Analysis tools for the design of active structural acoustic control systems

Acoustic noise is an important problem in the modern society and provides much of the impetus for the development of noise reduction techniques. Passive methods, such as the use of sound absorbing materials, provide an adequate solution to many noise problems, but for noise reduction at low frequencies (below 1000 Hz) they often lead to an unacceptable increase in mass and volume. Active control methods are better suited for low frequency noise problems. This thesis deals with an active control method for reducing the noise produced by vibrating structures, which is referred to as active structural acoustic control (ASAC). In ASAC, the minimisation of the sound radiation is achieved by modifying the vibration using actuators directly attached to the structure. In this research, emphasis is on the use of piezoelectric patches as control actuators. The key benefits of using piezoelectric patches instead of other actuator principles are their low weight and volume, low cost, and furthermore the possibility of integration into the structure. The goal of this research is to develop and validate efficient analysis tools for ASAC, and to apply them for the design of active control systems. In contrast to work that was presented in the literature, in this thesis a wide range of analysis tools are combined, resulting in an analysis environment for the design of ASAC systems. As a first step, the dynamical behaviour of a structure with surface bonded piezoelectric patches is studied with an analytical beam model. This analytical model proved very useful for studying the fundamental issues of ASAC, but is not suitable for realistic structures with complex geometries. Therefore, numerical techniques are applied to model the structural vibration and sound radiation of arbitrary structures with piezoelectric patches. The structural and acoustic responses are determined with an uncoupled analysis. The dynamical behaviour of the structure including piezoelectric patches is modelled with the finite element method. A model reduction technique is applied to obtain a model which can be evaluated with low computational effort. The free field sound radiation associated with the structural vibration is modelled with the Rayleigh integral method. Both the structural and acoustic models were successfully validated with experiments performed on a clamped plate setup with surface bonded piezoelectric patches. The analysis tool was applied to investigate the effect of two control strategies. First, the feedforward control of harmonic disturbances was demonstrated for a control system consisting of piezoelectric patches as actuators, and accelerometers or microphones as error sensors. Second, the concept of multiple independent feedback loops, each consisting of a piezoelectric actuator patch, an accelerometer and a direct velocity feedback loop, was applied to reduce the sound radiation of a lightly damped structure in a broad frequency range. The numerical and experimental results show that significant reductions in sound power can be obtained with both strategies. Furthermore, the predicted control performances, in terms of sound power, are in good agreement with the experimental results. Finally, a strategy is proposed for the optimisation of ASAC systems, which is based on the numerical model. A genetic algorithm is applied as the optimisation routine because it is suited for solving optimisation problems with multiple optima. The optimisation strategy was successfully applied for the optimal placement of independent direct velocity feedback controllers. It was found that a setup with optimally located controllers gives a better control performance than a setup with arbitrarily located controllers. Furthermore, there is a good agreement between the predicted and measured sound powers for the optimised setup.