Electro-acoustic Analogy Research Articles

Acoustics for engineers: Troy Lectures

Introduction - Mechanic and acoustic oscillators - Electromechanic and electroacoustic oscillations - Electromechanic and electroacoustic analogies - Electromechanic and electroacoustic transduction - Magnetic-field transducers - Electric-field transducers - The wave equation in fluids - Horn and stepped ducts - Spherical sound sources and line arrays - Piston membranes, diffraction and scattering - Dissipation, reflection and absorption - Geometric acoustics and diffuse sound fields - Isolation of air- and structure-borne sound - Noise control: a survey - Appendices, e.g, complex notation for sinusoidal signals, power and intensity.

Influence of cavity wall elasticity on resonant frequency of small underwater cylindrical Helmholtz resonator

Influence of cavity wall elasticity on resonant frequency of small underwater cylindrical Helmholtz resonator is studied theoretically and experimental. Based on the theory of electroacoustic analogy, the simplified low frequency lumpedparameter model of the Helmholtz resonator is constructed. A general, convenient for calculation expression of the resonant frequency is given by circuit analysis. The influence of the thickness and the material of the resonator on the resonant frequency is investigated by numerical method. And the approximate rigid conditions for small underwater cylindrical Helmholtz resonators of different sizes are given. Small cylindrical Helmholtz resonators of different wall thickness and material were tested in a standingwave tube filled with water. Experimental results well testified the theoreticl results and the approximate rigid condition. This paper is useful for the design and application of the underwater cylindrical Helmholtz resonators.

Mechanical anti-aliasing acoustic low-pass filtering fiber-optic hydrophones with side cavities

A novel mechanical anti-aliasing fiber-optic hydrophone with an acoustic low-pass filter of side cavities has been reported，to the best of our knowledge，for the first time. The low frequency lumped parameters model and the effective acoustic circuit of the hydrophone is constructed based on the theories of electro-acoustic analogy，and the acoustic performance is predicted by the circuit analysis methods. Theoretical results show that the hydrophone has three resonant frequencies and one inverse resonant frequency induced by the side cavities，and the hydrophone has good high frequency attenuation properties. A hydrophone with side cavities，designed and fabricated by us，is tested in a standing-wave tube filled with water. The measured frequency response curve，on the whole，has identical form as that predicted by theory, over the test frequency range of 50 to 7000 Hz. To be speaific，the low frequency responses are in good accordance，and the acoustic sensitivity is about -140 dB re 1 rad/μPa. The high frequency responses have obvious difference，which is mainly induced by the operation limitation of the low frequency model. It is expected that this new type of fiber-optic hydrophone will work as an important class of sensors used to eliminate the aliasing in the future fiber-optic sonar systems.

Design of the Mathematical Model of the Respiratory System Using Electro-acoustic Analogy

Design of the Mathematical Model of the Respiratory System Using Electro-acoustic Analogy

Novel mechanical antialiasing fiber-optic hydrophone with a fourth-order acoustic low-pass filter

A novel mechanical antialiasing interferometric fiber-optic hydrophone with a fourth-order acoustic low-pass filter has been fabricated and demonstrated for the first time to the best of our knowledge. The low-frequency lumped parameters model of the hydrophone is constructed based on the theories of an electroacoustic analogy, and the acoustic performance is predicted by the circuit analysis methods. The measured low-frequency response is very flat, and the acoustic sensitivity is about -140 dB with regard to 1 rad/microPa. The system has two measured resonant frequencies, i.e., 850 and 4000 Hz, which is in agreement with the simulation results. It is expected that this new type of fiber-optic hydrophone will become an important class of sensors used to eliminate the aliasing in future sonar systems.

Acoustic characteristics of underwater cylindrical Helmholtz resonator

The acoustic characteristics of underwater cylindrical Helmholtz resonator are analyzed theoretically. Based on the theories of electro-acoustic analogy, a low frequency lumped-parameter model of the Helmholtz resonator is constructed with due consideration of the effects of the elasticity and the radiation impedance of the resonator. To our knowledge, this is the first time such a complete model is constructed. The input impedance and the transfer function of the system are given by circuit analysis. The effects of parameter values of the resonator on the acoustic characteristics are studied by numerical method. Some useful conclusions are drawn. A small aluminum cylindrical Helmholtz resonator is measured in a standing-wave tube filled with water. Error analysis is made in detail. The experimental results are in agreement with the simulation results considering the effect of the piezoelectric hydrophone. The validity of the theoretical analysis is testified. This paper supplies a theoretical and experimental basis for the design of underwater cylindrical Helmholtz resonators, and is useful for the estimation of underwater acoustic performance of Helmholtz resonators of other shapes.

