subject:(weak Galerkin)

Wayne State University

1. Zhao, Ren. Polynomial Preserving Recovery For Weak Galerkin Methods And Their Applications.

Degree: PhD, Mathematics, 2017, Wayne State University

URL: https://digitalcommons.wayne.edu/oa_dissertations/1904

► Gradient recovery technique is widely used to reconstruct a better numerical gradient from a finite element solution, for mesh smoothing, a posteriori error estimate… (more)

▼ Gradient recovery technique is widely used to reconstruct a better numerical gradient from a finite element solution, for mesh smoothing, a posteriori error estimate and adaptive finite element methods. The PPR technique generates a higher order approximation of the gradient on a patch of mesh elements around each mesh vertex. It can be used for different finite element methods for different problems. This dissertation presents recovery techniques for the weak Galerkin methods and as well as applications of gradient recovery on various of problems, including elliptic problems, interface problems, and Stokes problems. Our first target is to develop a boundary strategy for the current PPR algorithm. The current accuracy of PPR near boundaries is not as good as that in the interior of the domain. It might be even worse than without recovery. Some special treatments are needed to improve the accuracy of PPR on the boundary. In this thesis, we present two boundary recovery strategies to resolve the problem caused by boundaries. Numerical experiments indicate that both of the newly proposed strategies made an improvement to the original PPR. Our second target is to generalize PPR to the weak Galerkin methods. Different from the standard finite element methods, the weak Galerkin methods use a different set of degrees of freedom. Instead of the weak gradient information, we are able to obtain the recovered gradient information for the numerical solution in the generalization of PPR. In the PPR process, we are also able to recover the function value at the nodal points which will produce a global continuous solution instead of piecewise continuous function. Our third target is to apply our proposed strategy and WGPPR to interface problems. We treat an interface as a boundary when performing gradient recovery, and the jump condition on the interface can be well captured by the function recovery process. In addition, adaptive methods based on WGPPR recovery type a posteriori error estimator is proposed and numerically tested in this thesis. Application on the elliptic problem and interface problem validate the effectiveness and robustness of our algorithm. Furthermore, WGPPR has been applied to 3D problem and Stokes problem as well. Superconvergent phenomenon is again observed. Advisors/Committee Members: Zhimin Zhang.

Subjects/Keywords: finite element methods; polynomial preserving recovery; weak Galerkin methods; Mathematics

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APA (6^th Edition):

Zhao, R. (2017). Polynomial Preserving Recovery For Weak Galerkin Methods And Their Applications. (Doctoral Dissertation). Wayne State University. Retrieved from https://digitalcommons.wayne.edu/oa_dissertations/1904

Chicago Manual of Style (16^th Edition):

Zhao, Ren. “Polynomial Preserving Recovery For Weak Galerkin Methods And Their Applications.” 2017. Doctoral Dissertation, Wayne State University. Accessed February 28, 2021. https://digitalcommons.wayne.edu/oa_dissertations/1904.

MLA Handbook (7^th Edition):

Zhao, Ren. “Polynomial Preserving Recovery For Weak Galerkin Methods And Their Applications.” 2017. Web. 28 Feb 2021.

Vancouver:

Zhao R. Polynomial Preserving Recovery For Weak Galerkin Methods And Their Applications. [Internet] [Doctoral dissertation]. Wayne State University; 2017. [cited 2021 Feb 28]. Available from: https://digitalcommons.wayne.edu/oa_dissertations/1904.

Council of Science Editors:

Zhao R. Polynomial Preserving Recovery For Weak Galerkin Methods And Their Applications. [Doctoral Dissertation]. Wayne State University; 2017. Available from: https://digitalcommons.wayne.edu/oa_dissertations/1904

Colorado State University

2. Harper, Graham Bennett. Weak Galerkin finite element methods for elasticity and coupled flow problems.

Degree: PhD, Mathematics, 2020, Colorado State University

URL: http://hdl.handle.net/10217/211829

► We present novel stabilizer-free weak Galerkin finite element methods for linear elasticity and coupled Stokes-Darcy flow with a comprehensive treatment of theoretical results and the… (more)

