Reciprocity Technique Research Articles

A numerical Green's function and dual reciprocity BEM method to solve elastodynamic crack problems

A computational model based on the numerical Green's function (NGF) and the dual reciprocity boundary element method (DR-BEM) is presented for the study of elastodynamic fracture mechanics problems. The numerical Green's function, corresponding to an embedded crack within the infinite medium, is introduced into a boundary element formulation, as the fundamental solution, to calculate the unknown external boundary displacements and tractions and in post-processing determine the crack opening displacements (COD). The domain inertial integral present in the elastodynamic equation is transformed into a boundary integral one by the use of the dual reciprocity technique. The dynamic stress intensity factors (SIF), computed through crack opening displacement values, are obtained for several numerical examples, indicating a good agreement with existing solutions.

110 相反定理を用いた音響伝達関数計測法の開発 : 防音エンクロージャへの適用(振動・音響の評価技術,騒音・振動改善技術)

110 相反定理を用いた音響伝達関数計測法の開発 : 防音エンクロージャへの適用(振動・音響の評価技術,騒音・振動改善技術)

Dual boundary element method for anisotropic dynamic fracture mechanics

AbstractIn this work, the dual boundary element method formulation is developed for effective modelling of dynamic crack problems. The static fundamental solutions are used and the domain integral, which comes from the inertial term, is transformed into boundary integrals using the dual reciprocity technique. Dynamic stress intensity factors are computed from crack opening displacements. Comparisons are made with quasi‐isotropic as well as anisotropic results, using the sub‐region technique. Several examples are presented to assess the accuracy and efficiency of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.

相反定理を用いた音響伝達関数計測法の開発 : 防音エンクロージャへの適用(振動・騒音実験・解析技術,特別オーガナイズドセッション「音色・音質設計技術〜開発者と利用者・第三者を繋ぐ」,振動・騒音改善技術)

相反定理を用いた音響伝達関数計測法の開発 : 防音エンクロージャへの適用(振動・騒音実験・解析技術,特別オーガナイズドセッション「音色・音質設計技術〜開発者と利用者・第三者を繋ぐ」,振動・騒音改善技術)

Behaviour of acoustic emission sensors using broadband calibration techniques

For a quantitative study of acoustic emission signals or for the analysis oftransient waveforms the transfer function of the sensors both in Rayleigh andlongitudinal wave sound fields has to be known. To this end, the reciprocitycalibration is applied to measure the response of acoustic emission sensors to thenormal displacement velocity of Rayleigh and longitudinal waves. In this methodneither a reference acoustic source nor a calibrated sensor is needed. Thesensitivity is obtained through electrical measurements only, with threetransducers alternately working as the sound source and receiver. Ourcontribution to this well-established calibration technique (the reciprocitymethod) comes from the use of spectral analysis techniques with shortpulses, which enables the efficient determination of both the phase and theamplitude of the sensitivity in a broad frequency range. This study focuses onthree points. First, we compare this method with laser interferometrycalibration. Then we use the reciprocity technique to study the following points:the aperture effect and the fact that for quantitative acoustic emissionanalyses it is very important to take account of the material under test.

Calculation of uncertainty in calibration of microphones by the pressure reciprocity technique

At the primary level, acoustical measurement standards are realized through calibration of the sensitivity level of Laboratory Standard microphones by the reciprocity technique. The technique is described in International Standard IEC 61094-2, which allows for various implementations of the measurement method. The pressure sensitivity levels of a set of three microphones are determined from the electrical and acoustical transfer impedances of pairs of the microphones. The transfer impedances in turn depend on the design and performance of the measurement apparatus, the dimensions and acoustical properties of the microphones and the cavity that acts as an acoustical coupler between the microphones, and the prevailing environmental conditions. The uncertainty in the pressure sensitivity level depends on the uncertainties in these input quantities and on how the sensitivity level varies with changes in the input quantities. The ISO/IEC Guide Express: 1995 Guide to the Expression of Uncertainties in Measurement provides internationally agreed models and guidance for evaluating the expanded uncertainty of a measurement. The uncertainty model, the nature of the input variables, and the steps involved in the calculation of the expanded uncertainty are described for the realization of a particular implementation of the reciprocity technique.

Boundary Element Analysis of Cracks in Shear Deformable Plates and Shells. Topics in Engineering, Vol 43

Boundary Element Analysis of Cracks in Shear Deformable Plates and Shells. Topics in Engineering, Vol 43

Boundary element analysis of reinforced shear deformable shells

AbstractIn this paper, stiffened shear‐deformable shells are analysed using the boundary element method. Coupled boundary integral equations are presented for describing curved shells under general loading conditions. The equations are based on boundary integral equations for plane stress and plate bending, with coupling terms arising from the curvature of the shell. Domain integrals are transformed into boundary integrals using the dual reciprocity technique. Stiffeners are modelled as curved beams, continuously attached to the shell. Numerical solutions calculated using the present method are compared with finite element results in two examples. Copyright © 2002 John Wiley & Sons, Ltd.

