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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.

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.

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 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

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.

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.

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.

The resonant sound transmission has been regarded to be negligible in finite single partitions compared to the non-resonant transmission. In this study, the sound transmission coefficient is reconsidered by using the general modal expansion method in order to estimate the contribution of resonant components to the whole sound transmission at frequency bands below the coincidence frequency. By investigating the band-average difference between the total and non-resonant transmission losses, the validity of the aforementioned assumption is discussed. In the analysis, the participation factor comprised of size, thickness, and loss factor is employed. Based on this factor, the valid range of neglecting the resonant sound transmission is proposed, in which the inclusion of the resonant component makes difference being less than 1 dB.

Scattering of obliquely incident plane acoustic wave by an air-filled, transversely isotropic cylindrical shell immersed in water is investigated theoretically and experimentally. The normal mode expansion technique is employed for analyzing the scattering field, and then resonance modes of the shell appearing in modal scattering form functions are identified performing the resonance scattering analysis. Dispersion curves for Sholte–Stoneley, SH and Lamb waves are obtained and their characteristics are interpreted. Calculated backscattering and resonance spectra as well as dispersion curves are compared with those from ultrasonic experiments for two composite samples having the same nominal composition but fabricated under different conditions. Sensitive change of the dispersion curves is observed for both normal and oblique incidences, which demonstrates the feasibility of systematic inverse evaluation of damage or elastic constants of the composite shell using data from the acoustic scattering measurements.

For the prediction of the acoustic performance of an engine intake system with a porous woven hose, the acoustic wall impedance of the hose should be known. In this paper, a measurement technique is proposed that is valid over the low frequency range in the absence of mean flow. The impedance measurement is performed in two stages. The first stage of impedance measurement is performed in a cylindrical apparatus, within which a short specimen of given ‘porous frequency’ is laid. Because the predicted transmission loss (TL) does not agree with the measured one, due to error in the measured resistance, the second stage of impedance measurement is attempted to estimate the resistance from the measured reactance in the first stage and the measured TL data. Using such new impedance data measured in the second stage for the prediction of TL for samples of different lengths, the agreement between measured and predicted TL is generally improved, as compared to the initial comparison in the first stage. When the curve-fitted impedance for an arbitrary porous frequency is used, it is shown that the measured TL for samples with both arbitrary length and porous frequency generally agree reasonably well with the predicted ones. Exceptions are samples which require the impedance to be extrapolated from measured results, or samples with highly inhomogeneous weaving and coating conditions, and in particular samples with low porous frequency.

It is suggested from a previous theoretical study that an angular distribution function can be successfully used for describing the directional distribution of incident energy on the wall, instead of the field incidence assumption being used in the prediction of sound transmission loss. This study is devoted to an experimental investigation on the directionality of incidence sound field for validating the underlying assumption in the theoretical work. To this end, the directional magnitudes of incident energy on a wall in a reverberation chamber are measured by employing the sound intensimetry. The experimental results suggest that the transmission coefficient formula should be revised by introducing a proper angular distribution function as a weighting function for describing the directional energy density distribution, which replaces the conventional field incidence method. The revised formula is applied to the prediction of transmission loss for a double-leaf panel with an air cavity, in which its effectiveness is strongly supported by good agreements between measured and predicted values.

In order to evaluate the acoustic field within a duct system some knowledge is required about the acoustic source, which is characterized by frequency-dependent values of both strength and impedance. However, in using various experimental techniques for various types of source to obtain these values, negative real parts of the source impedance have been measured. Negative source resistance is physically implausible. In some instances, one measurement method gives positive values of source resistance where another gives negative values. This paper reviews the possible causes of the problem, with reference to experimental and theoretical results, in an attempt to clarify the issue. Various possible origins of a negative source resistance have been investigated. It is noted that, for the time being, the violation of the assumption of a time-invariant source and the defect in the inherent algorithm of the load method are the most probable origins of the negative source resistance.

