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The bending wave generated by the actuator exciting a panel can be controlled to be in the traveling wave form void the structural resonances, which deteriorates the radiated sound if the panel is used as a speaker. Although such traveling-wave control method (TCM) yields a wider effective frequency range than the modal control method, the requirement of using many actuators is the practical problem yet. If a beam is employed instead of a plate as a panel speaker, the number of actuators can be reduced despite a smaller radiating surface than a plate. This study adopts three actuators for the beam control using TCM. An actuator excites the beam in the middle position, and the two actuators near the two edges are used to suppress the reflected waves from the boundaries. The control result shows that the driving-point mobility of the primary actuator is converted into that of an infinite beam, which means that the boundaries are changed into anechoic ones and the structural resonances are eliminated. Accordingly, the beam radiates a smooth sound spectrum without sharp peaks and troughs related to the resonant responses. Effects of material and dimension in determining the effective frequency range are also explored.

The distribution of measurement points is important in reconstructing the vibro-acoustic source field using the near-field acoustical holography (NAH) based on the equivalent source method (ESM). Because too close measurement impose a limit in the implementation of ESM, an optimal arrangement of the hologram data is needed to enable a longer distance measurement although the points are still within the near field. In this work, the optimal measurement positions are determined by adopting the method that assures the independence among the measuring positions as far as possible. Singular value decomposition of the transfer matrix is employed in the loop-iteration calculation fashion, in which the candidate measuring point affecting the increase of singularity is eliminated at each iteration step. Comparison is made with the uniformly distributed hologram points, the monopole version of ESM model, and the patch holography method. The test results reveal that the acoustic field of sound sources can be reconstructed meaningfully from the optimized hologram points of underdetermined condition. Under the predetermined reconstruction accuracy, the test results varying the hologram distance show that it is possible to realize the underdetermined far-distance measurement than the usual NAH.

The radiated sound from a conventional panel speaker, often excited by an actuator, is usually distorted due to the multi-modal response of the regular panel. To avoid such an acoustically disadvantageous feature of the conventional panel speakers, an array of actuators can be used for controlling the panel vibration to obtain the desired acoustic response. In this paper, two different control methods by using the actuator array are compared in the viewpoint of the solution stability, the input efficiency, and the acoustic performance, in particular at low frequencies rendered in a hemispherical uniform radiation. The indirect inverse rendering method is to create a vibration pattern composed of a virtual speaker and baffle, and the direct inverse rendering method controls the array actuators to form a spatial distribution of panel vibration to directly produce the uniform radiation field. The actuator positions are confined at the periphery of the plate, which are advantageous in exciting the multiple modes and saving the central zone covered by the plate for other purposes. Numerical simulations are conducted for a thin rectangular plate with simply supported boundary condition in the frequency range below 300 Hz. It is found that both rendering methods can produce the uniform hemispherical sound radiation field, but the rendering error is −20 dB for indirect method and −50 dB for direct method. The singularity problem due to the ill-conditioning of the system appears in the direct method. Effect of applying the regularization technique to obtain a stable solution is studied for the system contaminated with a large amount of noise. It is observed that the result of using the direct method becomes dramatically stable with a reduction of condition number from O (10 17 ) to O (10 4 ). Also, the input gains of the actuator are reduced as much as 35 dB for both rendering methods.

The three-dimensional (3D) acoustic intensity probe is not popularly used for the source localization of acoustic source because of the large error even though the technique has been well known. In particular, the measured direction-of-arrival strongly depends on the frequency, which is a detrimental drawback that hampers the use of this method. Such spectral bias error, due to the discrete positioning and spacing of sensors surrounding the acoustic center, fluctuates in a nearly regular spectral pattern when a 3D acoustic intensity probe configured in a tetrahedral shape is used. In this work, two error compensation methods are tried: The first method is to adopt a double-module configuration, which is formed by the connected assembly of two intensity modules, but with different locations of acoustic centers for a spatial averaging effect. The second one is the 1/3-octave band averaging of the measured intensity spectrum within the effective measurement range. Because two probe modules are attached, they concatenate 1–3 sensors in the overlap position. Four double-module probes different in assembly configuration of involved two single-modules are tested: modules having a same acoustic center but twisted by 60°, inverted modules sharing one microphone and twisted by 60°, symmetric modules having the joint angle of 60° in the sharing edge, symmetric modules to a common face thus sharing three microphones. Measurements are conducted in an anechoic chamber by changing the source positions for 4 azimuth and 3 elevation angles. The results reveal that the maximum mean bias error of about 4° can be obtained by the double-module 3D acoustic intensity method, depending on the module configuration and angular source position. This contrasts to the fluctuating direction-of-arrival within about ±10° error range, which is obtained by each single-module in a concatenated double-module. In particular, when the band averaging technique is applied to the measured data by the probe module composed of the inverted single modules, the maximum bias error can be reduced to less than 1° in both azimuth and elevation angles.

The pattern of bending vibration on a thin plate is controlled to create a virtual speaker and baffle set. An actuator array at the plate edges is used to generate the bending wave to form the desired vibration pattern. The speaker zone is rendered to maintain a uniform phase as a speaker, whilst the rest of the plate is kept to be tranquil to serve as a baffle. From the rendering information and the potential positions of the actuators, the actuator gains are determined in an inverse manner. Vibration on a finite plate is modeled by the superposition of Green's functions between the actuators and field points, which depend on the speaker size and location, and the shape and material of plates. Parametric studies are conducted to determine the effect of those functions on the radiated sound characteristics. Simulation results show that the radiated sound spectrum features similar dips at some Helmholtz numbers would cause the deterioration of sound quality and reproducibility. These dips appear because of two typical reasons. The first condition is that the Helmholtz number becomes about 3.8 and 7.0, corresponding to the low-order radial modes of the circular speaker zone having circumferential nodes. The other arises when the distance between the speaker center and the plate edges is an integer multiple of the bending wavelength. The proposed method is tested on the roof panel of a car to compensate for the poor response of the built-in speakers. It is shown that the virtual speaker has a uniform phase in the speaker zone and that the low-frequency performance is reinforced well.