DEVELOPMENT OF A BLOCKED PRESSURE CRITERION FOR APPLICATION OF THE PRINCIPLE OF ACOUSTIC RECIPROCITY

The principle of acoustic reciprocity can be applied in practice to estimate the sound radiation of a vibrating surface, from an inverse measurement of the Green function. This principle is especially useful in evaluating and ranking the sound radiation from individual vibrating components of a complex mechanical system. Usually, a blocked pressure assumption is needed in order to simplify the formulation of the reciprocity technique. This paper examines the validity of the blocked pressure hypothesis in the context of the reciprocity method, and suggests a “blocked pressure criterion” to rigorously quantify the impact of this hypothesis on the sound radiation prediction. This criterion is tested numerically on a system consisting of two coplanar, simply supported thin baffled plates that are mechanically uncoupled. It is shown that the numerical results support the conclusions obtained from the blocked pressure criterion.

Application of Vibrational Power Flow to a Passenger Car for Reduction of Interior Noise

Reduction of structure-borne noise in the compartment of a car is an important task in automotive engineering. Transfer path analysis using the vibroacoustic reciprocity technique or multiple path decomposition method has generally been used for structure-borne noise path analysis. These methods are useful for solving a particular problem, but they do not quantify the effectiveness of vibration isolation of each isolator of a vehicle. To quantify the effectiveness of vibration isolation, vibrational power flow has been used for a simple isolation system or a laboratory-based isolation system. It is often difficult to apply the vibrational power flow technique to a complex isolation system like a car. In this paper, a simple equation is derived for calculation of the vibrational power flow of an isolation system with multiple isolators such as a car. It is successfully applied not only to quantifying the relative contributions of eighteen isolators, but also to reducing the structure-borne noise of a passenger car. According to the results, the main contributor of the eighteen isolators is the rear roll mount of an engine. The reduced structure-borne noise level is about 5dBA.

Considerations for a new high-accuracy transfer-coupler reciprocity system for absolute electro-acoustic calibration

A new, closed-chamber, reciprocity technique for determining the free-field voltage sensitivity of hydrophones to a very high accuracy has been described in a previous publication by the author. The subject of the current paper is a detailed uncertainty analysis for a proposed system based on this new technique. This system, which is under development, will have an overall uncertainty of 0.1 dB in the measurement of the free-field voltage sensitivity of hydrophones. All significant uncertainties are analysed and a realistic choice of individual uncertainties is made to achieve the target uncertainty. Design implications as a result of the uncertainty choices are indicated.

Microphone calibration techniques

Primary calibration of microphones is well described and standardized by IEC 1094-2 using the reciprocity technique. When the standard microphone is calibrated, a reference source is needed for transfer of the calibration value to the acoustical measuring devices or systems employing the working measurement microphone. A reliable transfer device is the pistonphone. Another method may be the use of a comparison against a working standard microphone. Sound reference sources called ‘‘calibrators’’ are standarized by IEC in 60942:1997. Sound calibrators may often be inferior in accuracy and stability to the systems they are being applied to. They should therefore be labelled check devices. Other techniques have been employed for many years. The use of a reference voltage coupled to the system input is widely used. This may be extended to incorporate the preamplifier and incorporate features like modulating the polarization voltage whether internal or external or incorporating the cartridge capacity into a capacitive voltage divider. These techniques do not allow a calibration but only supply a means of injecting a signal in the electrical system to check the ability to transfer a signal. Calibration is not obtained.

Determination of acoustic center correction values for type LS2aP microphones at normal incidence

Frequency-dependent acoustic center correction values are required to obtain accurate microphone calibrations in the free-field by the reciprocity technique. These values were determined for IEC type LS2aP microphones at normal incidence by utilizing the theoretical inverse relationship between the sound pressure amplitude at the acoustic center of a receiver and the distance between acoustic centers of source and receiver. A dynamic signal analyzer was used to measure the gain factor between the amplified output voltage of the receiver and the source input voltage at 500-Hz intervals in the extended frequency range 2–50 kHz. This procedure allowed all the data for a microphone pair to be gathered within several hours for microphone diaphragm separations from 101–311 mm at 10-mm intervals. At each frequency, the reciprocal of this gain factor as a function of microphone diaphragm separation was fit to a straight line after correction for atmospheric effects, including attenuation of sound caused by atmospheric absorption. Mean acoustic center correction values (from four microphones combined in six pairs) were calculated using the parameters obtained from the fit and found to be in good agreement with published values calculated by the boundary element method, as well as with values predicted by scaling published values of the acoustic center correction for microphones with a geometrical configuration similar to that of IEC type LS1P microphones.

Measurement of microphone random-incidence and pressure-field responses and determination of their uncertainties

For many applications it is important to know the frequency response of the measurement microphone. In an earlier paper the determination of the free-field response and the uncertainties of the responses based on actuator calibration for 1/2″ microphones was discussed [J. Gramtorp and E. Frederiksen, J. Acoust. Soc. Am. 100, 2672 (1996)]. This paper continues by discussing the determination of the pressure-field and random-incidence responses and the determination of their uncertainties. The pressure-field responses are based on estimated pressure-field corrections obtained using the pressure-field reciprocity technique and electrostatic actuator calibration. The random-incidence responses are based on a large number of free-field measurements with different angles of incidence increased in small steps, and calculated according to IEC 1183, combined with electrostatic actuator calibration. From most manufacturers no information on the uncertainties is available, but a complete set of uncertainty values for pressure-field and random-incidence corrections and responses for the new Bruel & Kjaer Falcon Range microphones will be presented and discussed.