▼ We present novel stabilizer-free weak Galerkin finite element methods for linear elasticity and coupled Stokes-Darcy flow with a comprehensive treatment of theoretical results and the numerical methods for each. Weak Galerkin finite element methods take a discontinuous approximation space and bind degrees of freedom together through the discrete weak gradient, which involves solving a small symmetric positive-definite linear system on every element of the mesh. We introduce notation and analysis using a general framework that highlights properties that unify many existing weak Galerkin methods. This framework makes analysis for the methods much more straightforward. The method for linear elasticity on quadrilateral and hexahedral meshes uses piecewise constant vectors to approximate the displacement on each cell, and it uses the Raviart-Thomas space for the discrete weak gradient. We use the Schur complement to simplify the solution of the global linear system and increase computational efficiency further. We prove first-order convergence in the L2 norm, verify our analysis with numerical experiments, and compare to another weak Galerkin approach for this problem. The method for coupled Stokes-Darcy flow uses an extensible multinumerics approach on quadrilateral meshes. The Darcy flow discretization uses a weak Galerkin finite element method with piecewise constants approximating pressure and the Arbogast-Correa space for the weak gradient. The Stokes domain discretization uses the classical Bernardi-Raugel pair. We prove first-order convergence in the energy norm and verify our analysis with numerical experiments. All algorithms implemented in this dissertation are publicly available as part of James Liu's DarcyLite and Darcy+ packages and as part of the deal.II library. Advisors/Committee Members: Liu, Jiangguo (advisor), Bangerth, Wolfgang (committee member), Guzik, Stephen (committee member), Tavener, Simon (committee member), Zhou, Yongcheng (committee member).

Subjects/Keywords: Darcy; linear elasticity; weak Galerkin; finite element method; coupling; Stokes

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Harper, G. B. (2020). Weak Galerkin finite element methods for elasticity and coupled flow problems. (Doctoral Dissertation). Colorado State University. Retrieved from http://hdl.handle.net/10217/211829

Chicago Manual of Style (16^th Edition):

Harper, Graham Bennett. “Weak Galerkin finite element methods for elasticity and coupled flow problems.” 2020. Doctoral Dissertation, Colorado State University. Accessed February 28, 2021. http://hdl.handle.net/10217/211829.

MLA Handbook (7^th Edition):

Harper, Graham Bennett. “Weak Galerkin finite element methods for elasticity and coupled flow problems.” 2020. Web. 28 Feb 2021.

Vancouver:

Harper GB. Weak Galerkin finite element methods for elasticity and coupled flow problems. [Internet] [Doctoral dissertation]. Colorado State University; 2020. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/10217/211829.

Council of Science Editors:

Harper GB. Weak Galerkin finite element methods for elasticity and coupled flow problems. [Doctoral Dissertation]. Colorado State University; 2020. Available from: http://hdl.handle.net/10217/211829

University of Minnesota

3. Stoter, Klaas. The variational multiscale method for discontinuous Galerkin type finite element formulations.

Degree: PhD, Civil Engineering, 2019, University of Minnesota

URL: http://hdl.handle.net/11299/213098

► In this dissertation, we develop the foundation for a framework that unifies variational multiscale analysis and discontinuous Galerkin type methods. We adopt the variational multiscale… (more)

Subjects/Keywords: Discontinuous Galerkin; Residual-based; Subgrid-scale; Turbulence; Variational multiscale; Weak boundary condition

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APA (6^th Edition):

Stoter, K. (2019). The variational multiscale method for discontinuous Galerkin type finite element formulations. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/213098

Chicago Manual of Style (16^th Edition):

Stoter, Klaas. “The variational multiscale method for discontinuous Galerkin type finite element formulations.” 2019. Doctoral Dissertation, University of Minnesota. Accessed February 28, 2021. http://hdl.handle.net/11299/213098.

MLA Handbook (7^th Edition):

Stoter, Klaas. “The variational multiscale method for discontinuous Galerkin type finite element formulations.” 2019. Web. 28 Feb 2021.

Vancouver:

Stoter K. The variational multiscale method for discontinuous Galerkin type finite element formulations. [Internet] [Doctoral dissertation]. University of Minnesota; 2019. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/11299/213098.