There are various structures constructed with periodically stiffened thin plates. Vibration prediction of such structures is not easy compared to the structures comprised of uniform plates only due to the mathematical complexity stemmed from the periodic nature. This study provides the analytic method to predict the wave transmission at junctions connecting two semi-infinite periodic structures and the response of a finite periodic structure to an external harmonic point force. The same theoretical framework is employed for dealing with both phenomena. First, free wave solutions are obtained by solving the governing equation for the bending motion of a periodically stiffened, infinite plate using the spatial Fourier Transform and the Floquet's theorem. Then, the free wave solutions are linearly superposed, and the linear coefficients are calculated by applying the appropriate boundary conditions. Numerical simulation is conducted. In dealing with the periodic finite structure, the result is compared with that by the finite element analysis. It is revealed that the periodic nature of the structures affects both the energy transmission and the vibration response of the periodically stiffened plates.

The three-dimensional acoustic intensimetry employing multiple probe-modules are implemented for estimating the source distance by calculating the nearest intersection points of the vectors. The probe spacing, source localization error, and source distance affect the estimation error. It is found that the intensity vectors indicating the source location diverge in some directions due to the geometric singularity. Numerical and experimental tests are conducted with three probe-modules configured as an equilateral triangle on a plane. The result reveals that the large error due to geometric singularity can be significantly reduced by only excluding the corresponding vectors that cause the divergence.

Linear acoustic theory is used for estimating the acoustical performance of the air cleaner box composed of the porous filter and encasing box in the engine intake system. The pleated filter structure is modeled as coupled multiple ducts having permeable micro-perforated walls and rectangular section, in which each duct area is assumed being homogeneous or inhomogeneous. Mathematical models describe the sound propagation within the narrow duct considering the visco-thermal effect at the filter pleats. For the validation, transmission loss (TL) is measured, and a change in TL spectrum is clearly observed by including the filter into the box. It is shown that the predicted TL counting the effect of visco-thermal loss agrees reasonably well with the experimental results. Noticeable effects of the filter on the TL are observed as highly smoothing effect at high frequencies and enhancing the TL magnitudes at troughs and lobes at low frequencies. Comparing homogeneous and inhomogeneous channel modelings, the latter is superior in precisely predicting the trough frequencies of TL curve, but the former is a bit better in predicting its magnitude. Parametric study on material and shape factors reveals that the number of pleats, length of the pleated filter, and distance between neighboring pleats are the key factors in determining the TL. It is concluded that an air filter element that has small number of long pleats with high flow resistance would bear the best acoustical performance among all designs.

Vibrational energy transmission through the bolt-nut system joining two elastic structures is important as it is one of the widely used fastening methods. In this work, the effects of fastening torque and washers are studied as major factors influencing the vibrational power transmission. An experimental method using the structural intensity technique is employed to investigate the characteristics of the power flow through the joint. It is found that the energy dissipation decreases with the increase of fastening torque until reaching the nominal one in the elastic range. Also, the test result reveals that increasing the number of washers is effective in attenuating the vibration energy transmission through the joint, but it is found that using more than 3 washers is not efficient in reducing the vibration transmission.

A method to facilitate the efficient positioning of sound absorbing materials on the walls of an enclosure is proposed by quantifying the contribution of each wall segment to the sound field in a vibro-acoustic transfer matrix. Wall reflections can be considered as secondary sources of radiation, whose strengths depend on the primary source and the amount of absorption by the walls. Based on this idea, the proposed evaluation method to quantify the degree of effectiveness for each wall segment is to quantify the linear independence of the rows or columns in a transfer matrix. The multiplication of quantified linear independence of elements in two transfer matrices consisting of the transfer path of sound is suggested as an observation parameter for selection. The proposed method is verified through numerical simulations and experiments. As absorbing patterns are treated at the surfaces with the highest linear independence in the transfer matrix, the sound pressure at most frequencies decreases for a point receiver or a finite region of receivers. The proposed method has advantages in terms of required effort, because it does not require any iteration process. The proposed method can produce a practically applicable solution without any detailed assumptions about the sound source and boundary conditions which are not clearly known at the design stage.

Various applications require a compact system for acoustic source localization. Intensimetry methods based on three-dimensional (3D) acoustic intensity are favorable for miniaturizing localization array systems because of the small errors at low Helmholtz numbers. However, in practice, conventional 3D intensimetry has not performed well at high Helmholtz numbers because of large spatial and spectral bias errors. In this work, the spatial bias error of 3D acoustic intensimetry is analyzed with respect to the irregularities in directivity. The magnitude of spatial bias error is found to be proportional to the gradient of the array directional response. Therefore, the maximum spatial bias error occurs in the vicinity of the direction corresponding to the maximum or minimum value of the array directional response. For smoothing the spatial array directional response, a combination of array modules with mutual symmetry in directivity is proposed as a compensation method. A stellated octahedral shape, and its truncated form, can regularize the array directional response while maintaining a small number of microphones. Source localization is tested using single and combined modules. The root-mean-square error of the bearing angle when using the combined modules is 1.0° in the Helmholtz number range of 2.0–3.0, which is far smaller than the error of 10.1° when using the single modules. Moreover, the truncated stellated octahedral probe, which is composed of a combination of tetrahedral and hexahedral arrays, is the most efficient array configuration for source localization and achieves high precision at high Helmholtz numbers with only five microphones.

