Optimization of shell structure acoustics

This thesis analyzes a mathematical model for shell structure acoustics, and develops and implements the adjoint equations for this model. The adjoint equations allow the computation of derivatives with respect to large parameter sets in shape optimization problems where the thickness and mid-surface of the shell are computed so as to generate a radiated sound field subject to broad-band design requirements. The structure and acoustics are modeled, respectively, via the Naghdi shell equations, and thin boundary integral equations, with full coupling at the shell mid-surface. In this way, the three-dimensional structural-acoustic equations can be posed as a problem on the two-dimensional mid-surface of the shell. A wide variety of shapes can thus be explored without re-meshing, and the acoustic field can be computed anywhere in the exterior domain with little additional effort. The problem is discretized using triangular MITC shell elements and piecewise-linear Galerkin boundary elements, coupled with a simple one-to-one scheme. Prior optimization work on coupled shell-acoustics problems has been focused on applications with design requirements over a small range of frequencies. These problems are amenable to a number of simplifying assumptions. In particular, it is often assumed that the structure is dense enough that the air pressure loading can be neglected, or that the structural motions can be expanded in a basis of low-frequency eigenmodes. Optimization of this kind can be done with reasonable success using a small number of shape parameters because simple modal analysis permits a reasonable knowledge of the parts of the design that will require modification. None of these assumptions are made in this thesis. By using adjoint equations, derivatives of the radiated field can be efficiently computed with respect to large numbers of shape parameters, allowing a much richer space of shapes, and thus, a broader range of design problems to be considered. The adjoint equation approach developed in this thesis is applied to the computation of optimal mid-surfaces and shell thicknesses, using a large shape parameter set, proportional in size to the number of degrees of freedom in the underlying finite element discretization

Generalization of a 3-D resonator model for the simulation of spherical enclosures

A rectangular enclosure has such an even distribution of resonances that it can be accurately and efficiently modelled using a feedback delay network. Conversely, a non rectangular shape such as a sphere has a distribution of resonances that challenges the construction of an efficient model. This work proposes an extension of the already known feedback delay network structure to model the resonant properties of a sphere. A specific frequency distribution of resonances can be approximated, up to a certain frequency, by inserting an allpass filter of moderate order after each delay line of a feedback delay network. The structure used for rectangular boxes is therefore augmented with a set of allpass filters allowing parametric control over the enclosure size and the boundary properties. This work was motivated by informal listening tests which have shown that it is possible to identify a basic shape just from the distribution of its audible resonances.Comment: 39 pages, 16 figures, 6 tables. Accepted for publication in Applied Signal Processin

Noise control by sonic crystal barriers made of recycled materials

A systematic study of noise barriers based on sonic crystals made of cylinders that use recycled materials like absorbing component is here reported. The barriers consist of only three rows of perforated metal shells filled with rubber crumb. Measurements of reflectance and transmittance by these barriers are reported. Their attenuation properties result from a combination of sound absorption by the rubber crumb and reflection by the periodic distribution of scatterers. It is concluded that porous cylinders can be used as building blocks whose physical parameters can be optimized in order to design efficient barriers adapted to different noisy environments

Project MAXWELL: Towards Rapid Realization of Superior Products

We describe a new methodology for the design and manufacture of mechanical components. The methodology is a synergism of a new, mathematically rigorous procedure for the concurrent design of shape and material composition of components, and a new manufacturing process called MD* for their realization. The concurrent design strategy yields information about the global shape of the component and its material composition. The fabrication of such designs with novel microstructural configurations require unconventional manufacturing processes. MD* is a shape deposition process for the free-form fabrication of parts from single or composite materials and is ideally suited for realizing the aforementioned designs. Project MAXWELL, therefore, promotes the use of layered manufacturing beyond prototyping tasks and offers the possibility of their integration into the mainstream product development and fabrication process..Mechanical Engineerin

Time dependent seafloor acoustic backscatter (10-100kHz)

A time-dependent model of the acoustic intensity backscattered by the seafloor is described and compared with data from a calibrated, vertically oriented, echo-sounder operating at 33 and 93 kHz. The model incorporates the characteristics of the echo-sounder and transmitted pulse, and the water column spreading and absorption losses. Scattering from the water–sediment interface is predicted using Helmholtz–Kirchhoff theory, parametrized by the mean grain size, the coherent reflection coefficient, and the strength and exponent of a power-law roughness spectrum. The composite roughness approach of Jackson et al. [J. Acoust. Soc. Am. 79, 1410–1422 (1986)], modified for the finite duration of the transmitted signal, is used to predict backscatter from subbottom inhomogeneities. It depends on the sediment’s volume scattering and attenuation coefficients, as well as the interface characteristics governing sound transmission into the sediment. Estimation of model parameters (mean grain size, roughness spectrum strength and exponent, volume scattering coefficient) reveals ambiguous ranges for the two spectral components. Analyses of model outputs and of physical measurements reported in the literature yield practical constraints on roughness spectrum parameter settings appropriate for echo-envelope-based sediment classification procedures