Analysis on acoustic directivity of spherical cap transducers

The Journal of the Acoustical Society of America, 2010

It has been argued that the sound radiation of a loudspeaker is modeled realistically by assuming the loudspeaker cabinet to be a rigid sphere with a resilient spherical cap. Series expansions, valid in the whole space outside the sphere, for the pressure due to a harmonically excited cap with an axially symmetric velocity distribution are presented. The velocity profile is expanded in functions orthogonal on the cap rather than on the whole sphere. As a result only a few expansion coefficients are sufficient to accurately describe the velocity profile. An adaptation of the standard solution of the Helmholtz equation to this particular parametrization is required. This is achieved by using recent results on argument scaling of orthogonal (Zernike) polynomials. The approach is illustrated by calculating the pressure due to certain velocity profiles that vanish at the rim of the cap to a desired degree. The associated inverse problem, in which the velocity profile is estimated from pressure measurements around the sphere, is also feasible as the number of expansion coefficients to be estimated is limited. This is demonstrated with a simulation.

Journal Audio Engineering Society Authors Version, 2011

It has been suggested by Morse and Ingard that the sound radiation of a loudspeaker in a box is comparable with that of a spherical cap on a rigid sphere. This has been established recently by the authors of this paper who have developed a computation scheme for the forward and inverse calculation of the pressure due to a harmonically excited, flexible cap on a rigid sphere with an axially symmetric velocity distribution. In this paper, the comparison is done for other quantities that are relevant for audio engineers, viz. the baffle-step response, sound power and directivity, and the acoustic center of the radiator.

Acta Acustica united with Acustica, 2010

This work concerns the theoretical analysis and synthesis of sound fields by a compact spherical loudspeaker array. Such an electroacoustic device consists of several transducers mounted on a sphere-like structure, which are driven independently in order to achieve non-uniform directivity patterns. The control strategy usually adopted is to provide the array with some preprogrammed basic directivities corresponding to spherical harmonic functions. Thus, an arbitrary radiation pattern can be approximately achieved by changing the gains associated with these basic directivities. Here, a different approach based on the acoustic radiation modes of the array is proposed. Unlike spherical harmonics, radiation modes constitute a finite set of vectors that spans a subspace on which any radiation pattern the array is able to reproduce can be projected.

INFLIBNET, 2011

Front Cover: (Left) Far-field acoustic radiation from a phased array of cylindrical transducers (blue) and a rectangular piston (red); and (Right) the magnitude of the interior pressure field in an embedded fluid cylinder ensonified by a plane acoustic wave computed using ray theory iii THESIS CERTIFICATE This is to certify that the thesis entitled "Acoustic radiation and scattering from cylindrical bodies and analysis of transducer arrays" submitted by JASMINE MATHEW to the Cochin University of Science and Technology, Cochin for the award of degree of Doctor of Philosophy under the Faculty of Science is a bonafide record of research work carried out by her under my supervision. The contents of this thesis, in full or in parts, have not been submitted to any other institute or University for the award of any degree or diploma. The research work has been carried out

2012

It has been argued that the sound radiation of a loudspeaker is modeled realistically by assuming the loudspeaker cabinet to be a rigid sphere with a moving rigid spherical cap. Series expansions, valid in the whole space on and outside the sphere, for the pressure due to a harmonically excited, flexible cap with an axially symmetric velocity distribution are presented. The velocity profile is expanded in functions orthogonal on the cap rather than on the whole sphere. This has the advantage that only a few expansion coefficients are sufficient to accurately describe the velocity profile. An adaptation of the standard solution of the Helmholtz equation to this particular parametrization is required. This is achieved by using recent results on argument scaling in orthogonal Zernike polynomials. The efficacy of the approach is exemplified by calculating various acoustical quantities with particular attention to certain velocity profiles that vanish at the rim of the cap to a desired degree. These quantities are: the sound pressure, polar response, baffle-step response, sound power, directivity, and acoustic center of the radiator. The associated inverse problem, in which the velocity profile is estimated from pressure measurements around the sphere, is feasible as well since the number of expansion coefficients to be estimated is limited. This is demonstrated with a simulation.

The Journal of the Acoustical Society of America, 2008

Spherical loudspeaker arrays have been used to generate non-uniform directivity patterns. It is known that the poor radiation efficiency of spherical sources and the loudspeaker electroacoustic behavior impose constraints on the directivity synthesis at low frequencies, which are aggravated as the source volume is made smaller. In this work, the effects of the enclosure design on the loudspeaker signal powers are analyzed. Two different approaches have been reported in literature, although quantitative comparisons have not been provided. In the first approach, the drivers share the same enclosure volume and in the second, they have their own independent sealed cavities. Here, an analytical model that takes into account the interior and exterior acoustic coupling is used in order to evaluate the voltages that must feed the array drivers. It is shown that the signal powers can be reduced at low frequencies by letting the drivers share the same enclosure volume. However, this leads to controllability problems, since some natural frequencies of the enclosure are in the operation range of the spherical array. If controllability at natural frequencies is neglected, a simple lumped parameter model of the enclosure presents good agreement with the continuous model, indicating that heavy calculations may be unnecessary.

arXiv: Applied Physics, 2019

In this paper, we present an analytical modeling technique for circularly symmetric piezoelectric transducers, also called as Fresnel Lens. We also present the design of a flat/piston transducer that can generate unique acoustic wave patterns, having both converging and vortexing effects. The converging effect is generated by designing the transducer electrodes in the shapes of circular rings using Fresnel formula and exciting it with an RF signal of resonant frequency. The vortexing effect is achieved by cutting the rings to different sector angles: 90, 120, 180 and 270 degrees. We use the analytical model to simulate the performance of these transducers.

IMA Journal of Applied Mathematics, 2015

This article considers the theoretical modelling of a novel electrostatic transducer in which the backplate consists of many spherical resonators. Three analytical models are considered, each of which produce impedance profiles of the device, in addition to transmission voltage responses and reception force responses, all of which closely agree. Design parameters are then varied to investigate their influence on the resonant frequencies and other model outputs.

The Journal of the Acoustical Society of America, 2010

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit Receiving Sensitivity and Transmitting Voltage Response of the transducer.

Revista Mexicana De Fisica - REV MEX FIS, 2003

Recibido el 30 de julio de 2002; aceptado el 9 de abril de 2003 Acoustic pressure fields generated by pulsed ultrasonic transducers under different boundary conditions are analyzed. Numerical simulations of the near-field pressure were evaluated considering rigid and soft baffles as boundary conditions. These field simulations were perfomed using the temporal convolution between the numerical derivative of the impulse response and the longitudinal wave velocity for both cases. Experimental pressure data were obtained by measuring the peak, peak to peak and root mean squared voltages. Simulated and experimental results were compared to investigate the temporal behavior of the acoustic signal as well as their spatial distribution on planes parallel to the transducer face. Special attention is given to the Fresnel region where the diffraction effect affects the pressure field measurements. Experimental readings were done using circular transducers with the same geometric characteristics and with resonant frequencies of 3.5 MHz and 5 MHz.