The inherent weakness of conventional panel speakers is the inevitable multi-modal vibration behavior, resulting in severe fluctuation in the radiated sound spectrum, which is detrimental to the sound quality. A panel speaker that is actively controlled by array actuators at the panel edges has been proposed as a solution to the problem, but the increased cost and complexity due to a large number of actuators remain a challenge. In this study, a panel speaker using a thin beam, called a strip speaker, that adopts only three actuators is proposed to alleviate the modal fluctuation problem. When the middle position of the beam is excited by the primary actuator, the propagated bending wave field there from is controlled by two actuators at either end of the beam that prevents reflection of the wave. To achieve this, the inverse problem is derived by using the transfer function between the actuators and the coefficients of the reflected waves, from which an appropriate gain of the two control actuators is obtained as the inverse solution. For validation, a thin beam with a size of 315 × 40 × 2 mm3 is tested by simulation and experiment. Peaky resonant responses are made to disappear by controlling the vibration field, and the input mobility of the primary actuator becomes like that of an infinite beam. The boundary of the beam, which is newly defined at the location of the control actuators, is converted into an anechoic termination. The effect of the beam material is also tested by comparing aluminum and acrylic beams. It is shown that the damping of the acrylic beam is favorable in resulting a flat response, but its effective frequency range is lowered from that of the aluminum beam. In the experiment, the control actuators near the ends of unknown boundary conditions are located at the position to minimize the total input power for control. The experimental results of the controlled vibration field and radiated sound spectrum agree well with the predicted characteristics. It is shown that the proposed strip speaker with the traveling wave control method can be used to produce excellent acoustic performance.

For developing the quiet axial fans, the spatial distribution of acoustic source parameters over the source plane provides essential information. In this study, the previously suggested source identification technique by authors is newly applied to an axial fan. To obtain the acoustic source parameters in a duct, one should overcome many technical difficulties related with: the turbulent flow, high order modes, rotating sources, inverse estimation. Measurements are conducted with several arrays of flush mounted microphones deployed on the periphery of the duct wall. A reference trigger signal obtained from the rotating blade is used to suppress the effect of turbulent flow in the measured pressure spectra with a reduction of about 25 dB in the present work. The maximum error between measurement and estimation is generally-20 dB in the measurement plane in the very vicinity to the source. The visualized source images clearly indicate the locations and the strengths of main contributors to the radiated sound, e.g., for the inlet of the axial fan, the tip clearance between fan blades and shroud wall.

When a primary actuator excites the centre point of a rectangular panel speaker, the reflected bending waves at the edges of the plate are superposed with the incident wave and other reflected waves, and this results in a strong modal behaviour. Accordingly, the radiated sound spectrum possesses strong amplitude fluctuations, which results in a poor sound quality. This paper considers via simulations a rectangular panel speaker excited at its centre by a primary actuator and controlled by an edge-located array of control actuators to suppress the multi-modal behaviour of the panel. The basic concept is to eliminate the bending wave reflection from the panel boundary using the control actuator array; thus, only a freely travelling cylindrical wave generated by the main actuator remains. The input gain of the control actuators is obtained via the solution of the inverse problem derived using the transfer matrix between the actuator input and the velocity response on the plate. To ensure the economical use of the input energy required by the control actuators while maintaining the desired acoustic performance, regularisation is employed when solving the inverse problem. By assuming the linearity between the input voltage and the generated force of the actuator, the input efficiency of the control actuators is compared. The control performance is investigated by using a 2-mm thick aluminium panel with an area of 0.7 × 0.4 m2. The controlled result shows that the driving-point mobility of the primary actuator approaches that of the infinite plate, which means that the boundary, now the connection line of the control actuators, is converted into an anechoic one. Elimination of the modal effect yields the smoothed spectrum of the radiated sound without severe peaks and troughs.

For the design of duct silencers, one should satisfy the essential constraints on the sound attenuation band, additional volume, and backpressure. For wideband sound attenuation, various acoustic metamaterials (AMM) using multiple resonators have been proposed. However, they often do not satisfy the spatial constraint, and the blocking of the conduit makes them impractical. This study proposes a compact silencing AMM unit for wideband sound reduction without deteriorating the mechanical performance. Previous works on the stacked micro-perforated panels (MPP) with different backing air gaps provide the basic idea of this work, which reveals the benefit of multiple resonators in adjusting the bandwidths to attain a wideband attenuation characteristic. The resistive element is also exploited in the MPP for suppressing the acoustic transparency of the detuned resonators. The formulated theoretical design method is tested by using a resonant unit cell configured with a serial connection of quadruple MPP layers, each air gap with a length of 30 mm and a uniform sectional area of 8 × 8 mm2. For minimizing the occupied volume, each cell surrounds the outer periphery of the main duct by folding, and the cell entry is flush-mounted on the duct wall. The test is conducted with the main duct of 30 × 30 mm2, and the attached 50 cells are arranged periodically with a 10-mm interval. The additional width of the duct is less than 1% of the wavelength. The measured power transmission coefficient is less than 0.2 for the range of 0.4–4.05 kHz, which agrees well with the prediction.

For rendering a desired characteristics of a sound field, a proper conditioning of acoustic actuators in an array are required, but the source condition depends strongly on its position. Actuators located at inefficient positions for control would consume the input power too much or become too much sensitive to disturbing noise. These actuators can be considered redundant, which should be sorted out as far as such elimination does not damage the whole control performance significantly. It is known that the inverse approach based on the acoustical holography concept, employing the transfer matrix between sources and field points as core element, is useful for rendering the desired sound field. By investigating the information indwelling in the transfer matrix between actuators and field points, the linear independency of an actuator from the others in the array can be evaluated. To this end, the square of the right singular vector, which means the radiation contribution from the source, can be used as an indicator. Inefficient position for fulfilling the desired sound field can be determined as one having smallest indicator value among all possible actuator positions. The elimination process continues one by one, or group by group, until the remaining number of actuators meets the preset number. Control examples of exterior and interior spaces are taken for the validation. The results reveal that the present method for choosing least dependent actuators, for a given number of actuators and field condition, is quite effective in realizing the desired sound field with a noisy input condition, and in minimizing the required input power.