Council of Science Editors:

Stoter K. The variational multiscale method for discontinuous Galerkin type finite element formulations. [Doctoral Dissertation]. University of Minnesota; 2019. Available from: http://hdl.handle.net/11299/213098

4. André Francisco Santos Siqueira. Soluções Fracas para um Sistema Não-Linear Envolvendo o Operador p-Laplaciano.

Degree: 2010, Universidade Federal da Paraíba

URL: http://bdtd.biblioteca.ufpb.br/tde_busca/arquivo.php?codArquivo=992

Neste trabalho provaremos a existência de soluções fracas para um problema misto de equações diferenciais parciais n~ao-lineares do tipo Klein-Gordon envolvendo o operador pseudo-Laplaciano. Com esse fim, usaremos o método de Faedo-Galerkin juntamente com argumentos de compacidade e monotonicidade. Advisors/Committee Members: Nelson Nery de Oliveira Castro.

Subjects/Keywords: Soluções Fracas; Pseudo- Laplaciano; Problema de Evolução Não-Linear; Método de Faedo-Galerkin; MATEMATICA; Weak-Solutions; Pseudo-Laplacian; Non-Linear Evolution Problem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Siqueira, A. F. S. (2010). Soluções Fracas para um Sistema Não-Linear Envolvendo o Operador p-Laplaciano. (Thesis). Universidade Federal da Paraíba. Retrieved from http://bdtd.biblioteca.ufpb.br/tde_busca/arquivo.php?codArquivo=992

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Siqueira, André Francisco Santos. “Soluções Fracas para um Sistema Não-Linear Envolvendo o Operador p-Laplaciano.” 2010. Thesis, Universidade Federal da Paraíba. Accessed February 28, 2021. http://bdtd.biblioteca.ufpb.br/tde_busca/arquivo.php?codArquivo=992.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Siqueira, André Francisco Santos. “Soluções Fracas para um Sistema Não-Linear Envolvendo o Operador p-Laplaciano.” 2010. Web. 28 Feb 2021.

Vancouver:

Siqueira AFS. Soluções Fracas para um Sistema Não-Linear Envolvendo o Operador p-Laplaciano. [Internet] [Thesis]. Universidade Federal da Paraíba; 2010. [cited 2021 Feb 28]. Available from: http://bdtd.biblioteca.ufpb.br/tde_busca/arquivo.php?codArquivo=992.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Siqueira AFS. Soluções Fracas para um Sistema Não-Linear Envolvendo o Operador p-Laplaciano. [Thesis]. Universidade Federal da Paraíba; 2010. Available from: http://bdtd.biblioteca.ufpb.br/tde_busca/arquivo.php?codArquivo=992

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Houston

5. Liu, Puchen 1979-. Solutions of Equations for the Regulation of Kinase Activity in a Finite Cylindrical Cell.

Degree: PhD, Mathematics, 2013, University of Houston

URL: http://hdl.handle.net/10657/1207

► In this work, inspired by the reality in organisms and particularly the shape of axon of the neuron, new mathematical models of regulation of kinase… (more)

▼ In this work, inspired by the reality in organisms and particularly the shape of axon of the neuron, new mathematical models of regulation of kinase activity are presented. In the view of mathematician, those models are diffusion equations defined in finite cylinders but with mixed Robin boundary and Dirichlet boundary conditions. The first part of the thesis focuses mainly on the model with the linear mixed Robin boundary and Dirichlet boundary conditions. By use of variational principle and eigenvalue problem, the results are provided on the existence, uniqueness and boundedness of the weak solution ( kinase concentration ) of an abstract elliptical equation related to the kinase activity model. For the kinase activity model itself, the bound can be expressed as the function of relevant parameters. Furthermore, this work also obtains the existence of the time-dependent solution to the reaction diffusion equation generalized from this kinase activity model. Base on those results, the time-dependent solutions are presented in integral form. This work has shown the exponential convergence of the time-dependent solution to the solution of its corresponding steady state equation. The second part has demonstrated the existence and boundedness of the weak solution by use of variational principle for the kinase model with mixed nonlinear boundary conditions. Then the series representation of the nonzero solution is shown. Moreover, a critical equality in bifurcation analysis is obtained. Based on this equality, when a parameter varies, bifurcation analysis is demonstrated from the special case to the more general case. Particularly, the critical (bifurcation) value of this biological parameter has been determined mathematically as a function of other biological parameters. By use of those theoretical results, some corresponding biological explanations are also provided. All of those have significance when considering biology signalling and biology control. Advisors/Committee Members: Auchmuty, Giles (advisor), Nicol, Matthew (committee member), Onofrei, Daniel (committee member), Tecarro, Edwin (committee member).

