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.

本文提出了一个集成的，新的，通用的框架，用于粘弹性阻尼的布局优化，以控制中频振动声系统的噪声。该方法基于耦合的结构子系统和声学子系统之间不同模态能量之间的功率平衡概念而开发，并在统计模态能量分布分析（SmEdA）的框架内制定。在新的优化公式中，选择声学子系统的总能量作为目标函数，以最小化振动声学系统中的内部声学响应。并使用体积保留的Heaviside函数将粘弹性元素组的相对材料体积密度选择为设计变量。通过SmEdA以半分析形式开发了一种新的灵敏度分析公式，用于解决振动声优化问题。给出两个数值示例，以证明本方法的效率和有效性。目前的数值结果揭示了两个重要发现：（a）所选振动声系统的总声能可以大大降低；（b）最佳的粘弹性材料布局，不仅降低了结构子系统和声学子系统之间的模态耦合强度的峰值，而且创造了相对更均匀的声模态能量分布。（a）所选振动声系统的总声能可以大大降低；（b）最佳的粘弹性材料布局，不仅降低了结构子系统和声学子系统之间的模态耦合强度的峰值，而且创造了相对更均匀的声模态能量分布。（a）所选振动声系统的总声能可以大大降低；（b）最佳的粘弹性材料布局，不仅降低了结构子系统和声学子系统之间的模态耦合强度的峰值，而且创造了相对更均匀的声模态能量分布。