Layout optimization of viscoelastic damping for noise control of mid-frequency vibro-acoustic systems

This paper presents an integrated, new, and generic framework for layout optimization of viscoelastic damping for noise control of mid-frequency vibro-acoustic systems. The method is developed based on the concept of power balance among different modal energies between coupled structural and acoustic subsystems and is formulated within the framework of a statistical modal energy distribution analysis (SmEdA). In the novel optimization formulation, the total energy of the acoustic subsystem is chosen as the objective function for minimizing the internal acoustic response in the vibro-acoustic system; and the relative material volume densities for viscoelastic element groups are selected as design variables using a volume-preserving Heaviside function. A new sensitivity analysis formulation is developed in a semi-analytical form via a SmEdA for solving the vibro-acoustic optimization problem. Two numerical examples are presented to demonstrate the efficiency and effectiveness of the present method. The present numerical results reveal two important findings: (a) the total acoustic energy of the chosen vibro-acoustic system can be significantly reduced; and (b) the optimum viscoelastic material layouts not only decrease the peak values of the modal coupling strengths between structural and acoustic subsystems but also create relatively more uniform acoustic modal energy distribution.