Two numerical methods to identify the surface areas of a vibrating structure that radiate sound are presented. The supersonic intensity identifies only the supersonic wave components of the sound field contributing to far-field radiated sound. The supersonic intensity is calculated using a two-dimensional convolution between a spatial radiation filter and the sound field. To compute the spatial radiation filter, the shortest surface distance between two points on the structure is calculated using the geodesic distance method. The non-negative intensity is based on acoustic radiation modes and identifies the radiated sound power from a vibrating structure. Numerical models of a baffled plate, a cylinder and an engine crankcase are presented. The supersonic intensity is shown to be difficult to implement at low frequencies due to the size of the spatial radiation filter and accuracy of the surface distances. A cut-off coefficient associated with the acoustic wavenumber of the spatial radiation filter is used to reduce the aperture error. A comparison of the two intensity-based techniques both in terms of a sound power ratio and the modal assurance criterion is introduced to identify the optimal values of the cut-off coefficients that result in better convergence between the intensity techniques.

Non-negative intensity (NNI) is an approach to identify the surface areas of a structure that contribute to sound power. NNI is evaluated in terms of the acoustic impedance matrix obtained directly at the structural surface and as such can only identify surface contributions to sound power at a far-field receiver surface that fully circumscribes the structure. In contrast, back-calculated NNI is evaluated in terms of the acoustic impedance matrix obtained at a far-field receiver surface, and hence can identify surface contributions to sound power at a far-field receiver surface that does not fully circumscribe the structure. In this work, NNI and acoustic intensity obtained numerically using the boundary element method and experimentally from near-field acoustic holography measurements are compared for different modes. Back-calculated NNI evaluated for full and partial receiver surfaces is also compared with acoustic intensity for the different modes. Results for back-calculated NNI show that different regions on the plate surface contribute sound to different receiver locations.

Acoustic cloaking has received significant interest due to the appealing ability to render an object acoustically invisible. In a similar concept to acoustic cloaking, acoustic illusions provide the capability to misrepresent the acoustic field of an object. Combining acoustic cloaking and illusions with numerical discretization methods allow objects of greater complexity to be considered. This work presents active acoustic cloaking and illusions of three-dimensional rigid objects. The boundary element method is utilized to efficiently predict the exterior acoustic domain. A multi-input/multi-output control system comprising monopole control sources, error sensors, and a controller based on a feedforward linear-quadratic regulator algorithm is employed. Active acoustic cloaking of a simple object corresponding to a sphere is demonstrated for both non-decaying and decaying incident fields. For the same control configuration but minimizing a cost function based on different error signals, acoustic illusions are generated to mimic the presence of a sphere within a free field. Illusional fields are also generated for a cube and a bird to misrepresent their size or orientation.

Non-negative intensity is used to identify the surface areas of a structure that contributes to the scattered sound power. In the acoustic near field, the scattered sound power is predicted using non-negative intensity, as well as the scattered acoustic intensity integrated directly over the scatterer's surface area. In the acoustic far field, the scattered acoustic intensity and the scattered sound power are evaluated for three different receiver surface areas, corresponding to a sphere representing a far-field area that fully circumscribes the scatterer, and two hemispherical surfaces that correspond to partial far-field areas that do not fully circumscribe the scatterer. Back-calculated non-negative intensity that defines the sound scattered from the full or partial far-field receiver surface areas is also calculated and compared to the non-negative intensity obtained directly from the surface of the scatterer. To illustrate the numerical technique, the scattered acoustic intensity and scattered sound power of a rigid sphere, a rigid cylinder, and a rigid hemispherical shell are examined.

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