To understand and reduce the flow noise generation from in-duct fluid machines, it is necessary to identify the acoustic source characteristics precisely. In this work, a source identification tech ...

Vibrations are rendered on the display panel of a mobile electronic device to transfer a tactile sensation to users. Because important electronic components are usually positioned in the central part of the devices, the only practical choice for actuator location is the periphery of the panel although the periphery is not the advantageous position for the excitation. As the basic principle to generate a rendered vibration pattern, two methods to determine the contributions of modes, viz., eigenfunction superposition or traveling wave control method, are implemented individually. The purpose is to generate a pattern of vibration amplitudes that can be felt by fingertip in the hot zone but not in the cold zone, which is outside the hot zone. General inverse methods are applied to obtain the actuator weightings for achieving the target pattern. Proper weighting for both amplitude and phase for each actuator in the array is determined by the relationship between modes or velocity responses and input signals of actuators. Two methods are implemented individually on the display panel of a commercial tablet computer using an array of moving-coil actuators, and the responses on the panel are measured. Performance index referred to as success ratio for evaluating satisfaction of target field constraints is proposed considering the different thresholds of vibration sensation. Reasonable fulfillment of achieving the target vibration pattern is observed experimentally. The success ratio is more than 86% by using the eigenfunction superposition, and more than 97% by using the traveling wave control for rendering 2×2 and 3×3 section.

This study is on the practical application of the acoustic metamaterials to the design of a silencer with high acoustic and geometric efficiencies, and negligible pressure drop. The object is to achieve broadband and low-frequency attenuation simultaneously by combining the effects of resonance, periodicity, phase difference, and impedance mismatch. An array of multiple small resonators, which is periodically applied to the wall of a duct, invokes the dispersion of sound propagating in the duct. This phenomenon is implemented to construct a virtual Herschel-Quincke (HQ) tube system. The main duct is split into two parallel ducts of the same length: a rigid duct and a duct with a wall covered by the periodic resonators. For a modelling of sound propagation in a dispersive duct, the phase speed of sound is analytically derived in the presence of a mean flow. Also, the attenuation conditions of the virtual HQ tube are proposed to establish a guideline in selecting the proper design parameters for achieving the required transmission loss (TL) in the desired frequency range. The predicted TL spectra are compared with the test results, for a virtual HQ tube system with 9 identical quarter-wavelength tube resonators, and they generally agree well. With increasing flow speed, the amount of attenuation decreases a bit, but the general spectral characteristics are maintained for | M | ≤ 0.1 . Based on the same principle, the acoustic metamaterials (AMM) are applied to the practical silencer design to achieve the wide-band sound reduction at low- to mid-frequencies for a given small space. A virtual HQ tube having 26 cells of AMM is tested, of which a cell is composed of 3 types of quarter-wavelength tube resonators. The experiment well validates the predicted TL. The results show that TL is at least 5 dB for a wide frequency range of 230–1000 Hz. The additional volume due to the attachment of the AMM layer is only 40%, while the TL is far larger than that of the simple expansion chamber or the dissipative silencer having the same excess volume.

Source identification of acoustic characteristics of in-duct fluid machinery is required for coping with the fluid-borne noise. By knowing the acoustic pressure and particle velocity field at the source plane in detail, the sound generation mechanism of a fluid machine can be understood. The identified spatial distribution of the strength of major radiators would be useful for the low noise design. Conventional methods for measuring the source in a wide duct have not been very helpful in investigating the source properties in detail because their spatial resolution is improper for the design purpose. In this work, an inverse method to estimate the source parameters with a high spatial resolution is studied. The theoretical formulation including the evanescent modes and near-field measurement data is given for a wide duct. After validating the proposed method to a duct excited by an acoustic driver, an experiment on a duct system driven by an air blower is conducted in the presence of flow. A convergence test for the evanescent modes is performed to find the necessary number of modes to regenerate the measured pressure field precisely. By using the converged modal amplitudes, very-close near-field pressure to the source is regenerated and compared with the measured pressure, and the maximum error was -16.3 dB. The source parameters are restored from the converged modal amplitudes. Then, the distribution of source parameters on the driver and the blower is clearly revealed with a high spatial resolution for kR < 1.84 in which range only plane waves can propagate to far field in a duct. Measurement using a flush mounted sensor array is discussed, and the removal of pure radial modes in the modeling is suggested.

The three-dimensional acoustic intensimetry has not been found useful for the sound source localization, although it was developed a long time ago. One of the leading causes is the significant amount of inherent bias error in the measured intensity vector. In addition to the well-known phase mismatch and finite difference errors, the two crucial bias error mechanisms exist yet. Both of them are principally caused by employing the limited number of microphones in estimating the direction-of-arrival vector. One is the spectral bias error exhibiting a significant fluctuation in the intensity spectrum, which is due to the time-delay of the incident and reflected sounds travelling between microphones. The other is the spatial bias error exhibiting the intensity variation depending on the probe orientation, which is due to the spatial inhomogeneity of the microphone distribution. In this work, two parameters are considered in the compensation of spectral bias error: the phase of cross-spectrum and the time contents of cross-correlation function. Also, an error map associated with the incident direction of sound is calculated for a sphere surrounding the probe to compensate for the spatial bias error. Experiments are conducted with two different source types emitting a band-limited noise and an impulsive sound, and also varying the source positions to investigate the effect of main parameters. A tetrahedral intensity probe consisted of 4 pressure microphones with 30-mm spacing is used for the test in a reverberant space. The result shows that the mean localization error is less than 3° for 0.3