Subjects/Keywords: Kinase activity; Signalling; Flux; Gradient; Mixed Nonlinear Boundary Condition; Sobolev Space; Variational Problem; Weak Form; Steklov Eigenproblems; Representation of Solution; Galerkin approximation; Bifurcation Diagram

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APA (6^th Edition):

Liu, P. 1. (2013). Solutions of Equations for the Regulation of Kinase Activity in a Finite Cylindrical Cell. (Doctoral Dissertation). University of Houston. Retrieved from http://hdl.handle.net/10657/1207

Chicago Manual of Style (16^th Edition):

Liu, Puchen 1979-. “Solutions of Equations for the Regulation of Kinase Activity in a Finite Cylindrical Cell.” 2013. Doctoral Dissertation, University of Houston. Accessed February 28, 2021. http://hdl.handle.net/10657/1207.

MLA Handbook (7^th Edition):

Liu, Puchen 1979-. “Solutions of Equations for the Regulation of Kinase Activity in a Finite Cylindrical Cell.” 2013. Web. 28 Feb 2021.

Vancouver:

Liu P1. Solutions of Equations for the Regulation of Kinase Activity in a Finite Cylindrical Cell. [Internet] [Doctoral dissertation]. University of Houston; 2013. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/10657/1207.

Council of Science Editors:

Liu P1. Solutions of Equations for the Regulation of Kinase Activity in a Finite Cylindrical Cell. [Doctoral Dissertation]. University of Houston; 2013. Available from: http://hdl.handle.net/10657/1207

6. Wang, Bin. Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.

Degree: PhD, Mathematics, 2017, University of Kansas

URL: http://hdl.handle.net/1808/27005

► Hybridizable Discontinuous Galerkin (HDG) is an important family of methods, which combine the advantages of both Discontinuous Galerkin in terms of flexibility and standard finite… (more)

Subjects/Keywords: Mathematics; BDDC; domain decomposition; hybridizable discontinuous Galerkin; saddle point problems; Stokes; weak Galerkin

…hybridizable discontinuous Galerkin 2 (HDG) and weak Galerkin (WG) methods… …properties of the hybridizable discontinuous Galerkin (HDG) and weak Galerkin (WG… …respectively. Both hybridizable discontinuous Galerkin and weak Galerkin methods are used to… …x29;. 2.5 Weak Galerkin Methods The idea of weak Galerkin finite element scheme is to… …outward normal direction to ∂Ω. Now, we are in a position to introduce the weak Galerkin finite…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Wang, B. (2017). Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/27005

Chicago Manual of Style (16^th Edition):

Wang, Bin. “Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.” 2017. Doctoral Dissertation, University of Kansas. Accessed February 28, 2021. http://hdl.handle.net/1808/27005.

MLA Handbook (7^th Edition):

Wang, Bin. “Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations.” 2017. Web. 28 Feb 2021.

Vancouver:

Wang B. Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. [Internet] [Doctoral dissertation]. University of Kansas; 2017. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/1808/27005.

Council of Science Editors:

Wang B. Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations. [Doctoral Dissertation]. University of Kansas; 2017. Available from: http://hdl.handle.net/1808/27005

Universidade do Rio Grande do Sul

7. Lima, Fabiana Goulart de. Soluções fracas para um sistema de equações de Oberbeck-Boussinesq.

Degree: 2002, Universidade do Rio Grande do Sul

URL: http://hdl.handle.net/10183/118194

►

Neste trabalho, utilizando o método espectral de Galerkin, provamos a existência de soluções fracas (quando a dimensão n é maior que 2) e existência e… (more)

Subjects/Keywords: Navier-Stokes equations; Equações de Navier-Stokes; Galerkin approximations; Aproximações de Galerkin; Fluído quimicamente ativo; Chemical active fluid; Weak solutions; Soluções fracas

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APA (6^th Edition):

Lima, F. G. d. (2002). Soluções fracas para um sistema de equações de Oberbeck-Boussinesq. (Thesis). Universidade do Rio Grande do Sul. Retrieved from http://hdl.handle.net/10183/118194

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Lima, Fabiana Goulart de. “Soluções fracas para um sistema de equações de Oberbeck-Boussinesq.” 2002. Thesis, Universidade do Rio Grande do Sul. Accessed February 28, 2021. http://hdl.handle.net/10183/118194.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lima, Fabiana Goulart de. “Soluções fracas para um sistema de equações de Oberbeck-Boussinesq.” 2002. Web. 28 Feb 2021.