At high frequencies, one is interested in both the energy distribution and the energy flow of connected vibrating structures. The prediction of time- and space-integrated energy quantity has been usually performed by the statistical energy analysis (SEA), whereas the vibration conduction analysis (VCA) was suggested for calculating the time-averaged spatial energy distribution in structures. However, the VCA has not been useful due to inaccuracies in predicting the energy distribution and estimating the vibration transmission through structural joints. In this article, the ray tracing method (RTM) for high-frequency plate flexural vibration is suggested for solving the foregoing problems. The ray tube concept is adopted for describing the emanating circular wave and the governing relationships are derived for incident, reflected, and transmitted ray tubes at the coupled boundaries. The proposed RTM is applied to the prediction of the time-averaged vibration distribution in a single square panel and two line-coupled square plates. In addition, a four-panel array is investigated for the performance of the proposed RTM in analyzing the vibration transmission characteristics by panel joints. The results reveal that an improved prediction of spatial energy distribution can be obtained compared with SEA and VCA. It is also noted that the performance of the RTM is very similar to that of the wave intensity analysis (WIA) although RTM results seems to be slightly better.

Because of the high performance and low weight requirements for modern machines including engines, the belts servicing high dynamic loads at high speed tend to be very susceptible to the transferred vibration. In this paper, a method is proposed for obtaining the physical characteristics of the transverse vibrational power flow through moving rubber belts. The governing equation is derived by applying Hamilton's principle to the description of the flexural vibrations in axially moving belts, where the tensioner is considered to be a one-degree-of-freedom system. The total power flow calculated and measured in the moving belt is the sum of the true power flow and the power component associated with the steady medium motion. Consequently, any component that is due solely to the belt movement should be subtracted from the total power flow in order to obtain the true, net power flow. This concept is employed in calculating the transverse vibrational power flow through belt–pulley systems that include a tensioner. An equivalent system including an idler instead of the tensioner is also considered, and the observed power flow in this condition is ascribed to the power flow due only to the movement of the medium. The results of analysis show that the vibrational power of the two belt-spans flows into the tensioner. It is shown that the energy flow, measured by using two laser sensors, agrees reasonably well with the predicted results.

An explicit formula of the transfer matrix is derived for evaluating the acoustic performance of the chamber including curved duct bends. Based on the derived transfer matrix, the reactive sound attenuation of the chamber can be easily calculated by using an empirical formula for estimating the normalized maximum radial pressure of the fundamental mode in the curved duct bend. Predicted results are compared with experimental ones and they show good agreements. It is found that the classical plane wave theory for the straight duct of equivalent length to the curved duct bend is not applicable if the normalized maximum pressure is greater than 1.3. In addition, the sound attenuation in curved expansion chamber is investigated by studying the effect of geometrical parameters. The derived transfer matrix for the curved duct bend can be easily incorporated as a basic module into any existing computer programs dealing with four-pole parameters for predicting the acoustic performance of HVAC and other silencing systems.

The two most popular frequency response function estimators,Ĥ1andĤ2give biased estimates when measured input and output signals are contaminated by uncorrelated noises. Recently, an improved frequency response function estimatorĤswas proposed for reducing the bias error due to measurement noises, but without any analysis on the random error. In this paper, the random error formula forĤshas been derived for accurate estimation of desired function. The result shows that the random error in the magnitude ofĤsis always smaller than that ofĤ2, but larger than that ofĤ1.

As a first step toward the acoustic analysis of catalytic converters in automotive exhaust systems, wave propagation through a capillary tube with steady flow is dealt with. Using the general formulations of conservation equations with non-isentropic conditions based on the low reduced frequency solution, the linearized equations are solved by the recursive use of numerical methods. No initial assumptions are imposed on the shape of axial velocity profiles and the radial velocity fluctuation is also included in the analysis. Characteristics of the forward and backward propagating acoustic waves are investigated under the influence of steady flow and the calculation is performed up to high shear wave numbers. The characteristics of hydrodynamic waves are also investigated when steady flow is present. The application limits of the previous work are demonstrated as the shear wave number increases. The numerical method is applied to the prediction of the transmission loss of a stack of capillary tubes with and without mean flow considering the effects of radial components and the calculated results agree reasonably well with experimental ones.

A weakly singular boundar integral equation and a non-singular one are derived for acoustic problems. By using the one-dimensional wave propagation mode, the degree of the singularities appearing in the conventional boundary integral equation can be reduced. Since the strong singularity is removed in the weakly singular equation, the jump term of the field pressure expression in the very vicinity of the boundary disappears. It is shown that the weak singularity can be also removed for a smooth boundary in the non-singular representation, and thus special treatments for singular integral are no longer needed. In order to test the proposed method, several simple problems have been solved by employing the triangular element with standard Gaussian quadrature integration points. The results obtained show the accuracy of the method in the near field as well as on the boundary.