Artificial ear is being used to evaluate the acoustic response and the sound quality of the mobile telephony devices, which simulates the practical listening condition of the outer ears. In this paper, a method to estimate the coupled acoustic response of the device with an artificial ear is studied to be effectively used in the design. To this end, an equivalent circuit model of the total receiver system including all accessory elements is established. Acoustic impedance of artificial ear, which is essential in the equivalent model, is directly measured by using three microphones arranged in tandem on the duct wall connected to the artificial ear. Input impedances of two artificial ears, Type 3.3 and 3.4, which are currently employed as the standard devices, are measured. The measured data is incorporated into the model to predict the acoustic response. To validate the proposed model using the measured impedance, the measured acoustic responses of two simulation systems including mobile phone and artificial ear are compared with the predicted ones. A reasonably good agreement between measurement and prediction is observed, and their difference is less than 4.5 dB at the narrow communication band for a mobile phone (f

The intake or exhaust noise of an internal combustion engine is usually predicted by the linear, time-invariant source model in frequency domain with reasonable precision. However, the actual finite amplitude pulsation involves the nonlinear, time-varying characteristics that are prominent in time-domain. To overcome the discrepancy between two source models, an approximate nonlinear and time-varying frequency domain source model can be employed by appending the nonlinear or time-varying terms to the linear, time-invariant source model. Proper selection of the nonlinear describing terms varying with time is important for the realistic and precise prediction of the radiated sound. For the selection of such terms, flow and motional characteristics in the valve and orifice of a simplified fluid machine comprised of very large reservoir, valve, and duct is considered. Effects of each describing term and the combined terms are investigated by comparing the sound spectrum predicted from nonlinear source model to that from linear source model. In the comparison, the sound spectrum calculated by the method of characteristics is used as a reference. It is found that the source model using only the velocityrelated terms yields the best result among all the models using various combinations of the terms with different characteristics. The best model yields a difference from the linear source model within ±5 dB in overall sound level. Change of acoustic loads results in a difference of 20–27 dB in linear source model from the reference data; however, maximum 10–22 dB deviations are observed in using the various nonlinear source models. It is concluded that more than 4 describing terms should be employed in the nonlinear model to obtain a realistic result of the radiated sound from the intake or exhaust system.

In the analysis of interior acoustic problems, the time domain boundary element method (TBEM) suffers the monotonically increasing instability when using the direct Kirchhoff integral. This instability is related to the non-oscillatory static acoustic mode describing the constant spatial response in an enclosure. In this work, nonphysical natures of non-oscillatory static mode influencing the instability of TBEM calculation are investigated, and a method for stabilization is studied. In TBEM calculation, the static mode is represented by two non-oscillatory eigenmodes with different eigenvalues. The monotonically increasing instability is caused by the unstable poles of non-oscillatory eigenmodes as well as very small, very low frequency noise of an input signal. Interior problems with impedance boundary condition also exhibit the monotonically increasing instability stemming from its pseudo non-oscillatory static mode due to the lack of dissipation at very low frequencies. Calculation of transient sound fields within rigid and lined boxes provides numerical evidences. It is noted that the stabilization effort by modifying the coefficient matrix based on the spectral decomposition can be used only for correcting the unstable pole. The filtering method based on the eigen-analysis must be additionally used to avoid the remaining instability caused by very low frequency noise of input signal.

The time domain boundary element method (TBEM) to calculate the exterior sound field using the Kirchhoff integral has difficulties in non-uniqueness and exponential divergence. In this work, a method to stabilize TBEM calculation for the exterior problem is suggested. The time domain CHIEF (Combined Helmholtz Integral Equation Formulation) method is newly formulated to suppress low order fictitious internal modes. This method constrains the surface Kirchhoff integral by forcing the pressures at the additional interior points to be zero when the shortest retarded time between boundary nodes and an interior point elapses. However, even after using the CHIEF method, the TBEM calculation suffers the exponential divergence due to the remaining unstable high order fictitious modes at frequencies higher than the frequency limit of the boundary element model. For complete stabilization, such troublesome modes are selectively adjusted by projecting the time response onto the eigenspace. In a test example for a transiently pulsating sphere, the final average error norm of the stabilized response compared to the analytic solution is 2.5%.

The accuracy of a phased beam tracing method in predicting transfer functions is investigated with a special focus on the positions of the source and receiver. Simulated transfer functions for various source-receiver pairs using the phased beam tracing method were compared with analytical Green’s functions and boundary element solutions up to the Schroeder frequency in simple rectangular rooms with different aspect ratios and absorptions. Only specular reflections were assumed and diffraction was neglected. Three types of error definitions were used: average error level over a narrow band spectrum, average error level over a 1/3 octave band spectrum, and dissimilarity measure. The narrow band error and dissimilarity increased with the source-to-receiver distance but converged to a certain value as the reverberant field became dominant. The 1/3 octave band error was found to be less dependent on the source-receiver distance. The errors are increased as the aspect ratio becomes more disproportionate. By changing the wall absorption from 0.2 to 0.8 for a rectangular room, the average narrow and 1/3 octave band error are deviated by around 1.5 dB. A realistic nonuniform distribution of the absorption increases the error, which might be ascribed to wave phenomena evoked by the impedance-discontinuous boundary.

