Sound Attenuation in Elliptic Mufflers Using a Regular Perturbation Method

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Banerjee, Subhabrata ; Jacobi, Anthony M. (2012)
  • Publisher: Purdue University
  • Subject: Transmission loss | Mufflers | Green's function | Mathieu function | Regular Perturbation

The study of sound attenuation in an elliptical chamber involves the solution of the Helmholtz equation in elliptic coordinate systems. The Eigen solutions for such problems involve the Mathieu and the modified Mathieu functions. The computation of such functions poses considerable challenge. An alternative method to solve such problems had been proposed in this paper. The elliptical cross-section of the muffler has been treated as a perturbed circle, enabling the use of a regular perturbation approach to solve the wave equation. The Eigen vectors of the perturbed system has been approximated by a series summation of the unperturbed Eigen solutions. The acoustic pressure in the elliptical duct has been derived from the perturbed Eigen vectors by using the Green’s function approach.
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