Application of a reciprocity technique for measurement of acoustic transfer functions to the prediction of road vehicle pass-by noise

A technique based on the principle of acoustic reciprocity has been developed for measuring acoustic transfer functions of sound radiation from vibrating surfaces of the engine, power train, exhaust system and tires. In many realistic cases of sound radiation, reciprocal measurements of transfer functions are usually more convenient and mostly more accurate than the corresponding direct measurements. This paper explain the basic acoustic reciprocity and experimental setup and illustrate its benefits by application to measurements of transfer functions of sound radiation from the engine of a fully trimmed vehicle.

Identification of the airborne component of tyre-induced vehicle interior noise

The dominant noise generation mechanism of a tyre below 1 kHz is the tyre wall vibration caused by collisions between the tread blocks and the road. This paper is concerned with the identification of the transmission path of this tyre noise into a vehicle. A stationary tyre is excited by an electrodynamic shaker and a description of surface velocity is obtained. A reciprocity technique is used to measure the transfer functions which describe the transmission of sound from points on a tyre wall to a point inside a vehicle. The combination of these measurements offers a means of separating airborne noise from structure-borne noise while, at the same time, providing information on the relative contribution of various regions of this vibrating tyre surface to vehicle interior noise.

New automated microphone reciprocity calibration system and results obtained

Microphone calibration by the reciprocity technique is performed by national and other high-level acoustic calibration laboratories. In the past, the electrical transfer function of coupled pairs of microphones was determined by manual measurements. As such measurements were very time-consuming, only a few calibrations were performed at a rather limited number of frequencies. A new automated measurement system has been developed. This has significantly increased the efficiency of transfer function measurements and extended the practical applications of the reciprocity technique. The uncertainty of voltage ratio measurements is less than 0.02 dB (k=2) between 40 Hz and 30 kHz, while the repeatability is about two times better. These numbers are so low that they have only a minor influence on the resulting uncertainty of laboratory standard microphone calibrations. Today, pressure response calibrations (according to IEC1094-2) can be performed with an uncertainty of 0.02 to 0.04 dB. The probe for measurement of electrical current through the transmitter and the preamplifier for the receiver microphones are both connected via cables. This makes it possible to place the microphones remotely from the main instrument, as required with environmental testing (pressure, temperature) and free-field calibrations. Calibration results obtained with the new system will be presented.

A Reciprocity Technique for Analysis of Sound Radiation from Vibrating Components of Vehicles. 2nd Report. Measurement of Contribution of Body Panels to Acoustic Transfer Functions.

One characteristic of a fully trimmed vehicle is that the properties of the acoustic field around the noise sources have approximately the same level of complexity as those of the acoustic field in the cabin. Another characteristic is that the partitions between the noise sources and the interior have double-wall structures consisting of interior trim and metal panels covered with damping materials. We present a method that combines direct and reciprocal measurements to determine the respective contributions of the metal panels and interior trim to the acoustic transfer functions between the noise source surfaces and the driver's ear position. We then explain how an analysis of the contribution of the metal panels to engine noise and transmission noise in a fully trimmed vehicle can be useful in achieving substantial noise reduction.

Free-field calibration of ‘‘1/2-in.’’ microphones

A precise free-field calibration system of type LS2 microphones by the reciprocity technique is proposed. A source and a receiver microphone are each attached to a cylinder of 1/2 in. diameter, respectively, and the cylinders are set up perpendicularly at the center of the anechoic room. The output voltage of the receiver microphone and the input voltage of the source microphone are measured by an FFT analyzer, and the frequency transfer functions are averaged to improve the signal-to-noise ratio. To reduce the influence of the disturbing reflections in the anechoic room, the gating technique is adopted. Values for the position of the acoustic centers of MR112 microphones were measured by two methods—gating and conventional. The uncertainty of the values by the gating method was less than by the conventional method.

Selected measurement issues and data, especially regarding primary and secondary free-field calibrations

During the last two decades, international research and cooperation have advanced the methods of primary calibration of microphones and developed improved International Electrotechnical Commission (IEC) standards for primary calibrations by the reciprocity technique in pressure fields and in the free field. However, for high-quality primary calibration, a laboratory must carefully investigate its procedures and apparatus to determine their contributions to the various uncertainty components that establish the overall uncertainty. Issues in secondary calibration (for example, comparison) and characterization of measurement microphones and other acoustical instruments also require careful, systematic effort, and increasingly are receiving international attention. Topics of current interest at NIST include acoustic center positions and source–receiver standing waves during primary free-field calibration, the influence of anechoic chamber imperfections on primary and secondary free-field calibrations, and the effects of instabilities and nonlinearities in sound sources and microphones. Recently improved instruments including dynamic signal analyzers capable of FFT and other signal processing, as well as relatively new concepts in their application to acoustical measurements, are necessary to this work.