Effective elastic properties of planar SOFCs: A non-local dynamic homogenization approach

The focus of the article is on the analysis of effective elastic properties of planar Solid Oxide Fuell Cell (SOFC) devices. An ideal periodic multi-layered composite (SOFC-like) reproducing the overall properties of multi-layer SOFC devices is defined. Adopting a non-local dynamic homogenization method, explicit expressions for overall elastic moduli and inertial terms of this material are derived in terms of micro-fluctuation functions. These micro-fluctuation function are then obtained solving the cell problems by means of finite element techniques. The effects of the temperature variation on overall elastic and inertial properties of the fuel cells are studied. Dispersion relations for acoustic waves in SOFC-like multilayered materials are derived as functions of the overall constants, and the results obtained by the proposed computational homogenization approach are compared with those provided by rigorous Floquet-Boch theory. Finally, the influence of the temperature and of the elastic properties variation on the Bloch spectrum is investigated

Tensor and Matrix Inversions with Applications

Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we derived new tensor decompositions which we have shown to be related to the well-known canonical polyadic decomposition and multilinear SVD. Moreover, within this group structure framework, multilinear systems are derived, specifically, for solving high dimensional PDEs and large discrete quantum models. We also address multilinear systems which do not fit the framework in the least-squares sense, that is, when the tensor has an odd number of modes or when the tensor has distinct dimensions in each modes. With the notion of tensor inversion, multilinear systems are solvable. Numerically we solve multilinear systems using iterative techniques, namely biconjugate gradient and Jacobi methods in tensor format

Uma metodologia numérica rápida para o cálculo de espalhamento acústico em placas poro-elasticas de geometrias arbritárias

Orientador: William Roberto WolfDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Uma metodologia numérica de baixo custo computacional é apresentada para o cálculo de espalhamento acústico em placas poro-elásticas de geometrias arbitrárias. O método de elementos de contorno, BEM, é aplicado para resolver a equação de Helmholtz submetida a condições de contorno relacionadas às vibrações estruturais da placa. Esta análise é realizada reescrevendo as condições de contorno do BEM em termos de uma base modal da placa poro-elástica que é calculada por uma ferramenta numérica que resolve o problema estrutural. A formulação atual permite uma solução direta do problema de interação fluido-estrutura completamente acoplado. A fim de acelerar a solução dos grandes sistemas lineares densos decorrentes da formulação BEM em problemas tridimensionais, um método de multipólos rápidos, FMM, com multi-níveis adaptativos de banda larga é empregado. Um estudo paramétrico é realizado para o espalhamento acústico de bordos de fuga para várias fontes acústicas, representativas de vórtices turbulentos não correlacionados ou de um jato turbulento não compacto. Os mecanismos físicos relacionados à redução de ruído devido à porosidade e elasticidade em frequências baixas e altas são discutidos. A redução de ruído pela combinação de porosidade e elasticidade com bordos de fuga enflexados e com extensões de serrilhados é investigada. As aplicações de espalhamento acústico também são apresentadas para aplicações aquáticas, onde as reduções de ruído são mais efetivas. Em geral, este trabalho mostra que as placas elásticas finitas são mais efetivas na redução do ruído espalhado para frequências mais altas. Por outro lado, a porosidade é mais eficaz na redução de ruído espalhado para frequências mais baixas. Os resultados demonstram que a elasticidade e a porosidade podem ser combinadas com bordos de fuga enflexados e com serrilhados no bordo de fuga para reduzir o ruído espalhado em um espectro mais amplo de freqüências para placas poro-elásticas. Diferentes configurações de interação fluido-estrutura são analisadas para placas com alongamentos baixos e altos. Uma avaliação do espalhamento acústico por placas isotrópicas metálicas e anisotrópicas de materias compósitos também é apresentada. Com a ferramenta numérica proposta, novos dispositivos podem ser projetados e otimizados para obter um espalhamento acústico mais eficiente para aplicações aéreas e aquáticasAbstract: We present a fast numerical framework for the computation of acoustic scattering by poro-elastic plates of arbitrary geometries. A boundary element method, BEM, is applied to solve the Helmholtz equation subjected to boundary conditions related to structural vibrations. This analysis is performed by rewriting the BEM boundary conditions in terms of a modal basis of the poro-elastic plate which is computed by a structural solver. The current formulation allows a direct solution of the fully coupled fluid-structure interaction problem. In order to accelerate the solution of the large dense linear systems arising from the BEM formulation in three-dimensional problems, a wideband adaptive multi-level fast multipole method, FMM, is employed. A parametric study is carried out for the trailing-edge scattering of sample acoustic sources, representative of either uncorrelated turbulent eddies or a non-compact turbulent jet. We discuss about the physical mechanisms related to the reduction of noise scattering due to porosity and elasticity at low and high frequencies. Noise reduction by the combination of porosity and elasticity with swept and serrated trailing edges is demonstrated. Applications of acoustic scattering are also shown for underwater applications, where the most effective noise reductions are obtained. Overall, it is shown that finite elastic plates are more effective in reducing the scattered noise at higher frequencies. On the other hand, porosity is more effective in reducing the radiated sound for lower frequencies. Results demonstrate that elasticity and porosity can be combined with trailing-edge sweep and serrations to reduce the scattered noise at a broad range of frequencies for poro-elastic plates. Different fluid-structure interaction configurations are analyzed for plates of low and high aspect ratios. We also present an assessment of noise scattering by isotropic metallic and anisotropic composite plates. With the current numerical framework, novel low-noise-emission devices can be designed for aerial and underwater applicationsMestradoTermica e FluidosMestre em Engenharia Mecânica1581546CAPE

On non-coercive mixed problems for parameter-dependent elliptic operators

We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain $D$ of ${\mathbb R}^n$ for a second order parameter-dependent elliptic differential operator $A (x,\partial, \lambda)$ with complex-valued essentially bounded measured coefficients and complex parameter $\lambda$. The differential operator is assumed to be of divergent form in $D$, the boundary operator $B (x,\partial)$ is of Robin type with possible pseudo-differential components on $\partial D$. The boundary of $D$ is assumed to be a Lipschitz surface. Under these assumptions the pair $(A (x,\partial, \lambda),B)$ induces a holomorphic family of Fredholm operators $L(\lambda): H^+(D) \to H^- (D)$ in suitable Hilbert spaces $H^+(D)$ , $H^- (D)$ of Sobolev type. If the argument of the complex-valued multiplier of the parame\-ter in $A (x,\partial, \lambda)$ is continuous and the coefficients related to second order derivatives of the operator are smooth then we prove that the operators $L(\lambda)$ are conti\-nu\-ously invertible for all $\lambda$ with sufficiently large modulus $|\lambda|$ on each ray on the complex plane $\mathbb C$ where the differential operator $A (x,\partial, \lambda)$ is parameter-dependent elliptic. We also describe reasonable conditions for the system of root functions related to the family $L (\lambda)$ to be (doubly) complete in the spaces $H^+(D)$, $H^- (D)$ and the Lebesgue space $L^2 (D)$