Vancouver:

Lima FGd. Soluções fracas para um sistema de equações de Oberbeck-Boussinesq. [Internet] [Thesis]. Universidade do Rio Grande do Sul; 2002. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/10183/118194.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lima FGd. Soluções fracas para um sistema de equações de Oberbeck-Boussinesq. [Thesis]. Universidade do Rio Grande do Sul; 2002. Available from: http://hdl.handle.net/10183/118194

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Kansas

8. Nunez, Daniel. J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework.

Degree: MS, Aerospace Engineering, 2008, University of Kansas

URL: http://hdl.handle.net/1808/4045

► This thesis presents an infrastructure for computations of the J-integral for mode I linear elastic fracture mechanics in h,p,k mathematical and computational framework using finite… (more)

▼ This thesis presents an infrastructure for computations of the J-integral for mode I linear elastic fracture mechanics in h,p,k mathematical and computational framework using finite element formulations based on the Galerkin method with weak form and the least squares process. Since the differential operators in this case are self-adjoint, both the Galerkin method with weak form and the least square processes yield unconditionally stable computational processes. The use of h,p,k frameworks permits higher order global differentiability approximations in the finite element processes which are necessitated by physics, calculus of continuous and differentiable functions and higher order global differentiability features of the theoretical solutions. The significant aspect of this research is that with the proposed methodology very accurate J-integral computations are possible for all paths including those in very close proximity of the crack without use of special crack tip or quarter point elements at the crack tip. A center crack panel under isotropic homogeneous plane strain linear elastic behavior, subjected to uniaxial tension (mode I) is used as model problem for all numerical studies. The investigations presented in this thesis are summarized here: (i) J-integral expression is derived and it is shown that its path independence requires the governing differential equations (GDEs) to be satisfied in the numerical process used for its computations (ii) It has been shown that the J-integral path must be continuous and differentiable (iii) The integrand in the J-integral must be continuous along the path as well as normal to the path (iv) Influence of the higher order global differentiability approximations on the accuracy of the J-integral is demonstrated (v) Stress intensity correction factors are computed and compared with published data. The work presented here is a straight-forward finite element methodology in h,p,k framework is presented in which all mathematical requirements for J-integral computations are satisfied in the computational process and as a result very accurate computations of J-integral are possible for any path surrounding the crack tip without using any special treatments. Both the Galerkin method with weak form and the least square processes perform equally well. Advisors/Committee Members: Surana, Karan S. (advisor), Ewing, Mark (advisor), Taghavi, Ray (cmtemember), Hale, Richard (cmtemember).

Subjects/Keywords: Aerospace engineering; Mechanical engineering; J-integral; Galerkin method with weak form; Least squares processes; Linear elastic fracture mechanics

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APA (6^th Edition):

Nunez, D. (2008). J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework. (Masters Thesis). University of Kansas. Retrieved from http://hdl.handle.net/1808/4045

Chicago Manual of Style (16^th Edition):

Nunez, Daniel. “J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework.” 2008. Masters Thesis, University of Kansas. Accessed February 28, 2021. http://hdl.handle.net/1808/4045.

MLA Handbook (7^th Edition):

Nunez, Daniel. “J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework.” 2008. Web. 28 Feb 2021.

Vancouver:

Nunez D. J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework. [Internet] [Masters thesis]. University of Kansas; 2008. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/1808/4045.

Council of Science Editors:

Nunez D. J-integral Computations for Linear Elastic Fracture Mechanics in h,p,k Mathematical and Computational Framework. [Masters Thesis]. University of Kansas; 2008. Available from: http://hdl.handle.net/1808/4045

Pontifical Catholic University of Rio de Janeiro

9. THIAGO GAMBOA RITTO. [en] VIBRATION ANALYSIS OF LINEAR AND NON-LINEAR SYSTEMS IN THE CONTEXT OF WEAK-FORMULATION, MODAL ANALYSIS AND KARHUNEN-LOÈVEN BASIS.

