**Dr. Sean F. Wu**

Wayne State University, Detroit, MI

**"Combined Helmholtz Equation Least Squares (CHELS) Method for Reconstructing Radiated Acoustic Pressures from Vibrating Structures"**

**Abstract:**

A Helmholtz Equation-Least Squares (HELS) method is recently developed [Wang and Wu, JASA, 102, 2020 - 2032 (1997); Wu and Yu, JASA, 104, 2054 2060, 1998] to reconstruct the radiated acoustic pressures from vibrating structures. In this method the acoustic pressures are expressed in terms of an expansion of generating functions, which are obtained by using Gram-Schmidt orthonormalization with respect to the particular solutions to the Helmholtz equation. The coefficients associated with these expansion functions are determined by requiring the assumed-form solution to satisfy the pressure boundary condition at measurement points. The errors incurred in this process are minimized by the least-squares method. The advantages of the HELS method are that: (1) acoustic pressures can be reconstructed over entire space; (2) reconstruction can be done in both exterior and interior regions; and (3) efficiency of numerical computation is high. This is because the number of measurements is determined by that of expansion functions, which is small when a right coordinate system is selected for particular source geometry under consideration. However, the HELS method is only valid outside a minimum generating surface that completely encloses the source for an exterior problem, or inside a maximum generating surface that is tangent to the source boundary for an interior problem. To overcome these limitations, a combined HELS (known as CHELS) method is developed which takes the advantages of both the HELS and Kirchhoff integral
formulations. Theoretically, the CHELS method is valid anywhere. Moreover, the radiated acoustic pressures from an arbitrary object can be reconstructed with only a few measurements. Examples of reconstruction of the radiated acoustic pressure fields from a full-size vehicle front end are demonstrated.

#### Friday, October 15, 1999

3:00 PM in 335 Jabara Hall

Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.

[ Fall 1999]