, and shorter convergence time.

An iterative approach for estimating the sound speed and attenuation constant of air in a standing wave tube

In the present work, an iterative method based on the four-microphone transfer matrix approach was developed for evaluating the sound speed and attenuation constant of air within a standing wave tube. In particular, when the air inside the standing wave tube is treated as the material under test, i.e., as if it were a sample of porous material, the transfer matrix approach can be used to identify the air’s acoustic properties. Note that the wavenumber within the tube is complex owing to the formation of a visco-thermal boundary layer on the inner circumference of the tube. Starting from an assumed prior knowledge of the air properties, an iterative method can be applied in the post-processing stage to estimate the complex wavenumber accurately. Experimental results presented here show that although the results are sensitive to ambient temperature, a formula previously proposed by Temkin matches closely with the measured sound speed and attenuation constant. Furthermore, it is shown that the Temkin prediction accurately represents the variation of sound speed with frequency, in contrast to the formula recommended in the ASTM E1050 standard, in which the sound speed is assumed to be independent of frequency.

Design and analysis of monolithic integrated MEMS vector hydrophone micro-array

Based on the high sensitivity and miniaturization advantages of MEMS vector hydrophone, we proposed and designed a monolithic integrated micro-array vector hydrophone composed of multiple sensor units. The theoretical model shows that the micro-array can improve the structural sensitivity and output signal-to-noise ratio while eliminating the problem of port and starboard ambiguity. Meanwhile, the micro-array structure clearly reduces the installation error of conventional vector array and improve the directional accuracy. Taking 5-element micro-array as an example, the resonance frequency in wet mode reaches 956 Hz that meets the requirement of test frequency band. Through theoretical and computational analysis, the sensitivity of micro-array is increased 14 dB and the SNR is increased 3.1 dB compared with that of the single vector hydrophone. The standing-wave tube experiment verified the directional effect of vector micro-array. The research of vector hydrophone micro-array is helpful to the application of underwater acoustic engineering.

Research on Direction of Arrival Estimation Based on Self-Contained MEMS Vector Hydrophone.

A self-contained MEMS vector hydrophone with a scalar–vector integrated design is proposed in this paper. Compared with traditional MEMS vector hydrophones, this design solves the problem of ambiguity in the port and starboard during orientation, and also realizes the self-contained storage of acoustic signals. First, the sensor principle and structural design of the self-contained MEMS hydrophone are introduced, and then the principle of the combined beamforming algorithm is given. In addition to this, the amplitude and phase calibration method based on the self-contained MEMS vector hydrophone is proposed. Then, the sensitivity and phase calibrations of the sensor are carried out in the standing wave tube. The sensitivity of the vector channel is −182.7 dB (0 dB@1 V/Pa) and the sensitivity of the scalar channel is −181.8 dB (0 dB@1 V/Pa). Finally, an outdoor water experiment was carried out. The experimental results show that the self-contained MEMS vector hydrophone can accurately pick up and record underwater acoustics information. It realizes the precise orientation of the target by combining beamforming algorithms. The direction of arrival (DOA) error is within 5° under the outdoor experimental conditions with an SNR of 13.67 dB.

Research and design of broadband muffler based on second-order Helmholtz resonators

Noise is always a serious factor affecting people's quality of life. The most common sound-absorbing materials are porous materials, which work based on the principle that sound waves entering into the pores inside the material are subjected to air friction and viscous resistance, thus converting sound energy into heat. Porous materials have excellent performance of absorbing medium-frequency and high-frequency sound , but they are required to be thick enough to control the low-frequency sound waves with large wavelengths, which limits the application of porous materials in low-frequency noise control. In recent years, acoustic artificial structures have become a research hotspot, which can realize exotic effective acoustic parameters based on periodical structure or local resonance. Acoustic artificial structure provides a new material basis for noise control, in which Helmholtz resonator plays an important role because of its simple geometry. In this study, a broadband muffler is designed based on the second-order neck embedded Helmholtz resonator. In order to achieve low-frequency and broadband sound insulation with a limited number of units and structure length, the second-order resonator is chosen as a basic structure unit, which has a stronger low-frequency noise reduction capability and has one high-frequency transmission loss peak more than a conventional Helmholtz resonator. The acoustic characteristics and insulation performance of second-order resonators are analyzed through theoretical calculation, simulation calculation and experimental test. Then, based on the theoretical model and empirical rules, a broadband muffler composed of nine second-order resonators is designed by carefully adjusting the geometry parameters of each resonator. The three-dimensional printed resonators are installed on the side wall of a square standing wave tube for experimental measurement. In the experiment, the transmission loss curve of the muffler is measured by the two-load method. The result shows that the designed muffler has good sound insulation performances in a frequency range of 267–927 Hz, with the whole transmission loss above 20 dB and the maximum sound insulation up to 60 dB. The experimental result is consistent with the calculation result and simulation result. The muffler has simple structure and high practicability, which will have a wide application prospect in noise control engineering.