This thesis represents the work that has been done by the author in the area of vibration analysis and control of smart structures during his PhD candidature. The research was concentrated on flexible structures, using piezoelectric materials as actuators and sensors. The thesis consists of four major parts. The first part (Chapter 2) is the modelling of piezoelectric laminate structures using modal analysis and finite element methods. The second part (Chapter 4) involves the model correction of pointwise and spatial models of resonant systems. The model correction solution compensates for the errors associated with the truncation of high frequency modes. The third part (Chapter 5) is the optimal placement methodology for general actuators and sensors. In particular, optimal placement of piezoelectric actuators and sensors over a thin plate are considered and implemented in the laboratory. The last part (Chapters 6 to 8) deals with vibration control of smart structures. Several different approaches for vibration control are considered. Vibration control using resonant, spatial H-2 and H-infinity control is proposed and implemented on real systems experimentally. It is possible, for certain modes, to obtain the very satisfactory result of up to 30 dB vibration reduction. / PhD Doctorate

Orientador: Gilberto Pechoto de Melo / Resumo: O uso da metodologia de observadores de estado para detecção de dano requer a análise da observabilidade do modelo físico-matemático do sistema e aponta para a necessidade de posicionar sensores de forma otimizada. Visto que plataformas veiculares podem se apresentar como sistemas com amortecimento não proporcional, é apresentada uma metodologia para o cálculo de índices de posicionamento H2 para este tipo de sistema. Para a plataforma veicular analisada com amortecimento proporcional, índices de posicionamento H2 são comparados com índices grammianos, sendo demonstrado que ambos resultam em uma mesma configuração ótima de sensores. A análise da observabilidade é conduzida a partir dos principais modos de vibrar , sendo utilizada a norma H2 para definição de quais modos devem ser retidos no modelo reduzido. Observadores robustos, atuando em paralelo com o sistema, são utilizados para localização e quantificação da severidade do dano. É mostrado que, para plataformas veiculares excitadas pela base com deslocamentos do tipo degrau, um índice de dano que compara as saídas medidas e estimadas permite alcançar este objetivo. / Abstract: The use of state observer's methodology for damage detection requires the observability analysis of the physical-mathematical model of the system and points to the need of positioning sensors optimally. Since vehicle platforms can be presented as systems with non-proportional damping, a methodology for calculating H2 positioning indices for this type of system is presented. For the vehicle platform analyzed with proportional damping, H2 positioning indices are compared with Grammian indices, showing that both result in the same optimal sensor con guration. The observability analysis is conducted from the main modes of vibration, using the H2 norm to define which modes should be retained in the reduced model. Robust observers acting in parallel with the system are used to locate and quantify the severity of the damage. It is shown that, for vehicle platforms stimulated by the base with step-type displacements, a damage index that compares the measured and estimated outputs reaches this goal. / Mestre