Simultaneous Structural-Control Optimization of a Coupled Structural-Acoustic Enclosure

Simultaneous structural-control optimization of a coupled structural-acoustic enclosure is investigated in this paper. The whole system has a rectangular parallelepiped sound field of which the entire bottom face and the partial top face are covered with two elastic plates while the other boundaries are enclosed with rigid walls. Two point forces applied on the two plates are used as disturbance and control inputs respectively. In the sound field, one sound sensor is placed to measure the sound pressure output. Feedback H ₁ control is used to generate the control input signal to reduce the noise at the sensor spot induced by the disturbance. The coupled structural-acoustic enclosure is modeled by the finite element method. The element thickness parameters of the top elastic plate along with the controller parameters are adopted as design variables for the simultaneous optimization in which the closed-loop H ₁ norm is minimized. To solve the simultaneous design problem, a nested approach is used in which the controller syntheses are considered as subprocesses included in the main optimization process dealing with the structural design variables. Moreover, since the matrices are unsymmetrical for structural-acoustic coupling problems, indirect modal analysis is used to reduce the computational cost instead of the direct method. Numerical example shows that the system performance is improved significantly by the simultaneous optimization. The effectiveness and potentiality of the design approach presented in this paper are also demonstrated by the results.