Space distribution of harmonic mode vibration amplitudes in nonlinear finite piezoelectric transducer

Nonlinear elastic vibrations of cylindrical piezoelectric transducers are investigated both experimentally and theoretically. A particular behaviour, that relates the space distribution of the fundamental mode vibration to those of the second and third harmonic components, is observed. A simplified physical interpretation of the phenomenon is given.     

Mode-switching: A new technique for electronically varying the agglomeration position in an acoustic particle manipulator

Acoustic radiation forces offer a means of manipulating particles within a fluid. Much interest in recent years has focussed on the use of radiation forces in microfluidic (or “lab on a chip”) devices. Such devices are well matched to the use of ultrasonic standing waves in which the resonant dimensions of the chamber are smaller than the ultrasonic wavelength in use. However, such devices have typically been limited to moving particles to one or two predetermined planes, whose positions are determined by acoustic pressure nodes/anti-nodes set up in the ultrasonic standing wave. In most cases devices have been designed to move particles to either the centre or (more recently) the side of a flow channel using ultrasonic frequencies that produce a half or quarter wavelength over the channel, respectively.It is demonstrated here that by rapidly switching back and forth between half and quarter wavelength frequencies - mode-switching - a new agglomeration position is established that permits beads to be brought to any arbitrary point between the half and quarter-wave nodes. This new agglomeration position is effectively a position of stable equilibrium. This has many potential applications, particularly in cell sorting and manipulation. It should also enable precise control of agglomeration position to be maintained regardless of manufacturing tolerances, temperature variations, fluid medium characteristics and particle concentration.     

Resonant acoustic scattering by a finite linear grating of elastic shells

Theoretical and experimental studies of the acoustic scattering by a finite linear grating of elastic cylindrical shells are performed. It is observed that a resonant interaction takes place at low frequency when the shells are very close to each other. This phenomenon can be clearly associated to the Scholte-Stoneley wave that propagates around a single shell. It is shown that each resonance of the Scholte-Stoneley wave is split up into N resonances when N shells compose the grating.     

Evolution of acoustic waves in microinhomogeneous media with quadratic elastic nonlinearity and relaxation

A nonlinear wave equation for the velocity “relaxator” is derived in the framework of the rheological model and the corresponding equation of state of a microinhomogeneous medium containing viscoelastic defects with quadratic nonlinear elasticity. The equation is qualitatively analyzed, and numerical solutions to it are presented for a stationary symmetric shock wave and the evolution of initially harmonic waves.     

High-pressure subsonic mode operation of chemical oxygen-iodine laser

A new regime of chemical oxygen-iodine laser (COIL), high-pressure subsonic mode operation, was demonstrated using a jet-type singlet oxygen generator (SOG). The laser output power of 342 W with chemical efficiency of 20.9% was obtained at the Cl₂ flow rate of 18 mmol/s and the operating pressure of 6.4 Torr in the laser cavity. The specific energy was 3.1 J/l which was four times higher than our supersonic device, and was comparable to the highest value for the supersonic regime. The experimental results were in good agreement with the numerical simulation results. Received: 26 February 1999 / Revised version: 13 July 1999 / Published online: 30 November 1999     

A comparison measurement of nonlinear ultrasonic waves in tubes by a microphone and by an optical interferometric probe

This paper deals with the analysis of ultrasonic fields inside waveguides generated by ultrasonic waves of high amplitude. These waves behave nonlinearly, so it is not possible to use standard linear equations to describe their behaviour. Therefore, we started with an experimental determination of the acoustic pressure of air in glass tubes. We chose two methods of measurement--by a microphone and by an optical interferometric probe. The conventional method by a microphone creates numerous problems, which can be avoided by using an optical method, a heterodyne laser interferometer.     

Normal modes of a poroelastic plate and their relation to the reflection and transmission coefficients

A poroelastic plate that obeys the Biot theory is considered. Compact new forms of its reflection and transmission coefficients, similar to those of the resonance scattering theory for an elastic plate, are derived. A numerical comparison of the reflection coefficient modulus with the plate normal modes, at low frequency, shows that a study of the reflection or transmission coefficient does not provide the same kind of information on the poroelastic plate than an investigation of guided leaky waves propagation.     