A theoretical formulation is carried out of acoustic wave propagation in a narrow capillary tube with steady gas flow. The transverse variations of the particle velocity, temperature, and viscosity are considered. A fully developed laminar steady flow is assumed and the concept of a complex propagation constant is introduced in the formulation. The final equation form reduces to a Kummer-type differential equation and its solution is obtained in terms of confluent hypergeometric functions. The dispersion equation for the complex propagation constants takes on a recursive form. A simplified form of the analysis permits comparison with previous results dealing with visco-thermal effects and includes the features of Poiseuille-type laminar steady flow for low and medium shear wave numbers. Numerical simulation results show that the effect of steady flow is very significant for the backward traveling waves, and the assumption of a parabolic velocity profile for shear wave numbers less than four should be used carefully when the flow Mach number is greater than 0·1. The present theory is applicable for shear wave numbers up to 10 or more, with the non-parabolic axial velocity fluctuations included, which encompasses almost all the possible situations of capillary duct dimension, temperature and flow velocity. The theory?!would be useful as an approximation in solving the acoustic problems of the monolith in catalytic converters for automotive exhaust systems and of the propagation of sound in a porous medium.

The volume velocity of an acoustic source is important in determining acoustic parameters such as the source strength and the acoustic transfer impedance, in the areas of transfer function analysis by using vibro-acoustic reciprocity, and in radiated power estimation. Measurement of volume velocity in ideal environments is often not available, so that simple and cheap estimation methods have been sought. One of the suggested techniques is the internal pressure method incorporating a loudspeaker attached to a chamber wall and a microphone inserted into the cavity. Although the method is easy to handle with a simple measurement set-up, the coupling effect between the dynamic system of the loudspeaker and acoustic field, and the effects of higher order modes introduced by the discontinuities in the acoustic field should be considered for precise results. In this study, an analytical and an experimental method are proposed to obtain the volume velocity in the chamber. In the analytical model, higher order modes due to the discontinuities of loudspeaker and microphone boundaries are included and the effects of these higher order modes are investigated by varying the non-dimensionalized geometrical parameters. Coupling effects are compensated for by using the results for two cylinders with different lengths. The volume velocity of a loudspeaker thus obtained agrees very well with that measured by a laser sensor.

A mathematical formulation for evaluating the acoustic performance of plenum chambers is derived by using the eigenfunction expansion technique. The chamber is modelled as a piston-driven rectangular rigid tube with no losses and containing a medium otherwise at rest. The residual acoustic velocity potential in the chamber is obtained by superposing the three-dimensional velocity potentials due to each of the uniformly fluctuating pistons. All the geometrical parameters such as the size of the chamber and ports, the arbitrary locations of inlet/outlet ports and the shapes of the ports are taken into consideration in the formulation as well as the acoustic higher order modes generated at the area discontinuities of port-chamber interfaces. By using the derived 2 × 2 transfer matrices, any type of reactive rectangular plenum chamber including the throughflow, flow-reversal, Helmholtz resonator and end-in/side-out configurations can be characterized, and their insertion or transmission losses can be estimated very easily through the appropriate truncation of acoustic modal series. Computed values are compared with those predicted by the foregoing numerical methods and by the classical plane wave theory, and the former agree very well with the results of the present study. In addition, 90° and 180° duct bends are analyzed and the results are in good agreement with previous experimental ones. The derived transfer matrices can be easily incorporated as basic modules in any existing computer programs incorporating four-pole parameters for predicting the acoustic performance of silencing systems.

A mathematical expression is derived for the prediction of the transmission loss of a reversing chamber muffler with circular cross-section. The chamber is modelled as a piston-driven circular rigid tube with no losses and the resultant actual velocity potential in the chamber is obtained by the superposition of the two velocity potentials due to each of the two input pistons. All the geometrical parameters such as the inlet/outlet offset distances from the center of chamber, the relative separation angle between the inlet and outlet, the length-to-diameter ratio and the area expansion ratio are taken into consideration in the formulation as well as the acoustic higher order modes generated at the area discontinuities. By using the derived four-pole parameters, the transmission loss of a reversing chamber muffler can be easily predicted at any frequency and for any configuration. The theoretical results of the present study are compared with the measured transmission losses and they agree very well.