Análise dinâmica de estruturas periódicas utilizando uma abordagem de propagação de ondas e técnicas de sub-estruturação

Author(s)

Priscilla Brandão Silva

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Mecânica
• Defense date: 2015-08-31

Examining board members

José Roberto de França Arruda; Renato Pavanello; Marco Lúcio Bittencourt; Arcanjo Lenzi; Domingos Alves Rade

• Advisor: José Roberto de França Arruda; Jean Mathieu Mencik

Abstract

In this thesis, the wave finite element (WFE) method is used for assessing the harmonic forced response of mechanical systems that involve structures with one-dimensional periodicity, i.e., structures which are made up of several identical substructures along one direction. Such mechanical systems can be quite complex and are commonly encountered in engineering applications, e.g., aircraft fuselages. The first part of the thesis is concerned with the computation of wave modes traveling along these structures. A brief literature review is presented regarding the available formulations for the WFE eigenproblem, which need to be solved for expressing the wave modes, as well as a study of the numerical errors induced by these eigenproblems in the case of a solid waveguide. In the second part of the thesis, the WFE-based superelement modeling of periodic structures is proposed. In this context, the dynamic stiffness matrices and receptance matrices of periodic structures are expressed in terms of wave modes. Compared to the conventional FE-based dynamic stiffness and receptance matrices, the WFE-based matrices can be computed in a very fast way without loss of accuracy. In addition, an accurate strategy for WFE-based model order reduction is presented. It provides significant computational time savings for the forced response analysis of periodic structures compared to WFE-based superelement modeling, which makes use of the full wave basis. Indeed, it is shown that higher-order numerical spectral elements can be built by means of the WFE method. This is an alternative to the conventional spectral element method, which is limited to simple structures for which closed-form wave solutions exist. The motivation behind the formulation of WFE-based superelement matrices is the use of the concept of numerical wave modes to assess the forced response of coupled mechanical systems that involve structures with one-dimensional periodicity and coupling elastic junctions through classic finite element assembly procedures or domain decomposition techniques. This issue is addressed in the third part of this thesis. In this case, the Craig-Bampton method is used to express superelement matrices of coupling junctions by means of static and fixed-interface modes. A WFE-based criterion is considered to select among junction modes those that contribute most to the system forced response. This also contributes to enhancing the efficiency of the numerical simulation of coupled systems. Finally, in the fourth part of this thesis, the WFE method is used to show the potential of designing periodic structures which work as vibration filters within specific frequency bands. In order to highlight the relevance of the developments proposed in this thesis, numerical experiments which involve solid waveguides, two-dimensional frame structures, and three-dimensional aircraft fuselage-like structures are carried out (AU)

• FAPESP's process: 10/17317-9 - Study of elastic wave propagation throught periodic media
• Grantee: Priscilla Brandão Silva
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)