Active vibration control to reduce vibrations and structure borne noise is considered using a powerful multi-disciplinary virtual design environment which enables control system design to be considered as an integral part of the overall vehicle design. The main application studied is active automotive engine vibration isolation where, first, the potential of large frequency band multi-input multi-output H2 feedback control is considered. Facilitated by the virtual environment, it is found necessary to take non-linear characteristics into account to achieve closed-loop stability. A physical explanation to why receiver structure flexibility insignificantly affect the open and closed-loop characteristics in case of total force feedback in contrast to acceleration feedback is then given. In this context, the inherent differences between model order reduction by modal and by balanced truncation are being stressed. Next, applying state-of-the-art algorithms for recursive parameter estimation, time-domain adaptive filtering is shown to lack sufficient tracking performance to deal with multiple spectral components of transient engine excitations corresponding to rapid car accelerations. Finally, plant non-linearity as well as transient excitation are successfully handled using narrow band control based on feedback of disturbance states estimates. To deal with the non-linear characteristics, an approach to generate linear parameter varying descriptions of non-linear systems is proposed. Parameter dependent quadratic stability is assessed using a derived affine closed-loop system representation. This thesis also considers actuator saturation induced limit cycles for observer-based state feedback control systems encountered when dealing with the active isolation application. It is stressed that the fundamental observer-based anti-windup technique could imply severely deteriorated closed-loop characteristics and even sustained oscillations. That is in the case when the observer is fed by the saturated control signal in contrast to the computed one. Based on piecewise affine system descriptions, analytical tools to conclude about limit cycles and exponential closed-loop stability are provided for the two observer implementations.

The goal of this work is to develop and demonstrate a comprehensive analysis of single and multi-body composite strip-beam systems using an asymptotically-correct geometrically nonlinear theory. The comprehensiveness refers to the two distinguishing features of this work, namely the unified framework for the analysis and the inclusion of the usually ignored cross-sectional nonlinearities in thin-beam and multi-beam analyses. The first part of this work stitches together an approach to analyse generally anisotropic composite beams. Based on geometrically exact nonlinear elasticity theory, the nonlinear 3-D beam problem splits into either a linear (conventionally considered) or nonlinear (considered in this work) 2-D analysis of the beam cross-section and a nonlinear 1-D analysis along the beam reference curve. The two sub-tasks of this work (viz. nonlinear analysis of the beam cross-section and nonlinear beam analysis) are accomplished on a single platform using an object-oriented framework. First, two established nonlinear cross-sectional analyses (numerical and analytical), both based on the Variational-Asymptotic Method (VAM), are invoked. The numerical analysis is capable of treating cross-sections of arbitrary geometry and material distributions and can capture certain nonlinear effects such as the trapeze effect. The closed-form analytical analysis is restricted to thin rectangular cross-sections for generally anisotropic composites but captures ALL cross-sectional nonlinearities, and not just the well-known Brazier and trapeze effects. Second, the well-established geometrically-exact nonlinear 1-D governing equations along the beam reference curve, after being generalized to utilize the expressions for nonlinear stiffness matrix, are solved using the mixed variational finite element method. Finally, local 3-D stress, strain and displacement fields for representative sections in the beam are recovered, based on the stress resultants from the 1-D global beam analysis. This part of the work is then validated by applying it to an initially twisted cantilevered laminated composite strip under axial force. The second part is concerned with the dynamic analysis of nonlinear multi-body systems involving elastic strip-like beams made of laminated, anisotropic composite materials using an object-oriented framework. In this work, unconditionally stable time-integration schemes presenting high-frequency numerical dissipation are used to solve the ensuing governing equations. The codes developed based on such time-integration schemes are first validated with the literature for two standard test cases: non-linear spring mass oscillator and pendulum. In order to apply the comprehensive analysis code thus developed to a multi-body system, the four-bar mechanism is chosen as an example. All component bars of the mechanism have thin rectangular cross-sections and are made of fiber reinforced laminates of various types of layups. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. Each component of the mechanism is modeled as a beam based on the first part of this work. Results from this analysis are compared with those available in the literature, both theoretical and experimental. The margins between the linear and non-linear results are evaluated specifically due to the cross-sectional nonlinearities and shown to vary with stacking sequences. This work thus demonstrates the importance of geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. To enable graphical visualization, the behavior of the four-bar mechanism is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS). Finally, the component-laminate load-carrying capacity is estimated using the Tsai-Wu-Hahn failure criterion for various layups and the same criterion is used to predict the first-ply-failure and the mechanism as a whole.