Degree: 2006, Pontifical Catholic University of Rio de Janeiro

URL: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=7650

►

[pt] Neste trabalho a Análise de Vibrações é tratada no contexto da formulação fraca. Um sistema contínuo é formulado abstratamente em um espaço de Hilbert… (more)

▼

[pt] Neste trabalho a Análise de Vibrações é tratada no contexto da formulação fraca. Um sistema contínuo é formulado abstratamente em um espaço de Hilbert e uma base de projeção é escolhida para a dinâmica. Um esquema de convergência para a aproximação é garantido à medida em que se aumenta o número de funções da base usada para representar a resposta do problema. Esta é a idéia por traz de métodos como o Método dos Elementos Finitos e o Método dos Modos Supostos, que derivam do Método de Galerkin. Esta estratégia é diferente do que comumente é ensinado nos cursos de vibrações, onde um sistema massa-mola é analisado, e sistemas discretos formados por massas, molas e amortecedores são discutidos. Nestes casos não se sabe qual é o erro cometido na análise numérica. A Análise de Vibrações é muito usada na manutenção preditiva de máquinas rotativas. Alguns fenômenos observados nesses equipamentos motivaram o desenvolvimento de um modelo numérico que pudesse reproduzir tais fenômenos para melhor entendê-los. Um sistema rotor-mancal é modelado e sua resposta dinâmica comparada qualitativamente com a resposta dinâmica captada através de acelerômetros fixados nos mancais de um exaustor da Companhia Siderúrgica de Tubarão (CST). Durante o trabalho diversos programas foram desenvolvidos através da plataforma MATLAB.

[en] Vibration Analysis is treated in the context of weak formulation. A continuous system is formulated in the Hilbert space and one base is selected to project the dynamics. An approximation scheme is guaranteed by increasing the number of functions in the base used to represent the response. This is the idea behind methods like the Finite Element Method and Assumed Modes Method, which derive from Galerkin Method. This strategy is different from what is commonly taught in vibration courses, where a mass-spring system is analyzed and discrete systems composed by masses, springs and dashpots are discussed. In those cases the error of the numerical analysis is not known. Vibration Analysis is very used in predictive maintenance of rotating machines. Some phenomenons observed in those machines motivated the development of a numerical model that could reproduce such phenomenons to better understand them. A rotor-bearing system is modelled and its dynamic response is qualitative compared to the dynamic response captured by accelerometers fixed on the bearings of a blower of the steel company Companhia Siderúrgica de Tubarão (CST). During this work several programs were developed using MATLAB software.

Advisors/Committee Members: RUBENS SAMPAIO FILHO.

Subjects/Keywords: [pt] ANALISE MODAL; [en] MODAL ANALYSIS; [pt] METODO DE GALERKIN; [en] GALERKIN METHOD; [pt] ANALISE DE VIBRACOES; [en] VIBRATION ANALYSIS; [pt] FORMULACAO FRACA; [en] WEAK FORMULATION; [pt] BASE DE KARHUNEN-LOEVE; [en] KARHUNEN-LOEVE BASIS

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APA (6^th Edition):

RITTO, T. G. (2006). [en] VIBRATION ANALYSIS OF LINEAR AND NON-LINEAR SYSTEMS IN THE CONTEXT OF WEAK-FORMULATION, MODAL ANALYSIS AND KARHUNEN-LOÈVEN BASIS. (Thesis). Pontifical Catholic University of Rio de Janeiro. Retrieved from http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=7650

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

RITTO, THIAGO GAMBOA. “[en] VIBRATION ANALYSIS OF LINEAR AND NON-LINEAR SYSTEMS IN THE CONTEXT OF WEAK-FORMULATION, MODAL ANALYSIS AND KARHUNEN-LOÈVEN BASIS.” 2006. Thesis, Pontifical Catholic University of Rio de Janeiro. Accessed February 28, 2021. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=7650.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

RITTO, THIAGO GAMBOA. “[en] VIBRATION ANALYSIS OF LINEAR AND NON-LINEAR SYSTEMS IN THE CONTEXT OF WEAK-FORMULATION, MODAL ANALYSIS AND KARHUNEN-LOÈVEN BASIS.” 2006. Web. 28 Feb 2021.

Vancouver:

RITTO TG. [en] VIBRATION ANALYSIS OF LINEAR AND NON-LINEAR SYSTEMS IN THE CONTEXT OF WEAK-FORMULATION, MODAL ANALYSIS AND KARHUNEN-LOÈVEN BASIS. [Internet] [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2006. [cited 2021 Feb 28]. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=7650.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

RITTO TG. [en] VIBRATION ANALYSIS OF LINEAR AND NON-LINEAR SYSTEMS IN THE CONTEXT OF WEAK-FORMULATION, MODAL ANALYSIS AND KARHUNEN-LOÈVEN BASIS. [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2006. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=7650

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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