This GOALI project is being carried out in collaboration with the Advanced Engineering Center of Ford Motor Company. The objectives of this investigation are two-fold: (1) to develop an innovative methodology to reconstruct the acoustic pressure fields accurately and cost-effectively, and (2) to extend this methodology to producing real-time acoustic holography that enables one to visualize the instantaneous acoustic pressure distributions and their evolution as the excitation forces change with time. The novelty of the methodology lies in the fact that the acoustic pressures are reconstructed through an expansion of acoustic modes, or a set of particular solutions to the Helmholtz equation. The coefficients associated with these acoustic models are determined by requiring the assumed form solution to satisfy pressure boundary conditions at measurement points. The errors incurred in this process are minimized by using the least squares method. The significance of this methodology is that solutions thus obtained are unique and the efficiency of numerical computations is high. This is because the acoustic modes employed represent a complete set of eigenfunctions that satisfy the Helmholtz equation. The number of acoustic modes determines the measurement points, which is small when a right coordinate system is selected for the source geometry under consideration. Hence numerical computations are fast and efficient. Moreover, the acoustic pressure is written as an explicit form of the acoustic modes. Therefore the time-domain signals can be obtained by taking a direct inverse Fourier transformation. This makes the generation of real-time acoustic holography possible. The investigation will yield an effective tool for diagnosing both structure and airborne noise sources. Using this tool, the design engineers can acquire a better understanding of the noise generation mechanisms, assess the noise performance of a complex machine cost-effectively, and develop effective measures to circumvent vibration and noise problems. This tool will also significantly enhance the teaching effectiveness in classroom education. It will enable students to `see` the radiation, reflection, and diffraction of sound waves, thus making the learning of complex acoustic concepts easier, and more interesting and effective.