Dispersion and frequency dependent nonlinearity parameters in a graphite-epoxy composite

Longitudinal phase velocity and nonlinearity parameter have been measured as a function of frequency in the low megaHertz range in a laminate graphite-fiber-epoxy-resin composite. Amplitudes of both the fundamental and generated second harmonics were measured absolutely with a capacitive receiver. Phase velocity and nonlinearity parameter vary with frequency. The extent of the variance depends on the orientation of the fiber layers. Comparison is made between the nonlinear differential equation appropriate for crystals and a new equation that accounts for frequency dependence of phase velocity and nonlinearity parameter. The newer equation describes the data more accurately than the crystalline model does, but appears to require additional terms.     

Experimental and theoretical investigation of photoacoustic-signal generation by wavelength-modulated diode lasers

The dependence of photoacoustic spectra on different experimental parameters was investigated by both theoretical and experimental means. The experiments were carried out with an inexpensive resonant optoacoustic system based on near-infrared laser diodes, which allowed photoacoustic and direct absorption spectra to be recorded simultaneously. The experimental observations were compared to theoretical predictions. It was also demonstrated that source-frequency (wavelength) modulation at the resonance frequency of the cell provides superior signal to noise ratio compared to amplitude modulation and eliminates background drifts and fluctuations.     

Flow acoustics in periodic structures

A recent paper [A.A. Krokhin, J. Arriaga, L.N. Gumen, Speed of sound in periodic elastic composites, Phys. Rev. Lett. 91 (2004) 264302-1-4] addresses the speed of sound in periodic elastic composites (phononic crystals) with particular emphasis to the case where air bubbles are present in water and arranged periodically. In such periodically arranged mixtures, the well-known phenomena of the drop of the speed of sound may occur and applications related to, e.g., sound-beam focusing and acoustic surgery are possible [F. Cervera, L. Sanchez, J.V. Sanchez-Perez, R. Martinez-Sala, C. Rubio, F. Meseguer, C. Lopez, D. Caballero, J. Sanchez-Dehesa, Phys. Rev. Lett. 88 (2002) 023902]. In this paper, the analysis is extended theoretically to include cases where a background flow in a periodic structure is maintained. Calculations of dispersion relations and group velocities are presented in cases with one- and two-dimensional material periodicity for background flow values in the range: 0-1m/s. Materials considered in the calculations are periodic water-air mixtures. It is shown that acoustic waves couple to the group velocities only if the (acoustic) wave vector has a component along the background flow velocity direction.     

Approximate analytical solution of the inhomogeneous Burgers equation

The method of the active second harmonic suppression in resonators is investigated in this paper both analytically and numerically. The resonator is driven by a piston which vibrates with two frequencies. The first one agrees with an eigenfrequency and the second one is equal to the two times higher eigenfrequency. The phase shift of the second piston motion is 180 degrees. It is known that for this case it is possible to describe generation of the higher harmonics by means of the inhomogeneous Burgers equation. The new approximate solution of inhomogeneous Burgers equation for real fluid is presented here. This work was supported by the grant GACR No. 202/01/1372 and the CTU research program J04/98:2123000016.     

Simultaneous determination of the ultrasound velocity and the thickness of solid plates from the analysis of thickness resonances using air-coupled ultrasound

A method that combines transmission of air-coupled ultrasound pulses through solid plates and amplitude and phase spectral analysis is presented. In particular, the method analyzes the first thickness resonance of the plates. The purpose is to determine, simultaneously, velocity and attenuation coefficient of the ultrasounds in the material and the thickness of the plate. This is especially useful when thickness can not be measured independently. The method is successfully applied to soft membranes, biological samples and FRP composites.     

The transmission of finite amplitude sound beam in multi-layered biological media

Based on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, a model in the frequency domain is given to describe the transmission of finite amplitude sound beam in multi-layered biological media. Favorable agreement between the theoretical analyses and the measured results shows this approach could effectively describe the transmission of finite amplitude sound wave in multi-layered biological media.     

Acoustic coupling between the loudspeaker and the resonator in a standing-wave thermoacoustic device

Thermoacoustic refrigerators work with high amplitude sound waves, which are often created using an acoustic source coupled to a resonator. This coupling can be calculated analytically using linear acoustic equations and a linear model of the loudspeaker. This paper makes a comparison between such a coupling and measurements obtained in a large-scale thermoacoustic resonator constructed at the University of Manchester. The resonator was driven from low to large pressure amplitudes, with drive ratios up to 10%. It is shown that a good agreement is obtained for small amplitudes and this progressively worsens as the amplitude is increased. In the absence of wave harmonics and loudspeaker nonlinearities, the increasing discrepancy is attributed to the presence of minor losses.     

