Reconstruction of transient acoustic radiation from a finite object subject to arbitrarily time-dependent excitation

• US 6,996,481 B2
• Filed: 01/08/2004
• Issued: 02/07/2006
• Est. Priority Date: 01/08/2004
• Status: Active Grant

• Current Assignee: Wayne State University
• Original Assignee: Wayne State University
• Inventors: Wu, Sean F.
• Primary Examiner(s): Williams, Hezron
• Assistant Examiner(s): SAINT SURIN, JACQUES M
• Application Number:
  US10/754,036
• Publication Number:
  US 20050150299A1
• Time in Patent Office: 761 Days
• Field of Search: 735/87, 735/89, 736/02, 736/46, 702/39, 702/56, 702/138, 367/129, 367/1, 367/8.13, 367/901
• US Class Current: 702/39
• CPC Class Codes: G06F 30/23 using finite element methods [FEM] or finite difference methods [FDM]

Abstract

General algorithms are developed for reconstructing the acoustic field generated by an arbitrary object subject to an arbitrarily time-dependent excitation. These algorithms enable one to visualize a time-domain acoustic pressure wave as it travels through three-dimensional space. Such a tool can be used to diagnose general noise sources and transmission since in engineering applications most structures are subject to arbitrarily time-dependent excitations. To facilitate the derivations of the temporal solutions, we make use of Laplace transform and expand the acoustic pressure in terms of the spherical Hankel functions and the spherical harmonics. The expansion coefficients are settled by solving an over-determined system of equations obtained by matching the assumed-form solutions to the measured acoustic pressures. To obtain a general expression for a temporal kernel, we replace the spherical Hankel functions by polynomials in s, recast the infinite integral in the inverse Laplace transform as a contour integral in the complex s-plane, and evaluate it via residue theorem. Once this is done, the transient acoustic quantities anywhere including a source surface can be obtained by convoluting the temporal kernels with respect to measured acoustic pressures.

Claims

1. A method for reconstructing transient acoustic radiation from an object including the steps of:

a) measuring transient acoustic pressure at a plurality of measurement points around the object subject to an arbitrarily time-dependent excitation; and

b) reconstructing the transient acoustic pressure at points other than the measurement points based upon the measurements at the plurality of measurement points.

2. The method of claim 1 wherein the object is an arbitrarily shaped object.

3. The method of claim 1 wherein said step b) further includes the step of expanding the acoustic pressure in terms of the spherical Hankel functions.

4. The method of claim 1 wherein the transient acoustic pressure everywhere is determined in said step b).

5. The method of claim 1 wherein the transient acoustic pressure on a surface of the object is determined in said step b).

6. The method of claim 1 further including the step of using a Laplace transform having an s-domain.

7. The method of claim 6 further including the step of expressing the acoustic pressure in the s-domain as an expansion.

8. The method of claim 7 further including the step of expressing the acoustic pressure in the s-domain as an expansion in terms of spherical Hankel functions.

9. A system for reconstructing an acoustic field comprising:

a plurality of transducers each measuring acoustic pressure at a measurement point around a noise source generating transient acoustic radiation; and

a computer reconstructing transient acoustic pressure at points other than the measurement points based upon the acoustic pressure as measured by the transducers.

10. The system of claim 9 wherein the source is an arbitrarily shaped object.

11. The system of claim 9 wherein the computer expands the acoustic pressure in terms of spherical Hankel functions.

12. The system of claim 9 wherein the computer determines the transient acoustic pressure everywhere.

13. The system of claim 9 wherein the computer determines the transient acoustic pressure on a surface of the source.

14. The system of claim 9 wherein the computer uses a Laplace transform having an s-domain to reconstruct the transient acoustic pressure.

15. The system of claim 14 wherein the computer expresses the acoustic pressure in the s-domain as an expansion.

16. The system of claim 15 wherein the computer expresses the acoustic pressure in the s-domain as an expansion in terms of spherical Hankel functions.

17. A computer-readable storage medium having a computer program stored thereon, which when executed by a computer performs the steps of:

a) receiving signals indicating sound at a plurality of measurement points around a noise source generating transient acoustic radiation; and

b) reconstructing a transient acoustic field at points other than the measurement points based upon the signals.

18. A system for reconstructing an acoustic field comprising:

a plurality of transducers each measuring acoustic pressure at a measurement point around a noise source generating transient acoustic radiation; and

means for reconstructing transient acoustic pressure at points other than the measurement points based upon the acoustic pressure as measured by the transducers.