The time domain boundary element method (BEM) is associated with numerical instability that typically stems from the time marching scheme. In this work, a formulation of time domain BEM is derived to deal with all types of boundary conditions adopting a multi-input, multi-output, infinite impulse response structure. The fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter, which can also invoke a modeling error. In the calculation, the response at each time step is projected onto the wave vector space of natural radiation modes, which can be obtained from the eigensolutions of the single iterative matrix. To stabilize the computation, unstable oscillatory modes are nullified, and the same decay rate is used for two nonoscillatory modes. As a test example, a transient sound field within a partially lined, parallelepiped box is used, within which a point source is excited by an octave band impulse. In comparison with the results of the inverse Fourier transform of a frequency domain BEM, the average of relative difference norm in the stabilized time response is found to be 4.4%.

The time-domain solution from the Kirchhoff integral equation for an exterior problem is not unique at certain eigen-frequencies associated with the fictitious internal modes as happening in frequency-domain analysis. One of the solution methods is the CHIEF (Combined Helmholtz Integral Equation Formulation) approach, which is based on employing additional zero-pressure constraints at some interior points inside the body. Although this method has been widely used in frequency-domain boundary element method due to its simplicity, it was not used in time-domain analysis. In this work, the CHIEF approach is formulated appropriately for time-domain acoustic boundary element method by constraining the unknown surface pressure distribution at the current time, which was obtained by setting the pressure at the interior point to be zero considering the shortest retarded time between boundary nodes and interior point. Sound radiation of a pulsating sphere was used as a test example. By applying the CHIEF method, the low-order fictitious modes could be damped down satisfactorily, thus solving the non-uniqueness problem. However, it was observed that the instability due to high-order fictitious modes, which were beyond the effective frequency, was increased.

At the idle engine speed, the exhaust discharge noise is influenced by resonances in the whole system, which is composed of connecting pipes and silencers. This pipe resonance radiates a high level of low frequency discharge noise, which is dominated by the low order harmonics of the engine firing frequency. This low frequency noise deteriorates the vehicle’s interior noise level and quality. The following study attempted to optimize the layout of an exhaust system to minimize low frequency noise by changing the position of silencers and the lengths of inlet and outlet pipes in each silencer. After modeling the exhaust system using four-pole parameters, the acoustical performance of the system was evaluated using the system insertion loss. In the optimization, the virtual attenuation coefficient, which corresponds to the amount of attenuation coefficient required for the silencers, was calculated to find a minimum value for the layout. The simulated annealing method, which is also known as finding an optimal, was employed in searching for the optimized exhaust layout. Test examples of two cases, for two and six design variables, were used. When the number of design variables was two, the positions of the center and rear silencers were considered. When the number of design variables was six, the positions of the two silencers and the lengths of the inlet and outlet pipes were considered. Three typical layouts for the exhaust system of each case were designed, including the given system and an optimal system. By comparing the predicted and measured discharge noise level, it was confirmed that the optimized exhaust layout has a higher noise reduction than the other layout designs.

In this paper, a method to establish a decision criterion to evaluate the quality of small window motors using sound quality (SQ) metrics is suggested. Although the sound level radiated from the motor is relatively small compared to other sounds in a car, the sound from an abnormal motor gives an uncomfortable feeling and the impression of abnormal operation, which can lead to customer complaints. To construct an objective decision criterion, the correlation between the SQ metrics and the subjective decision on the passing or failure of the motor were investigated. Four representative SQ metrics, viz., loudness, sharpness, roughness, and fluctuation strength, were calculated for the collected samples. It was observed that the loudness and roughness of the motor sample group classified as abnormal was higher than those of the normal motors. For a single figure rating for motor quality, an evaluation index for the motor sound was generated by combining the correlated SQ metrics with proper weightings. Evaluation results on the specimens that were not employed in generating the quality evaluation index showed a reasonable agreement with the subjective test at 73%. The suggested quality check method can replace the current subjective decision procedure to identify the faulty motors.

A planar, broadside acoustic array with uniform loudspeaker spacing is often adopted for generating a highly directional acoustic beam, but the performance in radiated power and spatial bandwidth should always compromise with the transverse size limit. To achieve a high-power, directional sound in a compact size, a multi-layered loudspeaker array configured in both broadside and end-fire types is devised. This design concept is tested with an array of 3 layers with 0.2 m spacing. Each layer contains 7 loudspeakers in a centrally symmetric arrangement on a plane with the longest dimension of 0.6 m. In each layer, the separation distance between loudspeakers is uniformly set as 0.2 m. The optimal beamforming method is employed for calculating the control filter. The compensation for the performance degradation due to self-scattering effect is also included in the control filter, for which the additional phase delay due to scattering is estimated from the simulated response of the array system. The maximum sound level at 1 m distance from the array center is achieved as 145 dB at 1.5 kHz, and, at 30 m position, the level decrease of 26–30 dB with the directivity index of 15 dB is observed for 1–5 kHz.

Panel speakers often adopts the vibration actuator attached to a plate center to excite the whole panel. When a thin rectangular plate is excited by a point force, the generated bending wave is reflected quickly from the edges, so the plate is governed by the reverberant field. Because many vibrational modes participate even in the low frequencies, the radiated sound spectrum is involved with many peaks and troughs resulting a poor sound quality. To minimize the modal participation, the vibration is rendered to be confined and in-phase within a circular area enclosing the actuator point, and the vibration is being suppressed outside of it. An additional multi-layer actuator array surrounding the speaker zone is employed to control the vibration, thus fulfilling the rendered field. The study aim is now to obtain an appropriate gain of the actuators by solving the inverse problem consisting of the transfer matrix between field points and control actuators. The effect of the number of arrays is tested for the radius of 0.05–0.2 m. The control result reveals that the signal-to-noise ratio in the speaker and baffle zone is improved 8–11 dB by the three-layer array than by the single-layer array with the same size.Panel speakers often adopts the vibration actuator attached to a plate center to excite the whole panel. When a thin rectangular plate is excited by a point force, the generated bending wave is reflected quickly from the edges, so the plate is governed by the reverberant field. Because many vibrational modes participate even in the low frequencies, the radiated sound spectrum is involved with many peaks and troughs resulting a poor sound quality. To minimize the modal participation, the vibration is rendered to be confined and in-phase within a circular area enclosing the actuator point, and the vibration is being suppressed outside of it. An additional multi-layer actuator array surrounding the speaker zone is employed to control the vibration, thus fulfilling the rendered field. The study aim is now to obtain an appropriate gain of the actuators by solving the inverse problem consisting of the transfer matrix between field points and control actuators. The effect of the number of arrays is tested for th...