Widening the sound absorption bandwidths of flexible micro-perforated curved absorbers using structural and acoustic resonances

In this paper, the sound absorptions of flexible curved micro-perforated panels that are backed by an air cavity are studied in detail. A theoretical model that is based on the classical plate equation coupled with an acoustic wave equation is developed for the prediction of sound absorption. This model considers both symmetrical and antisymmetrical structural acoustic responses. Using the electro-acoustic analogy approach, another model is developed that only considers single structural and acoustic modes. It is proposed to make use of panel and cavity resonances to widen the absorption bandwidth of a single/double perforated absorber. The absorption of a flexible micro-perforated panel can be further enhanced by adjusting its curvature to bring the resonant frequencies closer together. The effects of various parameters such as boundary condition, incidence angle, and curvature on the absorption are studied. Predicted results for the single and double layer absorbers show good agreement with measurements.

Theoretical and Experimental Study on Sound Absorption of a Multi-leaf Microperforated Panel

A theoretical method is presented for calculating the absorption coefficient of a multi-leaf microperforated panel absorber. In this work, the possibility of using multi-leaf type of microperforated panels without solid backing panel is investigated. The number of panels varies from 2 to n (≥2). The sound absorption coefficient is calculated based on electro-acoustic analogy by taking the sound transmission coefficient due to the absence of solid backing panel into consideration. The optimum performance of leaf microperforated panel absorber is also investigated as the function with respect to the design parameters such as perforation ratio, diameter of holes and distance between panels. The numerical results show that the configuration of leaf of microperforated panels can increase absorption coefficient at low frequency region. This fact will give an advantage to the multi-leaf microperforated panel over conventional microperforated panel arrangements. That is, to solve the problem of quite narrow frequency band absorption effect, especially in mid-high frequency region corresponding to their resonant frequencies, that the conventional microperforated panel arrangements inherently possess. Experiment results are also presented that show a reasonable agreement with the theoretical results. Some feasible application ideas of the multi-leaf type of arrangement are also presented.

A method for calculating the absorption coefficient of a multi-layer absorbent using the electro-acoustic analogy

A theoretical method for calculating the absorption coefficient of the multi-layer absorbers composed of perforated plates, airspaces and porous materials is proposed. Initially, for multi-layer absorbers composed either of perforated plates and airspaces or perforated plates and porous materials, the acoustic impedance is calculated using an electro-acoustic analogy. Then, for multi-layer absorbers composed of perforated plates, airspaces and porous materials, the acoustic impedance is calculated using an iterative method. Finally, theoretical calculations for the absorption coefficient of three types of multi-layer absorbers composed of different materials and including perforated plates are carried out. The results are validated by experimental results.

Modeling the Influence of Pore Structure on the Acoustic Absorption of Enhanced Porosity Concrete

This paper describes a model to predict the acoustic absorption of Enhanced Porosity Concrete (EPC). The acoustic absorption coefficient was determined experimentally using an impedance tube, while an electro-acoustic analogy was implemented to develop the predictive model, considering the pore structure of EPC as a series of resistors and inductors. The physical features of the pore network were experimentally characterized using image analysis and a pore volume characterization technique. A parameter termed “structure factor” was introduced to account for the increased density of air that is not displaced by the acoustic wave pressure. The maximum acoustic absorption coefficient was found to decrease linearly with an increase in the structure factor. The development of this model and its correlation with physical measurements enable the prediction of acoustic absorption in EPC based on the geometric features of the pore structure. This model enabled a parametric study to be conducted to ascertain the effects of pore size, aperture size, porosity, and specimen thickness on acoustic absorption. An optimal pore to aperture diameter ratio was observed to exist, that maximizes acoustic absorption. The parametric study is believed to be able to aid in the design of EPC for acoustic absorption by better understanding the type of pore features that should be targeted for best performance.

A Ring Silencer Design for Reducing Noise of Axial Fan

In this paper, a ring silencer design for reducing the noise of axial fans is presented. The noise sources on axial fans are usually caused by the fluctuating pressure distribution on the surface of fan blade. Most of the sources are near the trailing edge of blades or boundary region of blades. The ideation of proposed design is based on the principle of Helmholtz resonator for reducing the noise around the fan. The electro-acoustic analogy of this design is presented and simply discussed. Experimental measurement is carried out to evaluate the proposed design for reducing the axial fan noise. The result of experiment indicated that the ring silencer achieved 17 dB in blade passing frequency and 10 dB in other broadband frequency of power spectrum level.

Sound absorption of cellular metals with semiopen cells.

