The paper presents a topology optimization based method for designing acoustic focusing devices, capable of tailoring the sound emission pattern of one or several sources, across a chosen frequency band. The method is demonstrated numerically considering devices optimized for directional sound emission in two dimensions and is experimentally validated using three dimensional prints of the optimized designs. The emitted fields exhibit a level difference of at least 15 dB on axis relative to the off-axis directions, over frequency bands of approximately an octave. It is demonstrated to be possible to design focusing devices of dimensions comparable to the acoustic wavelength, a frequency range which is typically problematic, as well as devices operating at higher frequencies. The classical parabolic reflector is used as a benchmark. The devices designed using the proposed method are shown to outperform the latter in terms of directivity and maximum side-lobe level over nearly an octave band. A set of frequencies are considered simultaneously in the design formulation and performance robustness toward uniform spatial production errors in the designed devices is assured by including perturbations of the geometry in the design formulation.

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Design of passive directional acoustic devices using Topology Optimization - from method to experimental validation.

This Thesis treats the development and experimental validation of density-based topology optimization methods for wave propagation problems. Problems in the frequency regime where design dimensions are between approximately one fourth and ten wavelengths are considered. All examples treat problems from acoustics, however problems for TE or TM polarized electromagnetic waves and shear waves in solids in two dimensions may be treated using the proposed methods with minor modifications. A brief introduction to wave problems and to density-based topology optimization is included, as is a brief discussion of the finite element method and a hybrid of a wave based method and the finite element method, used to discretize the model problems under consideration. A short discussion of the benefits and drawbacks of applying the hybrid method compared to the finite element method, used in conjunction with topology optimization, is included. Preliminary results for novel preconditioners used in conjunction with the generalized minimal residual method for the iterative solution of wave problems, potentially suited for use with topology optimization, are discussed. The development of an extension to an existing method, for assuring geometric robustness of designs created using density-based topology optimization, is presented. The method is applied to acoustic cavity design, and a significant improvement in the geometric robustness of several cavities demonstrated. Experimental validation of an acoustic cavity designed using the proposed method is provided. A novel approach for designing meta material slabs with selectively tuned negative refractive behavior is outlined. Numerical examples demonstrating the behavior of a slab under different conditions is provided. Results from an experimental study demonstrating agreement with numerical predictions are presented. Finally an approach for designing acoustic wave shaping devices is treated. Three examples of applications are presented, a directional sound emission device, a wavesplitting device and a flat focusing lens. Experimental results for the first two devices, demonstrating good agreement between measurements and the numerical predictions, are provided.

Topology Optimization for Wave Propagation Problems with Experimental Validation

An aplanatic Straubel mirror was designed for underwater acoustic imaging. However, there was a problem in that incident sound waves coming into the aplanatic Straubel mirror were interrupted by a receiver array placed in front of the mirror. An off-axis Straubel mirror is proposed to solve this problem. In this study, an off-axis aplanatic Straubel mirror is designed and evaluated using numerical calculation to verify the feasibility of the off-axis design. Upon comparison of the off-axis and ordinary aplanatic Straubel mirrors, the off-axis mirror shows almost the same convergence property as the ordinary one when a receiver array exists. The off-axis aplanatic Straubel mirror is compared with an aplanatic Fresnel lens because this lens is not affected by the receiver. The results show that the off-axis mirror showed a smaller aberration than the aplanatic Fresnel lens at a wider angle of view.

Design and Numerical Evaluation of Off-Axis Aplanatic Straubel Mirror for Underwater Acoustic Imaging

Results are presented of an experimental investigation of the use of thin metal parabolic reflectors to form underwater quasiplane wave regions in the nearfield of the reflector. This quasiplane wave volume is then used to calibrate underwater sound transducers in terms of directivity and sensitivity. Such reflectors, mass produced for use with electromagnetic wave devices, are readily available, inexpensive, and rugged. Experiments were conducted with reflectors ranging from 45 to 122 cm in diameter at frequencies from 30 to 300 kHz. It might be noted that at the higher frequencies the acoustic wavelength is approximately an order of magnitude shorter than that for which the reflectors were designed. Test transducers, typically half the size of the reflectors, were calibrated both in the nearfield of the reflector and in the farfield (using conventional techniques) and the results were compared. It was found that for the major lobe there was excellent agreement and that the levels of the minor lobes were...

M. Jean McKemie

Papers

An experimental investigation of the parabolic reflector as a nearfield calibration device for underwater sound transducers