A 3D acoustic intensimetry (AI) in tetrahedral configuration can be used for the source localization. Such a 3D AI module is compact, but it can also yield a precise bearing angle for the low Helmholtz numbers if some bias errors are compensated. In this study, besides the bearing angle, the source distance is estimated by using the multiple 3D AI probes with different acoustic centers. Because each AI module indicates a vector from the acoustic center to the source direction, the nearest point between any pair of line vectors can approximate the source position. The source position can be estimated by minimizing the least square error of the positions determined by multiple intensity vectors. Such idea is preliminarily tested with four 3D AI modules, of which each module is composed of 4 MEMS microphones separated by 30 mm. Four 3D AI modules are also arranged in a tetrahedron layout, and the source frequency range is 0.5–2 kHz. The distance between modules is varied for 150–250 mm range, and the source distance for 1–4 m range. Current test results reveal that the estimation error is less than about 2, 5, and 7% when the elevation angle is within 0–30°, 30–60°, 60–90°, respectively.

Near-field acoustical holography (NAH) is a useful tool for the identification and visualization of vibro-acoustic sources. In particular, NAH can be applied to many practical sources having irregular shape if the inverse boundary element method (BEM) is employed. Once the relation between the source and the radiated field is defined in the transfer matrix modeled by the BEM, the reconstruction of acoustic parameters on the source surface can be conducted by the multiplication of the inverse transfer matrix and the field data measured over the hologram surface. The usual practical way to measure the field data radiated from an irregular shaped source is to adopt a regular hologram surface, which can be a flat, cylindrical, or spherical shape, for the measurement ease. Then, the hologram surface is not conformal to the source surface and the resulting transfer matrix becomes further ill-posed than the conformal case. To investigate the effect of sensor proximity and distance variability on the reconstruction error, simulation and measurement were conducted for an interior problem comprised of a parallelepiped rigid box with a vibrating end plate. Flat, tilted, and randomized hologram surfaces were adopted in the test. It was shown that the reconstruction error is greatly affected by the conditioning of transfer matrix which is related to the positioning of sensor. To improve the reconstruction accuracy, an investigation was conducted to find proper field points among a large number of overdetermined field points. The number of field data was reduced gradually under various reduction schemes using condition number, effective independence value, and sensor distance. It was demonstrated that the quality of reconstruction result given by the non-conformal measurement can be improved by removing some field points that contribute to the ill-conditioning of the inverse problem. A small improvement of the reconstruction accuracy was observed by reducing the field points in the overdetermined situation. However, further reduction of the field points, becoming an underdetermined situation, yielded a drastic improvement of the reconstruction accuracy.

The acoustic design of exhaust mufflers has mainly focused on reducing the discharge noise from the tailpipe. However, the noise that is transmitted through the muffler jacket and the endplate becomes important since the muffler reduces the amount of discharge noise when it has an optimized design. It is known that the contribution to the overall exhaust noise of the muffler shell is significant in the mid- and high-frequency ranges. The current problem is that there are no appropriate computational tools at high frequencies. A simple method to analyze the 1/3-octave band of sound radiating from an arbitrary shape (like a muffler) was employed to predict the band spectrum of the radiated noise. The calculation method included formulating the boundary integral, which was modified into a quadratic form in order to enable the prediction of the intensity levels in a band analysis. Monopole and dipole source terms in the conventional BEM were transformed into the auto- and cross-spectra of the two vibrating sources, in which the cross-spectra could be eventually omitted by assuming that the correlation coefficients were negligible. The method was adopted in an abrupt calculation of the shell noise in 1/3-octave band levels without nonuniqueness problem. In comparison with the measured data, the simulation result showed roughly 3-dB errors at most of the field points, excluding several special points that were normal to the shell and exhibited a maximum 5-dB error.

At high frequencies, energy methods such as the statistical energy analysis and the power flow analysis have been popularly used to predict the averaged responses of vibro-acoustic subsystems. Usually, these energy methods ignore flexural nearfield components and phase information, mainly for simplicity. Such assumptions sometimes lead to an erroneous conclusion, in particular for complex structures and at medium frequencies around the Schroeder cutoff frequency. This paper deals with the effects of nearfield waves and phase information at medium to high frequencies by using the ray tracing method (RTM). A curved beam and a coupled beam system were chosen as test examples, which exhibit the typical mode conversion between various types of travelling waves. Propagation of longitudinal, flexural, and torsional waves was studied based on the Euler-Bernoulli beam theory. Analyses of the spatial distribution of vibrational energy quantities revealed that the conventional RTM could mimic the overall trend of the traveling wave solution. However, the results varied smoothly in space due to the neglect of wave interference. By considering the phase information, local fluctuations of vibration energy could be correctly described. It was confirmed that the flexural nearfield plays a significant role near boundaries and junctions. It was also shown that the accuracy of the analysis depends mainly on the modal overlap factor. Similar to other high frequency methods, the results become close to the traveling wave solutions as the modal overlap factor increases.

