A means for computing the Kirchhoff surface integral for a disk radiator as a single integral with fixed limits

Archer-Hall, J.A.; Bashter, A. I.; Hazelwood, A. J.

doi:10.1121/1.382798

Cited by 16 publications

(15 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Regarding mathematical treatments of the sound fields see Cavanagh [221], Zemanek [1686], Tojoetta [1528] (also concerning annular oscillators), Archer-Hall [79,80].…”

Section: Yo7 G Y-6db'mentioning

confidence: 99%

Ultrasonic Testing of Materials

Krautkrämer¹,

Krautkrämer²

1990

790

452

View full text Add to dashboard Cite

“…Regarding mathematical treatments of the sound fields see Cavanagh [221], Zemanek [1686], Tojoetta [1528] (also concerning annular oscillators), Archer-Hall [79,80].…”

Section: Yo7 G Y-6db'mentioning

confidence: 99%

Ultrasonic Testing of Materials

Krautkrämer¹,

Krautkrämer²

1990

790

452

View full text Add to dashboard Cite

“…Two other equivalent single integral expressions are described by Archer-Hall et al 6 and Hutchins et al 7 specifically for time-harmonic near-field calculations of the pressure generated by a circular piston. The expression in Archer-Hall et al 6 applies a cylindrical coordinate system with a movable origin 2 to the solution of the Kirchhoff integral.…”

Section: Introductionmentioning

confidence: 99%

An efficient grid sectoring method for calculations of the near-field pressure generated by a circular piston

McGough

Samulski

Kelly

2004

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

An analytical expression is derived for time-harmonic calculations of the near-field pressure produced by a circular piston. The near-field pressure is described by an efficient integral that eliminates redundant calculations and subtracts the singularity, which in turn reduces the computation time and the peak numerical error. The resulting single integral expression is then combined with an approach that divides the computational grid into sectors that are separated by straight lines. The integral is computed with Gauss quadrature in each sector, and the number of Gauss abscissas in each sector is determined by a linear mapping function that prevents large errors from occurring in the axial region. By dividing the near-field region into 10 sectors, the raw computation time is reduced by nearly a factor of 2 for each expression evaluated in this grid. The grid sectoring approach is most effective when the computation time is reduced without increasing the peak error, and this is consistently accomplished with the efficient integral formulation. Of the four single integral expressions evaluated with grid sectoring, the efficient formulation that eliminates redundant calculations and subtracts the singularity demonstrates the smallest computation time for a specified value of the maximum error.

show abstract

“…This scalar normalization factor was selected to prevent division by zero and to avoid exaggerating the error values where the field amplitudes are relatively small. The spatially varying error η (x,z) is thus defined as (9) and the maximum error is then (10) Thus, plots of η(x,z) show the spatial distribution of error values, and η max condenses all of the errors for each pressure field calculation into a single value.…”

Section: E Error Calculationsmentioning

confidence: 99%

Rapid calculations of time-harmonic nearfield pressures produced by rectangular pistons

McGough

2004

The Journal of the Acoustical Society of America

111

View full text Add to dashboard Cite

A rapid method for calculating the nearfield pressure distribution generated by a rectangular piston is derived for time-harmonic excitations. This rapid approach improves the numerical performance relative to the impulse response with an equivalent integral expression that removes the numerical singularities caused by inverse trigonometric functions. The resulting errors are demonstrated in pressure field calculations using the time-harmonic impulse response solution for a rectangular source 5 wavelengths wide by 7.5 wavelengths high. Simulations using this source geometry show that the rapid method eliminates the singularities introduced by the impulse response. The results of pressure field computations are then evaluated in terms of relative errors and computational speeds. The results show that, when the same number of Gauss abscissas are applied to both approaches for time-harmonic pressure field calculations, the rapid method is consistently faster than the impulse response, and the rapid method consistently produces smaller maximum errors than the impulse response. For specified maximum error values of 10% and 1%, the rapid method is 2.6 times faster than the impulse response for pressure field calculations performed on a 61 by 101 point grid. The rapid approach achieves even greater reductions in the computation time for smaller errors and larger grids.

show abstract

A means for computing the Kirchhoff surface integral for a disk radiator as a single integral with fixed limits

Cited by 16 publications

References 0 publications

Ultrasonic Testing of Materials

Ultrasonic Testing of Materials

An efficient grid sectoring method for calculations of the near-field pressure generated by a circular piston

Rapid calculations of time-harmonic nearfield pressures produced by rectangular pistons

Contact Info

Product

Resources

About