Air-coupled ultrasound stimulated optical vibrometry for resonance analysis of rubber tubes

Air-coupled ultrasound stimulated optical vibrometry is proposed to generate and detect the resonances of a rubber tube in air. Amplitude-modulated (AM) focused ultrasound radiation force from a broadband air-coupled ultrasound transducer with center frequency of 500 kHz is used to generate a low frequency vibration in the tube. The resonances of several modes of the tube are measured with a laser vibrometer of 633 nm wavelength. A wave propagation approach is used to calculate the resonances of the tube from its known material properties. Theoretical and experimental resonance frequencies agree within 5%. This method may be useful in measuring the in vitro elastic properties of arteries from the resonance measurements in air. It may also be helpful to better understand the coupling effects of the surrounding tissue and interior blood on the vessel wall by measuring the resonance of the vessel in vitro and in vivo.     

Calculation of the acoustic radiation force on coated spherical shells in progressive and standing plane waves

In this paper, analytical equations are derived for the time-averaged radiation force induced by progressive and standing acoustic waves incident on elastic spherical shells covered with a layer of viscoelastic and sound-absorbing material. The fluid surrounding the shells is considered compressible and nonviscous. The incident field is assumed to be moderate so that the scattered field from the shells is taken to linear approximation. The analytical results are illustrated by means of a numerical example in which the radiation force function curves are displayed, with particular emphasis on the coating thickness and the content of the hollow region of the shells. The fluid-loading on the radiation force function curves is analysed as well. This study attempts to generalize the various treatments of radiation force due to both progressive and standing waves on spherically-shaped structures immersed in ideal fluids. The results show that various ways can be effectively used for damping resonance peaks, such as by changing the fluid in the interior hollow region of the shells or by changing the coating thickness.     

Minimization of finite beam effects in the determination of reflection and transmission coefficients of an elastic layer

A special data acquisition technique was applied to determine the acoustic plane-wave reflection and transmission properties of a plane-parallel aluminum plate. In this technique, the reflected and transmitted wavefield along a plane or line normal to the reflected or transmitted wave vector is recorded at equidistant receiver positions. The obtained traces are subsequently added up in the temporal domain to satisfy plane-wave conditions, thus effectively removing the effect of the limited beam of commonly used transducers. The agreement between plane-wave theory and experiment was found to be excellent, both in the temporal and in the frequency domain.     

High-precision pulsed photoacoustic spectroscopy in NO2-N2

A method for high-precision pulsed photoacoustic spectroscopy applied to a simple system for detection of NO₂ traces in nitrogen is presented. The acoustic signal from a closed cell containing NO₂/N₂ samples irradiated by a pulsed visible laser is analyzed in the frequency domain. A signal-processing method to obtain a high-resolution Fourier spectrum of the signal was developed. An accurate fitting of the resonance peaks with Lorentzian profiles gives high-precision determination of the amplitude and width of the resonance peaks. The resonance maximum is proportional to the absorbed energy; therefore, the choice of the laser wavelength, linewidth and frequency stability are critical for a precise calibration due to the fine structure of the NO₂ optical spectrum. The method also allows high-accuracy measurement of the Q of the acoustic cavity. The dependence of Q on the buffer gas pressure is characteristic of an acoustic cavity where energy losses near the walls predominate. Consequently, an important enhancement of sensitivity takes place at high N₂ pressure. Received: 1 June 2001 / Revised version: 27 July 2001 / Published online: 7 November 2001     

Characterization of piezoelectric materials with large piezoelectric and electromechanical coupling coefficients

The relaxor based ferroelectric (1-x)Pb(Zn(1/3)Nb(2/3))O(3)-xPbTiO(3) and (1-x)Pb(Mg(1/3)Nb(2/3))O(3)-xPbTiO(3) single crystals provided new challenges in property characterization because their extraordinarily large piezoelectric coefficients and electromechanical coupling coefficients. Large errors may occur in some of the derived material constants using conventional characterization techniques. This paper will analyze the inadequacy of the traditional characterization methods and provide some basic guidelines for properly characterizing piezoelectric materials with extremely high piezoelectric and electromechanical coupling coefficients.