It is very important to predict the radiated noise from the engine intake system for the effective noise control and virtual prototyping of in-cavity and outdoor noise of a vehicle. To this end, one should precisely measure the in-duct acoustic source parameters of the intake system, viz., source strength and source impedance. Usually, the noise radiation characteristics need to be expressed as a function of engine speed. In this study, acoustic source parameters of an engine intake system under engine run-up condition were measured by using the direct method. Direct method employed two external loudspeakers, turned on simultaneously, and three microphones for the separation of upstream and downstream wave components. It was noted that the frequency spectra of source impedance hardly changes with the increase of engine speed. Utilizing this fact, source strength under the engine run-up condition was calculated by assuming invariant source impedance. Predicted insertion loss and radiated sound pressure level using the measured source parameters were compared with those of measured data and predicted data using several idealized source models, which have been adopted for the calculations. A reasonably good agreement was observed between measured sound spectra at the intake orifice and predicted one using the measured source data. It was shown that the source data obtained by the present method yielded a far better prediction accuracy than those by the idealized source models.

Automotive booming noise due to powertrain occurs when pure or narrow band tones related to the firing frequency of engine and its harmonics excite the passenger cavity, which entails a prominent increase of sound intensity. The booming sensation has been considered as very important to the acoustic comfort of passengers. In this study, a sound quality index which can objectively evaluate the booming sensation was derived. Because of the tonal nature of powertrain booming noise, subjective pitch was employed to find only aurally relevant tonal components which influence booming sensation as well as loudness. Using the empirical data and the frequency difference limen for just-noticeable change of booming sensation obtained from the listening test, an existing pitch extraction algorithm could be modified. The modified pitch model was applied to the interior noises of accelerating passenger cars together with a loudness analysis for representing the objective features of booming feeling. Subjective tests using the magnitude estimation method were conducted to evaluate the degree of booming sensation. Finally, booming strength was proposed for quantifying the booming sensation, which was validated by subjective results. The correlation coefficient between the derived booming strength and the degree of booming sensation obtained by the subjective test was 0.926.

In the simulation of acoustic response of a room, one cannot satisfactorily estimate the transfer function or the impulse response with a sparse frequency resolution. We have studied about the frequency resolution for a satisfactory estimation of room transfer function or the reverberation time using the phased beam tracing method. In order to investigate what happens with the frequency resolution, a number of frequency resolution (0.01–1 Hz), which are usually employed in the numerical analysis, was tested for a room model. It was found that the total accumulated phase in a transfer function and the late part of an impulse response of a room are influenced by the frequency resolution. Main reason for the difference is the correct detection of non-minimum phase zeros, depending on the frequency resolution. A criterion for a proper frequency resolution was suggested by considering the modal density of three-dimensional space. When a sparse dataset was initially given, we showed that cubic spline interpolation can be used to enhance the precision of detection for non-minimum phase zeros.

The phased beam tracing method (PBTM) was suggested as a medium-frequency simulation technique for the calculation of impulse response, although main assumptions of geometric acoustics still hold. The phased method needs the reflection coefficient for characterizing the acoustic property of a surface and the complex wave number for describing the propagation characteristics. In this study, two types of approximate real reflection coefficients derived from the measured absorption coefficient were tested for a practical applicability. As a test example, pressure impulse responses and energy impulse responses computed from the PBTM were compared with those from the measurement and the ordinary beam tracing method. The PBTM employing the approximate reflection coefficients greatly increased the accuracy of the prediction compared to the ordinary beam tracing method, in particular at the medium-frequency range in octave bands above the Schroeder cutoff frequency. A comparison was made between angle-dependent and angle-independent reflection coefficients in the calculation of acoustic measures. Although the angle-dependent reflection coefficient yielded best matched results with measured data, but the simple angle-independent reflection coefficient can be also used with a reasonably good precision.

It is known that the acoustical and, possibly, mechanical performance of the perforated resonator can be controlled by the porosity and distribution of holes. To analyze the effect of the porosity distribution pattern on resonator performance, in particular under the design condition of restricted volume, five typical perforation patterns of an acoustically long concentric resonator were investigated experimentally and numerically. Transmission loss and back pressure were used to represent the acoustic and mechanical performance indices, respectively. Prediction of transmission loss was made by segmental decoupling analysis with an empirical impedance model of orifices. Prediction of back pressure was done by computational fluid dynamics analysis. The overall trend of the calculated results matched well with the measured results. In terms of acoustic performance, it is noted that a specific frequency range was mostly influenced by the change of axial porosity pattern. For mechanical performance, a gradual change in porosity played a dominant role in stabilizing the flow field and static pressure distribution. It is concluded that an axial perforation pattern with a gradual change in porosity yields the best performance by forming a flow field with minimized loss and an acoustic field dominated by a quarter-wavelength resonance of equivalent extended pipes. In particular, the most preferred perforation pattern in terms of transmission loss and back pressure was the one with gradually increasing porosity from the upstream part and gradually decreasing porosity from the middle part as far as the downstream end.

A numerical model of the acoustic impedance of perforated plates under bias flow conditions was derived, with consideration given to the interaction effect between orifices. The normalized impedance divided by the mean flow Mach number of an orifice was expressed as a function of the Strouhal number varying the porosity and thickness-to-radius ratio. The prediction model was accomplished by solving the incompressible Euler equation for an orifice in a finite-thickness partition that spans a tube. The acoustic impedance was also measured experimentally using an error-controlled setup. As porosity increased, the reactance tended to decrease because the attached mass on the orifices is decreased by the interaction effect. The acoustic impedance predicted by the proposed model shows reasonable agreement with measured data over the wide range of porosity values tested, except where nonlinear effects are observed. For comparison of the performance of the new impedance model against two previous models that did not consider the interaction effect, each was used in the evaluation of the transmission loss of perforated baffles. The predicted transmission losses using the new impedance model agree better with the measured data than those using the previous models, in particular at high porosities and at high frequencies.