A combined experimental and theoretical study is presented for the feasibility of using aluminum foams with semiopen cells for sound-absorption applications. The foams are processed via negative-pressure infiltration, using a preform consisting of water-soluble spherical particles. An analytical model is developed to quantify the dependence of pore connectivity on processing parameters, including infiltration pressure, particle size, wetting angle, and surface tension of molten alloy. Normal sound-absorption coefficient and static flow resistance are measured for samples having different porosity, pore size, and pore opening. A theory is developed for idealized semiopen metallic foams, with a regular hexagonal hollow prism having one circular aperture on each of its eight surfaces as the unit cell. The theory is built upon the acoustic impedance of the circular apertures (orifices) and cylindrical cavities due to viscous effects, and the principle of electroacoustic analogy. The predicted sound-absorption coefficients are compared with those measured. To help select processing parameters for producing semiopen metallic foams with desirable sound-absorbing properties, emphasis is placed on revealing the correlation between sound absorption and morphological parameters such as pore size, pore opening, and porosity.

ANALYSIS AND DESIGN OF MUFFLERS—AN OVERVIEW OF RESEARCH AT THE INDIAN INSTITUTE OF SCIENCE

The reciprocating motion of the piston(s) of engines and compressors and the associated intake and discharge of gases are responsible for noise radiation to the atmosphere that ranks as a major pollutant of the urban environment. Mufflers have been developed over the last seventy years based on electro–acoustic analogies and experimental trial and error. Passive mufflers based on impedance mismatch, called reflective or reactive mufflers, have been most common in the automobile industry. Mufflers based on the principle of conversion of acoustic energy into heat by means of highly porous fibrous linings, called dissipative mufflers or silencers, are generally used in heating, ventilation and air-conditioning systems. The author has been working in this area for over 27 years. Of late, he has been researching in the vibro–acoustics of hoses used in automotive climate control systems. The present paper gives an overview of the research findings of the author and his students in different aspects of active as well as passive mufflers in the last decade. The same are related to the contemporary state of the art. Finally, areas needing further research are indicated.

Analysis of a hybrid noise control system for a duct

This letter proposes the combination of a passive muffler and an active noise control system for the control of very high-level noise in ducts used with large industrial fans and similar equipment. The analysis of such a hybrid system is presented making use of electroacoustic analogies and the transfer matrix method. It turns out that a passive muffler upstream of the input microphone can indeed lower the acoustic pressure and, hence, the power requirement of the auxiliary source. The parameter that needs to be optimized (or maximized) for this purpose is a certain velocity ratio that can readily be evaluated in a closed form, making it more or less straightforward to synthesize the configuration of an effective passive muffler to go with the active noise control system.

An analytical, one-dimensional, standing-wave model of a linear active noise control system in a duct

Assuming plane waves, and making use of the transfer matrices and electroacoustic analogies, a standing wave analysis of the active noise control system in a duct is presented incorporating the characteristics of the primary source as well as the auxiliary source. Analytical expressions have thus been derived for the ratio of the two source pressures and certain other ratios or relations of interest for complete or partial cancellation of noise downstream of the auxiliary source. The resulting closed-form expression for the filter transfer function H0 reveals the real role of the auxiliary source both when it is on and off, and the importance of the distance between the input microphone and the auxiliary source (generally, a loudspeaker). Finally, the analysis is extended to incorporate the convective and dissipative effects of the meanflow and viscothermal damping.

On uniqueness, transfer and combination of acoustic sources in one-dimensional systems

The use of electroacoustic analogies suggests that a source of acoustical energy (such as an engine, compressor, blower, turbine, loudspeaker, etc.) can be characterized by an acoustic source pressure ps and internal source impedance Zs, analogous to the open-circuit voltage and internal impedance of an electrical source. The present paper shows analytically that the source characteristics evaluated by means of the indirect methods are independent of the loads selected; that is, the evaluated values of ps and Zs are unique, and that the results of the different methods (including the direct method) are identical. In addition, general relations have been derived here for the transfer of source characteristics from one station to another station across one or more acoustical elements, and also for combining several sources into a single equivalent source. Finally, all the conclusions are extended to the case of a uniformly moving medium, incorporating the convective as well as dissipative effects of the mean flow.

Analytical modeling of an active noise control system in a duct

Making use of the transfer matrices and electroacoustic analogies, a standing wave analysis of the active noise control system in a duct is presented incorporating the characteristics of the primary source, as well as the auxiliary source. Analytical expressions have thus been derived for the ratio of the two source pressures and certain other ratios or relations of interest for complete cancellation of noise downstream of the auxiliary source. These expressions are then compared with those obtained from transfer functions of the various blocks constituting the block diagram of the entire system. In the process, equivalence has been established between the different entities involved in the two approaches, one of which is used in acoustics and the other in system theory. In particular, it has been shown that the pressure generated by a source against a load impedance can be looked upon as a sum of two pressure waves, one generated by the source against the characteristic impedance and the other by reflecting the rearward wave (incident on the source) off the source impedance. This principle is seminal in linking the two approaches.